Mastering Fraction Operations on the TI-84 Plus Calculator

Delving into the enigmatic world of fractions on the TI-84 Plus calculator could look like a frightening process, however concern not! This complete information will equip you with the data and methods to navigate this mathematical realm with ease. Whether or not you are a seasoned math wizard or an aspiring numerical fanatic, this insightful article will illuminate the trail to fraction mastery in your trusty TI-84 Plus.

Before everything, let’s break down the fundamentals: fractions are merely numbers expressed as a ratio of two integers. On the TI-84 Plus, you may enter fractions in two methods. For example, to enter the fraction 1/2, you may both sort “1/2” or “1 ÷ 2.” The calculator will mechanically acknowledge the fraction and retailer it internally. Alternatively, you need to use the devoted “Frac” button to transform a decimal into its fractional equal. As soon as you have inputted your fraction, you are able to embark on a world of mathematical potentialities.

The TI-84 Plus affords an array of highly effective capabilities that make working with fractions a breeze. For instance, you may simplify fractions utilizing the “simplify” command, which reduces fractions to their lowest phrases. Moreover, the calculator offers capabilities for addition, subtraction, multiplication, and division of fractions, permitting you to carry out complicated calculations with ease. And if it’s good to convert a fraction to a decimal or proportion, the TI-84 Plus has you lined with devoted conversion capabilities. By harnessing these capabilities, you’ll deal with fraction-based issues with confidence and precision.

Getting into Fractions into the TI-84 Plus

Fractions are a necessary a part of arithmetic, and the TI-84 Plus calculator makes it simple to enter and work with them. There are two foremost methods to enter a fraction into the TI-84 Plus:

1. Utilizing the fraction template: The fraction template is probably the most easy approach to enter a fraction. To make use of the fraction template, press the "2nd" key adopted by the "x-1" key. It will open up the fraction template, which has three elements: the numerator, the denominator, and the fraction bar.

   • To enter the numerator, use the arrow keys to maneuver the cursor to the numerator discipline. Then, use the quantity keys to enter the numerator.
   • To enter the denominator, use the arrow keys to maneuver the cursor to the denominator discipline. Then, use the quantity keys to enter the denominator.
   • To enter the fraction bar, press the "enter" key.

   After you have entered the numerator and denominator, the fraction will seem on the display screen. For instance, to enter the fraction 1/2, you’ll press the "2nd" key adopted by the "x-1" key. Then, you’ll use the arrow keys to maneuver the cursor to the numerator discipline and press the "1" key. You’d then use the arrow keys to maneuver the cursor to the denominator discipline and press the "2" key. Lastly, you’ll press the "enter" key. The fraction 1/2 would then seem on the display screen.

2. Utilizing the division operator: You may as well enter a fraction into the TI-84 Plus utilizing the division operator. To do that, merely enter the numerator adopted by the division operator (/) adopted by the denominator. For instance, to enter the fraction 1/2 utilizing the division operator, you’ll press the "1" key adopted by the "/" key adopted by the "2" key. The fraction 1/2 would then seem on the display screen.

   Utilizing the division operator to enter a fraction is usually quicker than utilizing the fraction template, however you will need to watch out to not make any errors. In the event you make a mistake, the fraction is not going to be entered appropriately and you have to to begin over.

Here’s a desk summarizing the 2 strategies for coming into fractions into the TI-84 Plus:

Methodology	Steps
Fraction template	1. Press the "2nd" key adopted by the "x-1" key.
	2. Use the arrow keys to maneuver the cursor to the numerator discipline.
	3. Enter the numerator utilizing the quantity keys.
	4. Use the arrow keys to maneuver the cursor to the denominator discipline.
	5. Enter the denominator utilizing the quantity keys.
	6. Press the "enter" key.
Division operator	1. Enter the numerator.
	2. Press the "/" key.
	3. Enter the denominator.

Utilizing the MATH Menu to Convert Decimals to Fractions

The TI-84 Plus calculator affords a complete MATH menu that features numerous instruments for working with fractions. One among these instruments is the "Frac" command, which lets you convert decimals to their equal fractions. This characteristic is especially helpful when coping with rational numbers or performing calculations that contain fractions.

To entry the Frac command, comply with these steps:

1. Be certain that your TI-84 Plus calculator is within the "MATH" mode.
2. Scroll right down to the "Frac" entry within the menu and press "ENTER."

The Frac command requires you to supply the decimal quantity you wish to convert to a fraction. This is tips on how to enter the decimal:

1. After urgent "ENTER," you will note a blinking cursor on the display screen.
2. Enter the decimal worth as you’ll usually write it, together with the decimal level.
3. Press "ENTER" once more to provoke the conversion.

The TI-84 Plus calculator will carry out the conversion and show the end result as a fraction. The fraction can be within the easiest kind, which means it is going to be lowered to its lowest phrases. For instance, when you enter the decimal 0.75, the calculator will convert it to the fraction 3/4.

Listed below are some further factors to notice in regards to the Frac command:

• The Frac command can solely convert terminating decimals to fractions. In the event you enter a non-terminating decimal (like 0.333…), the calculator will show an error message.
• The calculator will mechanically cut back the fraction to its easiest kind. You can not specify the specified type of the fraction.
• The Frac command is especially helpful when it’s good to convert decimals to fractions for calculations. For instance, if you wish to add 0.25 and 0.5, you need to use the Frac command to transform them to 1/4 and 1/2, respectively, after which carry out the addition as fractions.
• The Frac command may also be used to transform fractions to decimals. To do that, merely enter the fraction as a command, e.g., "Frac(1/2)."

Manipulating Fractions Utilizing the FRAC Command

The FRAC command on the TI-84 Plus calculator is a robust instrument for working with fractions. It may be used to transform decimals to fractions, simplify fractions, add, subtract, multiply, and divide fractions, and discover the best widespread issue (GCF) and least widespread a number of (LCM) of two or extra fractions.

To make use of the FRAC command, sort the command adopted by the numerator and denominator of the fraction in parentheses. For instance, to enter the fraction 1/2, you’ll sort: FRAC(1,2).

After you have entered a fraction utilizing the FRAC command, you need to use the calculator’s arrow keys to maneuver the cursor across the fraction. The up and down arrow keys transfer the cursor between the numerator and denominator, and the left and proper arrow keys transfer the cursor throughout the numerator or denominator.

You may as well use the calculator’s menu to carry out operations on fractions. To entry the menu, press the [2nd] key adopted by the [MATH] key. The menu will seem on the display screen. Use the arrow keys to maneuver the cursor to the specified operation and press the [ENTER] key.

The next desk summarizes the operations that you would be able to carry out on fractions utilizing the FRAC command:

Operation	Syntax	Instance
Convert a decimal to a fraction	FRAC(decimal)	FRAC(0.5) = 1/2
Simplify a fraction	FRAC(numerator, denominator)	FRAC(3,6) = 1/2
Add fractions	FRAC(numerator1, denominator1) + FRAC(numerator2, denominator2)	FRAC(1,2) + FRAC(1,3) = 5/6
Subtract fractions	FRAC(numerator1, denominator1) – FRAC(numerator2, denominator2)	FRAC(1,2) – FRAC(1,3) = 1/6
Multiply fractions	FRAC(numerator1, denominator1) * FRAC(numerator2, denominator2)	FRAC(1,2) * FRAC(1,3) = 1/6
Divide fractions	FRAC(numerator1, denominator1) / FRAC(numerator2, denominator2)	FRAC(1,2) / FRAC(1,3) = 3/2
Discover the best widespread issue (GCF) of two or extra fractions	GCD(FRAC(numerator1, denominator1), FRAC(numerator2, denominator2))	GCD(FRAC(1,2), FRAC(1,3)) = 1
Discover the least widespread a number of (LCM) of two or extra fractions	LCM(FRAC(numerator1, denominator1), FRAC(numerator2, denominator2))	LCM(FRAC(1,2), FRAC(1,3)) = 6

Including and Subtracting Fractions on the TI-84 Plus

The TI-84 Plus graphing calculator is a robust instrument that can be utilized to carry out quite a lot of mathematical operations, together with including and subtracting fractions. So as to add or subtract fractions on the TI-84 Plus, comply with these steps:

1. Enter the primary fraction into the calculator. To do that, press the “2nd” button adopted by the “frac” button. It will carry up the Fraction Editor. Enter the numerator of the fraction into the highest discipline and the denominator into the underside discipline. Press the “enter” button to save lots of the fraction.
2. Enter the second fraction into the calculator. To do that, repeat step 1.
3. So as to add the fractions, press the “+” button. To subtract the fractions, press the “-” button.
4. The results of the operation can be displayed within the calculator’s show. If the result’s a blended quantity, the integer a part of the quantity can be displayed first, adopted by the fraction half. For instance, when you add 1/2 and 1/3, the end result can be displayed as 5/6.

Here’s a desk summarizing the steps for including and subtracting fractions on the TI-84 Plus:

Operation	Steps
Addition	Enter the primary fraction into the calculator. Enter the second fraction into the calculator. Press the “+” button. The results of the operation can be displayed within the calculator’s show.
Subtraction	Enter the primary fraction into the calculator. Enter the second fraction into the calculator. Press the “-” button. The results of the operation can be displayed within the calculator’s show.

Listed below are some further ideas for including and subtracting fractions on the TI-84 Plus:

• You may as well use the “math” menu so as to add or subtract fractions. To do that, press the “math” button after which choose the “fractions” choice. It will carry up a menu of choices for working with fractions, together with including, subtracting, multiplying, and dividing fractions.
• In case you are working with a posh fraction, you need to use the “complicated” menu to enter the fraction. To do that, press the “complicated” button after which choose the “fraction” choice. It will carry up a menu of choices for working with complicated fractions, together with including, subtracting, multiplying, and dividing complicated fractions.
• The TI-84 Plus may also be used to simplify fractions. To do that, press the “math” button after which choose the “simplify” choice. It will carry up a menu of choices for simplifying fractions, together with simplifying fractions to their lowest phrases, simplifying fractions to blended numbers, and simplifying fractions to decimals.

Multiplying and Dividing Fractions on the TI-84 Plus

Getting into Fractions

To enter a fraction into the TI-84 Plus, use the fraction template:

(numerator / denominator)

For instance, to enter the fraction 1/2, sort:

(1 / 2)

Multiplying Fractions

To multiply fractions on the TI-84 Plus, use the asterisk (*) key.

(numerator1 / denominator1) * (numerator2 / denominator2)

For instance, to multiply 1/2 by 3/4, sort:

(1 / 2) * (3 / 4)

The end result can be 3/8.

Dividing Fractions

To divide fractions on the TI-84 Plus, use the ahead slash (/) key.

(numerator1 / denominator1) / (numerator2 / denominator2)

For instance, to divide 1/2 by 3/4, sort:

(1 / 2) / (3 / 4)

The end result can be 2/3.

Changing Blended Numbers to Improper Fractions

To transform a blended quantity to an improper fraction on the TI-84 Plus, use the next steps:

1. Multiply the entire quantity by the denominator of the fraction.
2. Add the numerator of the fraction to the results of step 1.
3. Place the results of step 2 over the denominator of the fraction.

For instance, to transform the blended quantity 2 1/3 to an improper fraction, sort:

(2 * 3) + 1 / 3

The end result can be 7/3.

Changing Improper Fractions to Blended Numbers

To transform an improper fraction to a blended quantity on the TI-84 Plus, use the next steps:

1. Divide the numerator by the denominator.
2. The quotient of step 1 is the entire quantity.
3. The rest of step 1 is the numerator of the fraction.
4. The denominator of the fraction is identical because the denominator of the improper fraction.

For instance, to transform the improper fraction 7/3 to a blended quantity, sort:

7 / 3

The end result can be 2 1/3.

Apply Issues

1. Multiply the fractions 1/2 and three/4.
2. Divide the fractions 1/2 by 3/4.
3. Convert the blended quantity 2 1/3 to an improper fraction.
4. Convert the improper fraction 7/3 to a blended quantity.
5. Simplify the fraction 12x^2 / 15x.

Reply Key:

1. 3/8
2. 2/3
3. 7/3
4. 2 1/3
5. 4x

Changing Fractions to Blended Numbers

Changing fractions to blended numbers is important for performing numerous mathematical operations. A blended quantity is a mixture of a complete quantity and a fraction, representing a price larger than 1. To transform a fraction to a blended quantity, comply with these steps:

1. Divide the numerator (high quantity) by the denominator (backside quantity) utilizing lengthy division.

2. The quotient obtained from the division represents the entire quantity a part of the blended quantity.

3. The rest from the division turns into the numerator of the fraction a part of the blended quantity.

4. The denominator stays the identical as the unique fraction.

For instance, to transform the fraction 7/3 to a blended quantity:

3 ) 7

3 2

6

1

Subsequently, 7/3 as a blended quantity is 2 1/3.

7. Changing Improper Fractions to Blended Numbers

An improper fraction is a fraction the place the numerator is bigger than or equal to the denominator. To transform an improper fraction to a blended quantity, comply with these steps:

1. Divide the numerator by the denominator utilizing lengthy division.
2. The quotient obtained from the division represents the entire quantity a part of the blended quantity.
3. The rest from the division turns into the numerator of the fraction a part of the blended quantity.
4. The denominator stays the identical as the unique fraction.

Instance:

Convert the improper fraction 11/4 to a blended quantity:

4 ) 11

4 8

8

3

Subsequently, 11/4 as a blended quantity is 2 3/4.

Changing Blended Numbers to Fractions

Changing blended numbers to fractions includes two steps:

1. Multiply the entire quantity by the denominator of the fraction

For instance, if you wish to convert 3 1/2 to a fraction, you’ll multiply 3 by 2 (the denominator of the fraction 1/2) to get 6.

2. Add the numerator of the fraction to the end result

Lastly, add the numerator of the fraction (1) to the results of the multiplication (6) to get 7. The fraction equal of three 1/2 is due to this fact 7/2.

Instance

Let’s convert 4 3/4 to a fraction.

1. Multiply the entire quantity (4) by the denominator of the fraction (4) to get 16.
2. Add the numerator of the fraction (3) to the results of the multiplication (16) to get 19.

Subsequently, 4 3/4 is equal to the fraction 19/4.

Changing Fractions to Blended Numbers

Changing fractions to blended numbers may be executed by utilizing the next steps:

1. Divide the denominator of the fraction into the numerator

For instance, if you wish to convert the fraction 7/2 to a blended quantity, you’ll divide 2 into 7 to get 3 because the quotient.

2. The rest of the division is the numerator of the fraction a part of the blended quantity

On this case, there isn’t a the rest, so the fraction a part of the blended quantity can be 0/2, which may be simplified to only 0.

3. The quotient of the division is the entire quantity a part of the blended quantity

Subsequently, 7/2 is equal to the blended quantity 3.

Instance

Let’s convert 19/4 to a blended quantity.

1. Divide the denominator (4) into the numerator (19) to get 4 because the quotient and three as the rest.
2. The rest (3) is the numerator of the fraction a part of the blended quantity, and the quotient (4) is the entire quantity a part of the blended quantity.

Subsequently, 19/4 is equal to the blended quantity 4 3/4.

Desk of Conversions

The next desk exhibits the conversions for some widespread fractions and blended numbers:

Blended Quantity	Fraction
3 1/2	7/2
4 3/4	19/4
2 1/3	7/3
1 3/8	11/8
5 2/5	27/5

Discovering Least Frequent Multiples and Denominators

The Least Frequent A number of (LCM) of two or extra fractions is the smallest optimistic integer that’s divisible by all of the denominators of the given fractions. The Least Frequent Denominator (LCD) of two or extra fractions is the smallest optimistic integer that every one the denominators of the given fractions divide into evenly. This is tips on how to discover the LCM and LCD utilizing the TI-84 Plus calculator:

Discovering the Least Frequent A number of (LCM) utilizing TI-84 Plus

1. Enter the numerators and denominators of the fractions into the calculator. For instance, if you wish to discover the LCM of 1/2 and 1/3, enter 1/2 and 1/3 into the calculator.
2. Press the “2nd” button, then press the “x-1” button to entry the “lcm()” perform.
3. Sort the fractions you entered in Step 1 as arguments to the “lcm()” perform, separating them with a comma. For instance, sort lcm(1/2, 1/3).
4. Press the “enter” button.
5. The calculator will show the LCM of the fractions.

Discovering the Least Frequent Denominator (LCD) utilizing TI-84 Plus

1. Enter the numerators and denominators of the fractions into the calculator. For instance, if you wish to discover the LCD of 1/2 and 1/3, enter 1/2 and 1/3 into the calculator.
2. Press the “2nd” button, then press the “x-1” button to entry the “liquid crystal display()” perform.
3. Sort the fractions you entered in Step 1 as arguments to the “liquid crystal display()” perform, separating them with a comma. For instance, sort liquid crystal display(1/2, 1/3).
4. Press the “enter” button.
5. The calculator will show the LCD of the fractions.

Instance

Discover the LCM and LCD of 1/2, 1/3, and 1/4.

LCM:

1. Enter 1/2, 1/3, and 1/4 into the calculator.
2. Press the “2nd” button, then press the “x-1” button to entry the “lcm()” perform.
3. Sort lcm(1/2, 1/3, 1/4) into the calculator.
4. Press the “enter” button.
5. The calculator shows 6, which is the LCM of 1/2, 1/3, and 1/4.

LCD:

1. Enter 1/2, 1/3, and 1/4 into the calculator.
2. Press the “2nd” button, then press the “x-1” button to entry the “liquid crystal display()” perform.
3. Sort liquid crystal display(1/2, 1/3, 1/4) into the calculator.
4. Press the “enter” button.
5. The calculator shows 12, which is the LCD of 1/2, 1/3, and 1/4.

Extra Examples

Fraction 1	Fraction 2	LCM	LCD
1/2	1/3	6	6
1/3	1/4	12	12
1/4	1/5	20	20
1/2	1/3	1/4	12

Evaluating and Ordering Fractions

To match and order fractions on the TI-84 Plus calculator, comply with these steps:

1. Enter the primary fraction into the calculator.
2. Press the “>” key.
3. Enter the second fraction.
4. Press the “ENTER” key.

The calculator will show “1” if the primary fraction is bigger than the second fraction, “0” if the primary fraction is lower than the second fraction, or “ERROR” if the fractions are equal.

You may as well use the “>” and “<” keys to check and order fractions in a listing.

1. Enter the fractions into the calculator in a listing.
2. Press the “STAT” key.
3. Choose the “EDIT” menu.
4. Choose the “Type” submenu.
5. Choose the “Ascending” or “Descending” choice.
6. Press the “ENTER” key.

The calculator will type the fractions in ascending or descending order.

Changing Fractions to Decimals

To transform a fraction to a decimal on the TI-84 Plus calculator, comply with these steps:

1. Enter the fraction into the calculator.
2. Press the “MATH” key.
3. Choose the “FRAC” menu.
4. Choose the “Dec” submenu.
5. Press the “ENTER” key.

The calculator will show the decimal illustration of the fraction.

Changing Decimals to Fractions

To transform a decimal to a fraction on the TI-84 Plus calculator, comply with these steps:

1. Enter the decimal into the calculator.
2. Press the “MATH” key.
3. Choose the “FRAC” menu.
4. Choose the “Frac” submenu.
5. Press the “ENTER” key.

The calculator will show the fraction illustration of the decimal.

Including and Subtracting Fractions

So as to add or subtract fractions on the TI-84 Plus calculator, comply with these steps:

1. Enter the primary fraction into the calculator.
2. Press the “+” or “-” key.
3. Enter the second fraction.
4. Press the “ENTER” key.

The calculator will show the sum or distinction of the fractions.

Multiplying and Dividing Fractions

To multiply or divide fractions on the TI-84 Plus calculator, comply with these steps:

1. Enter the primary fraction into the calculator.
2. Press the “*” or “/” key.
3. Enter the second fraction.
4. Press the “ENTER” key.

The calculator will show the product or quotient of the fractions.

Simplifying Fractions

To simplify a fraction on the TI-84 Plus calculator, comply with these steps:

1. Enter the fraction into the calculator.
2. Press the “MATH” key.
3. Choose the “FRAC” menu.
4. Choose the “Simp” submenu.
5. Press the “ENTER” key.

The calculator will show the simplified fraction.

Utilizing Fractions in Equations

You should use fractions in equations on the TI-84 Plus calculator. For instance, to unravel the equation 1/2x + 1/4 = 1/8, you’ll enter the next into the calculator:

1/2x + 1/4 = 1/8
resolve(1/2x + 1/4 = 1/8, x)

The calculator would show the answer x = 1/2.

Fraction	Decimal	Simplified Fraction
1/2	0.5	1/2
1/4	0.25	1/4
1/8	0.125	1/8
3/4	0.75	3/4
5/8	0.625	5/8

Fixing Equations Involving Fractions

This is a step-by-step information on tips on how to resolve equations involving fractions on the TI-84 Plus calculator:

1. Simplify the equation

Begin by simplifying the equation as a lot as potential. This may occasionally contain multiplying or dividing each side by the identical quantity to do away with fractions, or combining like phrases.

2. Multiply each side by the LCD

The least widespread denominator (LCD) of the fractions within the equation is the smallest quantity that’s divisible by all the denominators. Multiply each side of the equation by the LCD to do away with the fractions.

3. Remedy the ensuing equation

After you have multiplied each side by the LCD, you should have a brand new equation that not accommodates fractions. Remedy this equation utilizing the standard strategies for fixing equations.

4. Examine your resolution

After you have discovered an answer to the equation, verify your resolution by plugging it again into the unique equation. If the equation holds true, then your resolution is appropriate.

Instance:

Remedy the equation 1/2x + 1/4 = 1/3.

1. Simplify the equation

12(1/2x + 1/4) = 12(1/3)

6x + 3 = 4

2. Multiply each side by the LCD

6x = 1

3. Remedy the ensuing equation

x = 1/6

4. Examine your resolution

1/2(1/6) + 1/4 = 1/3

1/12 + 1/4 = 1/3

4/12 + 3/12 = 1/3

7/12 = 1/3

Extra Suggestions

– When multiplying fractions, multiply the numerators and multiply the denominators.

– When dividing fractions, invert the second fraction and multiply.

– The LCD may be discovered by discovering the least widespread a number of (LCM) of the denominators.

– Watch out to not divide by zero.

Utilizing Fractions to Remedy Phrase Issues

Fractions are a typical a part of on a regular basis life. We use them to explain parts of meals, time, and distance. When fixing phrase issues involving fractions, you will need to perceive the ideas of numerators, denominators, and equal fractions.

Numerators characterize the variety of elements being thought of, whereas denominators characterize the overall variety of elements into which an entire is split. Equal fractions are fractions that characterize the identical worth, regardless that they’ve totally different numerators and denominators.

For instance, the fractions 1/2, 2/4, and three/6 are all equal as a result of they characterize the identical worth, which is half of a complete.

When fixing phrase issues involving fractions, comply with these steps:

1. Learn the issue rigorously. Decide what info is being offered and what info is being requested for.
2. Determine the fractions in the issue. Decide the numerators and denominators of every fraction.
3. Convert any blended numbers to improper fractions. A blended quantity is a quantity that has an entire quantity half and a fraction half. To transform a blended quantity to an improper fraction, multiply the entire quantity half by the denominator of the fraction half after which add the numerator of the fraction half. The result’s the numerator of the improper fraction, and the denominator is identical because the denominator of the unique fraction.
4. Discover the least widespread a number of (LCM) of the denominators. The LCM is the smallest quantity that’s divisible by all the denominators. To search out the LCM, listing the prime elements of every denominator after which multiply the best energy of every prime issue that seems in any of the denominators.
5. Convert all of the fractions to equal fractions with the LCM because the denominator. To do that, multiply the numerator and denominator of every fraction by the suitable issue.
6. Carry out the operation(s) indicated by the issue. This may occasionally contain including, subtracting, multiplying, or dividing fractions.
7. Simplify the end result. Cut back the fraction to its lowest phrases by dividing the numerator and denominator by their best widespread issue (GCF). Categorical the end result as a blended quantity if applicable.

Instance:

A recipe for chocolate chip cookies calls for two 1/2 cups of flour. In the event you solely have 3/4 of a cup of flour, what fraction of the recipe are you able to make?

Answer:

1. Learn the issue rigorously. You might be given that you’ve 3/4 of a cup of flour and it’s good to decide what fraction of the recipe you may make.
2. Determine the fractions in the issue. The fraction 2 1/2 is equal to the improper fraction 5/2, and the fraction 3/4 is equal to the improper fraction 3/4.
3. Convert the blended quantity to an improper fraction. 5/2
4. Discover the least widespread a number of (LCM) of the denominators. The LCM of two and 4 is 4.
5. Convert all of the fractions to equal fractions with the LCM because the denominator. 5/2 x 2/2 = 10/4 and three/4 x 1/1 = 3/4
6. Carry out the operation indicated by the issue. 10/4 – 3/4 = 7/4
7. Simplify the end result. 7/4

Subsequently, you may make 7/4 of the recipe with 3/4 of a cup of flour.

Extra Suggestions:

• When including or subtracting fractions, be certain the fractions have the identical denominator.
• When multiplying fractions, multiply the numerators and multiply the denominators.
• When dividing fractions, invert the divisor and multiply.
• Do not be afraid to make use of a calculator to verify your solutions.

Evaluating Numerical Expressions with Fractions

The TI-84 Plus calculator can be utilized to judge numerical expressions involving fractions. To do that, you need to use the next steps:

1. Enter the numerator of the fraction into the calculator.
2. Press the “หาร” (÷) key.
3. Enter the denominator of the fraction into the calculator.
4. Press the “ENTER” key.

For instance, to judge the expression 1/2, you’ll enter the next into the calculator:

1÷2

and press the “ENTER” key. The calculator would then show the end result, which is 0.5.

Utilizing the Ans Variable

You may as well use the Ans variable to retailer the results of a earlier calculation. This may be helpful if you wish to use the results of one calculation in a subsequent calculation.

To retailer the results of a calculation within the Ans variable, merely press the “STORE” key after the calculation is full. For instance, to retailer the results of the expression 1/2 within the Ans variable, you’ll enter the next into the calculator:

1÷2STORE÷

The Ans variable can then be utilized in subsequent calculations by merely coming into its title. For instance, to calculate the expression 1/2 + 1/4, you’ll enter the next into the calculator:

Ans+1÷4

Utilizing the Fraction Key

The TI-84 Plus calculator additionally has a devoted fraction key, which can be utilized to enter fractions immediately into the calculator.

To enter a fraction utilizing the fraction key, press the “ALPHA” key adopted by the “x-1” key. The calculator will then show a fraction template. Enter the numerator of the fraction into the highest field and the denominator of the fraction into the underside field. Press the “ENTER” key to enter the fraction into the calculator.

For instance, to enter the fraction 1/2 into the calculator, you’ll press the next keys:

ALPHAx-11ENTER2ENTER

Evaluating Extra Complicated Expressions

The TI-84 Plus calculator may also be used to judge extra complicated expressions involving fractions. For instance, to judge the expression (1/2) + (1/4), you’ll enter the next into the calculator:

(

1÷2)+(1÷4)

The calculator would then show the end result, which is 3/4.

Desk of Examples

Expression	Calculator Enter	Consequence
1/2	1 ÷ 2	0.5
1/2 + 1/4	(1 ÷ 2) + (1 ÷ 4)	0.75
(1/2) * (1/4)	(1 ÷ 2) * (1 ÷ 4)	0.125
1/(1/2)	1 ÷ (1 ÷ 2)	2

Discovering Essential Factors of Features Involving Fractions

Essential factors are factors the place the primary spinoff of a perform is both zero or undefined. To search out the vital factors of a perform involving fractions, we will use the quotient rule.

The quotient rule states that if now we have a perform of the shape $f(x) = frac{p(x)}{q(x)}$, the place $p(x)$ and $q(x)$ are polynomials, then the spinoff of $f(x)$ is given by:

$$f'(x) = frac{q(x)p'(x) – p(x)q'(x)}{q(x)^2}$$

Utilizing this rule, we will discover the vital factors of any perform involving fractions.

Instance

Discover the vital factors of the perform $f(x) = frac{x^2+1}{x-1}$.

Utilizing the quotient rule, we discover that:

$$f'(x) = frac{(x-1)(2x) – (x^2+1)(1)}{(x-1)^2} = frac{2x^2 – 2x – x^2 – 1}{(x-1)^2} = frac{x^2 – 2x – 1}{(x-1)^2}$$

The vital factors are the factors the place $f'(x) = 0$ or $f'(x)$ is undefined.

To search out the place $f'(x) = 0$, we resolve the equation $x^2 – 2x – 1 = 0$. This equation elements as $(x-1)(x+1) = 0$, so the options are $x = 1$ and $x = -1$.

To search out the place $f'(x)$ is undefined, we set the denominator of $f'(x)$ equal to zero. This offers us $(x-1)^2 = 0$, so the one resolution is $x = 1$.

Subsequently, the vital factors of $f(x) = frac{x^2+1}{x-1}$ are $x = 1$ and $x = -1$.

Basic Process

To search out the vital factors of a perform involving fractions, we will comply with these steps:

1. Discover the spinoff of the perform utilizing the quotient rule.
2. Set the spinoff equal to zero and resolve for $x$.
3. Set the denominator of the spinoff equal to zero and resolve for $x$.
4. The vital factors are the factors the place the spinoff is zero or undefined.

Extra Notes

* If the denominator of the perform is a continuing, then the perform is not going to have any vital factors.
* If the numerator of the perform is a continuing, then the perform may have a vital level at $x = 0$.
* If the perform is undefined at a degree, then that time shouldn’t be a vital level.

Utilizing Derivatives to Analyze Features with Fractions

The spinoff of a perform is a measure of its charge of change. It may be used to research the perform’s conduct, together with its vital factors, maxima, and minima.

When coping with capabilities that include fractions, you will need to do not forget that the spinoff of a quotient is the same as the numerator occasions the spinoff of the denominator minus the denominator occasions the spinoff of the numerator, all divided by the sq. of the denominator.

$$ frac{d}{dx} left[ frac{f(x)}{g(x)} right] = frac{g(x)f'(x) – f(x)g'(x)}{g(x)^2} $$

This rule can be utilized to search out the spinoff of any perform that accommodates a fraction. For instance, the spinoff of the perform

$$ f(x) = frac{x^2 + 1}{x-1} $$

is

$$ f'(x) = frac{(x-1)(2x) – (x^2 + 1)(1)}{(x-1)^2} = frac{2x^2 – 2x – x^2 – 1}{(x-1)^2} = frac{x^2 – 2x – 1}{(x-1)^2} $$

This spinoff can be utilized to research the perform’s conduct. For instance, the spinoff is the same as zero on the factors x = 1 and x = -1/2. These factors are the vital factors of the perform.

The spinoff is optimistic for x > 1 and x < -1/2. Because of this the perform is rising on these intervals. The spinoff is unfavourable for -1/2 < x < 1. Because of this the perform is reducing on this interval.

The perform has a most on the level x = 1 and a minimal on the level x = -1/2. These factors may be discovered by discovering the vital factors after which evaluating the perform at these factors.

The spinoff may also be used to search out the concavity of the perform. The perform is concave up on the intervals (-∞, -1/2) and (1, ∞). The perform is concave down on the interval (-1/2, 1).

The concavity of the perform can be utilized to find out the perform’s form. A perform that’s concave up is a parabola that opens up. A perform that’s concave down is a parabola that opens down.

The spinoff is a robust instrument that can be utilized to research the conduct of capabilities. When coping with capabilities that include fractions, you will need to keep in mind the quotient rule for derivatives.

Instance

Discover the spinoff of the perform

$$ f(x) = frac{x^3 + 2x^2 – 1}{x^2 – 1} $$

Utilizing the quotient rule, now we have

$$ f'(x) = frac{(x^2 – 1)(3x^2 + 4x) – (x^3 + 2x^2 – 1)(2x)}{(x^2 – 1)^2} $$

$$ = frac{3x^4 + 4x^3 – 3x^2 – 4x – 2x^4 – 4x^3 + 4x^2 + 2x}{(x^2 – 1)^2} $$

$$ = frac{x^4}{(x^2 – 1)^2} $$

The spinoff of the perform is

$$ f'(x) = frac{x^4}{(x^2 – 1)^2} $$

Utilizing Integrals to Discover the Space Below a Curve Involving Fractions

1. Outline the Perform

Start by coming into the perform involving fractions into the TI-84 Plus. For example, to enter the perform f(x) = (x+2)/(x-1), press the next keys:

1. MODE
2. FUNC
3. Y=
4. Enter (x+2)/(x-1)

2. Set the Graph Window

Regulate the graph window to show the related portion of the curve. To do that, press the WINDOW button and enter applicable values for Xmin, Xmax, Ymin, and Ymax.

For instance, to set the window to show the curve from x=-5 to x=5 and y=-10 to y=10, enter the next values:

Setting	Worth
Xmin	-5
Xmax	5
Ymin	-10
Ymax	10

3. Discover the Roots of the Denominator

To arrange for integration, it’s good to discover the roots of the denominator of the perform. On this instance, the denominator is x-1. Press the CALC button, choose ZERO, then select ZERO once more. Use the arrow keys to maneuver the cursor to the zero level of the perform and press ENTER.

4. Use the Integration Characteristic

After you have outlined the perform and set the suitable window, you need to use the mixing characteristic to search out the world beneath the curve. Press the MATH button, choose NUMERICAL, after which select ∫f(x)dx.

5. Specify the Bounds of Integration

Enter the decrease and higher bounds of integration. For example, to search out the world beneath the curve from x=0 to x=3, enter 0 because the decrease sure and 3 because the higher sure.

6. Calculate the Integral

Press ENTER to calculate the integral worth, which represents the world beneath the curve throughout the specified bounds.

7. Resolve Indeterminate Types

If the integral result’s an indeterminate kind akin to ∞, -∞, or 0/0, you have to to analyze the conduct of the perform close to the purpose of discontinuity. Use restrict analysis methods or graphing to find out the suitable worth.

17. Instance: Discovering the Space Below a Hyperbola

Let’s discover the world beneath the hyperbola f(x) = (x-1)/(x+1) from x=0 to x=2 utilizing the TI-84 Plus.

Steps:

• Enter the perform: y1=(x-1)/(x+1)
• Set the graph window: Xmin=-5, Xmax=5, Ymin=-5, Ymax=5
• Discover the foundation of the denominator: x=-1
• Combine the perform:
  1. MATH
  2. NUMERICAL
  3. ∫f(x)dx
  4. 0, 2
• Consequence: ln(3) ≈ 1.0986

Methods to Calculate Limits of Features with Fractions on TI-84 Plus

The TI-84 Plus calculator can be utilized to calculate limits of capabilities, together with capabilities that include fractions. To calculate the restrict of a perform with a fraction, comply with these steps:

1. Enter the perform into the calculator.
2. Press the “CALC” button.
3. Choose the “restrict” choice.
4. Enter the worth of the variable at which you wish to calculate the restrict.
5. Press the “ENTER” button.

The calculator will show the restrict of the perform on the given worth of the variable.

For instance, to calculate the restrict of the perform f(x) = (x^2 – 1) / (x – 1) at x = 1, comply with these steps:

1. Enter the perform into the calculator: f(x) = (x^2 – 1) / (x – 1)
2. Press the “CALC” button.
3. Choose the “restrict” choice.
4. Enter the worth of x at which you wish to calculate the restrict: x = 1
5. Press the “ENTER” button.

The calculator will show the restrict of the perform at x = 1, which is 2.

Instance: Calculating the Restrict of a Rational Perform

Take into account the rational perform:

“`
f(x) = (x^2 – 4) / (x – 2)
“`

To search out the restrict of this perform as x approaches 2, we will use the TI-84 Plus calculator.

Step 1: Enter the perform into the calculator.

“`
f(x) = (x^2 – 4) / (x – 2)
“`

Step 2: Press the “CALC” button.

Step 3: Choose the “restrict” choice.

Step 4: Enter the worth of x at which you wish to calculate the restrict.

“`
x = 2
“`

Step 5: Press the “ENTER” button.

The calculator will show the restrict of the perform as x approaches 2, which is 4.

Enter	Output
f(x) = (x^2 – 4) / (x – 2)	4

Extra Notes

When calculating limits of capabilities with fractions, you will need to be aware the next:

* The restrict of a fraction is the same as the restrict of the numerator divided by the restrict of the denominator, offered that the denominator doesn’t strategy zero.
* If the denominator of a fraction approaches zero, the restrict of the fraction could also be indeterminate. On this case, you might want to make use of different methods to judge the restrict.
* It’s all the time a good suggestion to simplify fractions earlier than calculating limits. This might help to keep away from potential errors.

Dealing with Continuity of Features with Fractions

Manipulating fractions on the TI-84 Plus calculator empowers us to discover the conduct of capabilities containing fractions and assess their continuity. Features carrying fractions could possess discontinuities, factors the place the perform experiences abrupt interruptions or “jumps.” These discontinuities can come up as a result of specific nature of the fraction, akin to division by zero or undefined expressions.

To find out the continuity of a perform involving fractions, we should scrutinize the perform’s conduct at vital factors the place the denominator of the fraction approaches zero or turns into undefined. If the perform’s restrict at that time coincides with the perform’s worth at that time, then the perform is taken into account steady at that time. In any other case, a discontinuity exists.

Detachable Discontinuities

In sure instances, discontinuities may be “eliminated” by simplifying or redefining the perform. For example, take into account the perform:

f(x) = (x-2)/(x^2-4)

The denominator, (x^2-4), approaches zero at x = 2 and x = -2. Nonetheless, these factors aren’t detachable discontinuities as a result of the restrict of the perform as x approaches both of those factors doesn’t match the perform’s worth at these factors.

Level	Restrict	Perform Worth	Discontinuity Sort
x = 2	1/4	Undefined	Important Discontinuity
x = -2	-1/4	Undefined	Important Discontinuity

Important Discontinuities: Factors the place the restrict of the perform doesn’t exist or is infinite, making the discontinuity “important” or irremovable.

Instance: Figuring out Discontinuities

Let’s look at the perform:

g(x) = (x^2-9)/(x-3)

The denominator, (x-3), approaches zero at x = 3. Substituting x = 3 into the perform yields an undefined expression, indicating a possible discontinuity.

To find out the kind of discontinuity, we calculate the restrict of the perform as x approaches 3:

lim (x->3) (x^2-9)/(x-3) = lim (x->3) [(x+3)(x-3)]/(x-3) = lim (x->3) x+3 = 6

For the reason that restrict (6) doesn’t coincide with the perform’s worth at x = 3 (undefined), the discontinuity is important and can’t be eliminated.

Abstract of Continuity Circumstances

To find out the continuity of a perform involving fractions:

1. Issue the denominator to establish potential discontinuities.
2. Substitute the potential discontinuity into the perform to verify for an undefined expression.
3. If an undefined expression is discovered, calculate the restrict of the perform as x approaches the potential discontinuity.
4. If the restrict exists and equals the perform’s worth at that time, the discontinuity is detachable.
5. If the restrict doesn’t exist or doesn’t equal the perform’s worth at that time, the discontinuity is important.

Derivatives of Features with Fractions

The spinoff of a fraction is discovered utilizing the quotient rule, which states that the spinoff of $\frac{f\left(x\right)}{g\left(x\right)}$ is given by:

$f^{\prime }\left(x\right)g\left(x\right)-f\left(x\right)g^{\prime }\left(x\right)={\left(g\left(x\right)\right)}^2$

The place $f^{\prime }\left(x\right)$ and $g^{\prime }\left(x\right)$ characterize the derivatives of $f\left(x\right)$ and $g\left(x\right)$, respectively.

22. Instance

Discover the spinoff of $f\left(x\right)=\frac{x+1}{x-2}$.

Answer:

Utilizing the quotient rule, now we have:

$f^{\prime }\left(x\right)=\frac{(x-2)\left(1\right)-(x+1)\left(1\right)}{(x-2{)}^2}$

$=\frac{x-2-x-1}{(x-2{)}^2}$

$=\frac{-3}{(x-2{)}^2}$

Subsequently, $f^{\prime }\left(x\right)=\frac{-3}{(x-2{)}^2}$.

The next desk offers further examples of derivatives of capabilities with fractions:

Perform	Spinoff
$\frac{x+2}{x-1}$	$\frac{(x-1)\left(1\right)-(x+2)\left(1\right)}{(x-1{)}^2}$ $=\frac{x-1-x-2}{(x-1{)}^2}$ $=\frac{-3}{(x-1{)}^2}$
$\frac{2x-1}{x+3}$	$\frac{(x+3)\left(2\right)-(2x-1)\left(1\right)}{(x+3{)}^2}$ $=\frac{2x+6-2x+1}{(x+3{)}^2}$ Integrals of Fractions: Partial Fraction Decomposition With a view to discover the indefinite integral of a fraction, we will use a way known as partial fraction decomposition. This includes breaking down the fraction into less complicated fractions that may be built-in extra simply. For instance, take into account the next fraction: $$frac{x^2+2x+1}{x^2-1}$$ We are able to issue the denominator as: $$x^2-1=(x+1)(x-1)$$ So, we will decompose the fraction as follows: $$frac{x^2+2x+1}{x^2-1}=frac{A}{x+1}+frac{B}{x-1}$$ the place A and B are constants that we have to resolve for. To search out A, we multiply each side of the equation by x+1: $$x^2+2x+1=A(x-1)+B(x+1)$$ Setting x=-1, we get: $$1=2ARightarrow A=frac{1}{2}$$ To search out B, we multiply each side of the equation by x-1: $$x^2+2x+1=A(x-1)+B(x+1)$$ Setting x=1, we get: $$3=2BRightarrow B=frac{3}{2}$$ Subsequently, now we have: $$frac{x^2+2x+1}{x^2-1}=frac{1}{2(x+1)}+frac{3}{2(x-1)}$$ Now, we will combine every of those fractions individually: $$intfrac{x^2+2x+1}{x^2-1}dx=frac{1}{2}intfrac{1}{x+1}dx+frac{3}{2}intfrac{1}{x-1}dx$$ Utilizing the facility rule of integration, we get: $$intfrac{x^2+2x+1}{x^2-1}dx=frac{1}{2}ln|x+1|+frac{3}{2}ln|x-1|+C$$ the place C is the fixed of integration. Integration by Substitution One other technique that can be utilized to search out the indefinite integral of a fraction is integration by substitution. This includes making a substitution for part of the integrand that leads to a less complicated expression. For instance, take into account the next fraction: $$frac{1}{x^2+1}$$ We are able to make the substitution u=x^2+1, which supplies us: $$du=2xdx$$ Substituting into the integral, we get: $$intfrac{1}{x^2+1}dx=frac{1}{2}intfrac{1}{u}du$$ Now, we will use the facility rule of integration to get: $$intfrac{1}{x^2+1}dx=frac{1}{2}ln|u|+C$$ Substituting again for u, we get: $$intfrac{1}{x^2+1}dx=frac{1}{2}ln|x^2+1|+C$$ the place C is the fixed of integration. Integration by Components Integration by elements is a way that can be utilized to search out the indefinite integral of a product of two capabilities. This includes discovering two capabilities, u and dv, such that: $$du=v’dxqquadtext{and}qquad dv=udx$$ after which integrating by elements utilizing the next method: $$int udv=uv-int vdu$$ For instance, take into account the next fraction: $$frac{x}{x^2+1}$$ We are able to select u=x and dv=1/(x^2+1)dx, which supplies us: $$du=dxqquadtext{and}qquad dv=frac{1}{x^2+1}dx$$ Substituting into the method for integration by elements, we get: $$intfrac{x}{x^2+1}dx=xfrac{1}{x^2+1}-intfrac{1}{x^2+1}dx$$ Now, we will use the facility rule of integration to get: $$intfrac{x}{x^2+1}dx=xfrac{1}{x^2+1}-tan^{-1}x+C$$ the place C is the fixed of integration. Examples Listed below are some examples of tips on how to discover the indefinite integral of a fraction utilizing the varied methods mentioned above: Instance 1: Discover the indefinite integral of the next fraction: $$frac{x^2+1}{x^3-1}$$ We are able to use partial fraction decomposition to interrupt down the fraction as follows: $$frac{x^2+1}{x^3-1}=frac{A}{x-1}+frac{Bx+C}{x^2+x+1}$$ Multiplying each side by x^3-1, we get: $$x^2+1=A(x^2+x+1)+(Bx+C)(x-1)$$ Setting x=1, we get: $$2=A(3)Rightarrow A=frac{2}{3}$$ Setting x=0, we get: $$1=CRightarrow C=1$$ Equating coefficients of x, we get: $$1=A+BRightarrow B=-1/3$$ Subsequently, now we have: $$frac{x^2+1}{x^3-1}=frac{2/3}{x-1}-frac{x/3+1}{x^2+x+1}$$ Now, we will combine every of those fractions individually: $$intfrac{x^2+1}{x^3-1}dx=frac{2/3}intfrac{1}{x-1}dx-frac{1/3}intfrac{x}{x^2+x+1}dx-intfrac{1}{x^2+x+1}dx$$ Utilizing the facility rule of integration and the arctangent perform, we get: $$intfrac{x^2+1}{x^3-1}dx=frac{2/3}ln|x-1|-frac{1}{6}ln|x^2+x+1|-tan^{-1}x+C$$ the place C is the fixed of integration. Instance 2: Discover the indefinite integral of the next fraction: $$frac{1}{sqrt{x^2+1}}$$ We are able to use integration by substitution to search out the indefinite integral of this fraction. Let u=x^2+1, then du=2xdx. Substituting into the integral, we get: $$intfrac{1}{sqrt{x^2+1}}dx=intfrac{1}{sqrt{u}}frac{1}{2x}du=frac{1}{2}intfrac{1}{sqrt{u}}du$$ Now, we will use the facility rule of integration to get: $$intfrac{1}{sqrt{x^2+1}}dx=frac{1}{2}cdot 2sqrt{u}+C=sqrt{x^2+1}+C$$ the place C is the fixed of integration. Instance 3: Discover the indefinite integral of the next fraction: $$frac{e^x}{x^2+1}$$ We are able to use integration by elements to search out the indefinite integral of this fraction. Let u=e^x and dv=1/(x^2+1)dx. Then du=e^xdx and v=arctan(x). Substituting into the method for integration by elements, we get: $$intfrac{e^x}{x^2+1}dx=e^xarctan(x)-intarctan(x)e^xdx$$ Now, we will use integration by elements once more on the second time period to get: $$intfrac{e^x}{x^2+1}dx=e^xarctan(x)-arctan(x)e^x+intfrac{e^x}{x^ Functions of Fractions in Physics Resistance in Parallel Circuits When resistors are related in parallel, the overall resistance is lower than the resistance of any particular person resistor. The method for the overall resistance in parallel is: “` 1/R_total = 1/R_1 + 1/R_2 + … + 1/R_n “` the place R_1, R_2, …, R_n are the resistances of the person resistors. Capacitance in Parallel Circuits When capacitors are related in parallel, the overall capacitance is the same as the sum of the person capacitances. The method for the overall capacitance in parallel is: “` C_total = C_1 + C_2 + … + C_n “` the place C_1, C_2, …, C_n are the capacitances of the person capacitors. Inductance in Collection Circuits When inductors are related in sequence, the overall inductance is the same as the sum of the person inductances. The method for the overall inductance in sequence is: “` L_total = L_1 + L_2 + … + L_n “` the place L_1, L_2, …, L_n are the inductances of the person inductors. Frequency of a Pendulum The frequency of a pendulum is inversely proportional to the sq. root of its size. The method for the frequency of a pendulum is: “` f = 1/(2π)√(L/g) “` the place f is the frequency, L is the size of the pendulum, and g is the acceleration because of gravity. Projectile Movement The trajectory of a projectile is parabolic. The horizontal and vertical elements of the projectile’s velocity are: “` v_x = v_0 cos(θ) v_y = v_0 sin(θ) – gt “` the place v_0 is the preliminary velocity, θ is the angle of projection, g is the acceleration because of gravity, and t is the time. Work Achieved by a Pressure The work executed by a power over a distance is the same as the product of the power and the space moved within the course of the power. The method for the work executed by a power is: “` W = Fd cos(θ) “` the place W is the work executed, F is the power, d is the space moved, and θ is the angle between the power and the displacement. Energy Energy is the speed at which work is completed. The method for energy is: “` P = W/t “` the place P is the facility, W is the work executed, and t is the time. Effectivity Effectivity is the ratio of the helpful work executed by a machine to the overall work executed. The method for effectivity is: “` η = W_useful/W_total “` the place η is the effectivity, W_useful is the helpful work executed, and W_total is the overall work executed. Mechanical Benefit Mechanical benefit is the ratio of the output power to the enter power. The method for mechanical benefit is: “` MA = F_out/F_in “` the place MA is the mechanical benefit, F_out is the output power, and F_in is the enter power. Ideally suited Gasoline Legislation The best fuel regulation is a mathematical equation that relates the stress, quantity, temperature, and variety of moles of a fuel. The method for the perfect fuel regulation is: “` PV = nRT “` the place P is the stress, V is the amount, n is the variety of moles, R is the perfect fuel fixed, and T is the temperature. Functions of Fractions in Engineering Fractions are a elementary mathematical idea that discover widespread functions in numerous engineering disciplines. Engineers make the most of fractions to characterize ratios, mannequin bodily portions, and carry out calculations associated to design, evaluation, and optimization. 27. Mechanical Engineering In mechanical engineering, fractions play an important position in: Gear Ratios: Gears are important elements in mechanical methods, and their efficiency will depend on the ratio of their enamel. Fractions are used to characterize gear ratios, which decide the velocity discount or improve between gears. Stress Evaluation: Mechanical engineers analyze the stresses performing on constructions and elements to make sure their security and reliability. Fractions are used to characterize stress concentrations, which point out areas of elevated stress that require reinforcement. Fluid Circulation: Fractions are used to characterize the stream charge of fluids by pipes and different conduits. The Reynolds quantity, a dimensionless parameter used to foretell turbulent stream, is expressed as a fraction. Materials Properties: The mechanical properties of supplies, akin to tensile energy and yield energy, are sometimes expressed as fractions to convey their relative energy and ductility. Dimensional Tolerances: Fractions are used to specify dimensional tolerances in engineering drawings. These tolerances decide the appropriate vary of variation in dimensions, guaranteeing correct match and performance of elements. Conversion of Models: Mechanical engineers usually must convert between totally different models of measurement. Fractions are used to facilitate these conversions, akin to changing ft to inches or kilograms to kilos. The next desk offers particular examples of functions: Software Fraction Illustration Gear Ratio 12/30 Stress Focus Issue 2.5 Reynolds Quantity ρVD/μ Tensile Power 20,000 psi Dimensional Tolerance ±0.005 in Functions of Fractions in Laptop Science 1. Fractals Fractals are geometric patterns that repeat themselves at totally different scales. They’re usually used to create computer-generated artwork. Fractions are used to explain the scaling of fractals. For instance, the Koch snowflake is a fractal that’s generated by repeatedly dividing a triangle into smaller and smaller triangles. The ratio of the size of the aspect of a smaller triangle to the size of the aspect of the bigger triangle is a continuing fraction, generally known as the scaling issue. The scaling issue determines the general measurement of the snowflake. 2. Information Compression Information compression is the method of lowering the scale of a file with out dropping any info. Fractions are utilized in some information compression algorithms, such because the Lempel-Ziv-Welch (LZW) algorithm. LZW works by changing repeated sequences of symbols with shorter codes. The codes are represented as fractions, the place the numerator is the variety of occasions the image has been seen and the denominator is the overall variety of symbols within the file. This enables for extra environment friendly storage and transmission of information. 3. Laptop Graphics Fractions are utilized in laptop graphics to characterize the coordinates of factors in house. The x- and y-coordinates of a degree are usually represented as fractions of the width and peak of the display screen, respectively. This enables for the exact positioning of objects in a 2D or 3D scene. Fractions are additionally used to characterize colours in laptop graphics. The crimson, inexperienced, and blue elements of a colour are sometimes represented as fractions of the utmost potential worth for every part. 4. Synthetic Intelligence Fractions are utilized in synthetic intelligence (AI) to characterize chances. A likelihood is a price between 0 and 1 that expresses the chance of an occasion occurring. Fractions are additionally utilized in AI to characterize the weights of various options in a machine studying mannequin. The weights decide how a lot affect every characteristic has on the mannequin’s predictions. 5. Robotics Fractions are utilized in robotics to regulate the motion of robots. The velocity and course of a robotic’s motion are sometimes represented as fractions. For instance, a robotic could be commanded to maneuver ahead at a velocity of 0.5 meters per second. Because of this the robotic will transfer ahead by 0.5 meters for each second that it’s operating. 6. Laptop Networks Fractions are utilized in laptop networks to characterize IP addresses. An IP tackle is a singular identifier for a tool on a community. IP addresses are usually represented as 4 octets, every of which is a fraction between 0 and 255. For instance, the IP tackle 192.168.1.1 represents the gadget with the next octets: 192, 168, 1, and 1. 7. Internet Growth Fractions are utilized in internet improvement to specify the sizes and positions of parts on an online web page. The width and peak of a component may be specified as fractions of the width and peak of its guardian aspect. This enables for the creation of responsive internet pages that mechanically alter their structure to suit totally different display screen sizes. 8. Sport Growth Fractions are utilized in sport improvement to characterize the well being, mana, and different attributes of characters and objects. Fractions are additionally used to characterize the possibilities of various occasions occurring in a sport. For instance, a sport may use a random quantity generator to find out the likelihood of a personality hitting an enemy with an assault. The likelihood can be represented as a fraction between 0 and 1. 9. Arithmetic Fractions are utilized in arithmetic to characterize a variety of mathematical ideas, akin to ratios, proportions, and percentages. Fractions are additionally utilized in algebra, geometry, and calculus. For instance, the equation y = mx + b represents a straight line, the place m is the slope of the road and b is the y-intercept. The slope is represented as a fraction, the place the numerator is the change in y and the denominator is the change in x. 10. Physics Fractions are utilized in physics to characterize a variety of bodily portions, akin to velocity, acceleration, and power. Fractions are additionally used within the equations of movement, which describe the movement of objects in house. For instance, the equation F = ma represents the second regulation of movement, the place F is the power performing on an object, m is the mass of the thing, and a is the acceleration of the thing. The acceleration is represented as a fraction, the place the numerator is the change in velocity and the denominator is the change in time. 11. Chemistry Fractions are utilized in chemistry to characterize the composition of chemical compounds. The chemical method of a compound signifies the ratio of the totally different parts within the compound. For instance, the chemical method for water is H2O, which signifies that there are two atoms of hydrogen for each one atom of oxygen. The ratio of hydrogen to oxygen in water may be represented because the fraction 2/1. 12. Biology Fractions are utilized in biology to characterize a variety of organic ideas, akin to inhabitants density, progress charges, and genetic variety. Fractions are additionally used within the equations that describe the expansion and conduct of organisms. For instance, the logistic progress equation describes the expansion of a inhabitants in a restricted surroundings. The equation features a fraction that represents the carrying capability of the surroundings, which is the utmost variety of people that the surroundings can assist. 13. Drugs Fractions are utilized in medication to characterize a variety of medical ideas, akin to dosages of medicines, blood stress, and physique mass index (BMI). Fractions are additionally used within the equations that describe the perform of the human physique. For instance, the Fick equation describes the connection between cardiac output, oxygen consumption, and arteriovenous oxygen distinction. The equation features a fraction that represents the arteriovenous oxygen distinction. 14. Economics Fractions are utilized in economics to characterize a variety of financial ideas, akin to inflation charges, rates of interest, and unemployment charges. Fractions are additionally used within the equations that describe the conduct of financial methods. For instance, the Keynesian multiplier describes the impact of presidency spending on combination demand. The equation features a fraction that represents the marginal propensity to devour. 15. Psychology Fractions are utilized in psychology to characterize a variety of psychological ideas, akin to intelligence quotients (IQs), character traits, and psychological well being issues. Fractions are additionally used within the equations that describe the conduct of people and teams. For instance, the Fechner-Weber regulation describes the connection between the depth of a stimulus and the notion of the stimulus. The equation features a fraction that represents the Weber fraction. 16. Sociology Fractions are utilized in sociology to characterize a variety of social ideas, akin to revenue inequality, social mobility, and crime charges. Fractions are additionally used within the equations that describe the conduct of social methods. For instance, the Gini coefficient describes the inequality of revenue distribution in a society. The equation features a fraction that represents the cumulative distribution of revenue. 17. Anthropology Fractions are utilized in anthropology to characterize a variety of anthropological ideas, akin to kinship relations, cultural variety, and ritual practices. Fractions are additionally used within the equations that describe the conduct of human societies. For instance, the Lévi-Strauss mannequin of kinship describes the connection between marriage and descent. The mannequin features a fraction that represents the descent of a lineage. 18. Linguistics Fractions are utilized in linguistics to characterize a variety of linguistic ideas, such because the frequency of phonemes, the distribution of phrases, Utilizing Fractions to Convert Measurements The TI-84 Plus calculator can be utilized to transform between totally different models of measurement, together with fractions. This may be useful when it’s good to convert a measurement from one unit to a different, akin to from inches to ft or from gallons to liters. To transform a measurement utilizing a fraction, you need to use the next steps: 1. Enter the measurement you wish to convert into the calculator. 2. Press the “MODE” button and choose the “Math” choice. 3. Press the “FRAC” button to enter the fraction mode. 4. Enter the fraction that you just wish to use to transform the measurement. 5. Press the “ENTER” button. 6. The calculator will show the transformed measurement. For instance, to transform 1/2 of a gallon to liters, you’ll enter the next steps into the calculator: 1. Enter “1/2”. 2. Press the “MODE” button and choose the “Math” choice. 3. Press the “FRAC” button. 4. Enter “gal”. 5. Press the “ENTER” button. 6. The calculator will show “1.8927 liters”. Changing Fractions to Decimals If it’s good to convert a fraction to a decimal, you need to use the next steps: 1. Enter the fraction into the calculator. 2. Press the “MATH” button. 3. Choose the “Frac” choice. 4. Choose the “Dec” choice. 5. Press the “ENTER” button. For instance, to transform 1/2 to a decimal, you’ll enter the next steps into the calculator: 1. Enter “1/2”. 2. Press the “MATH” button. 3. Choose the “Frac” choice. 4. Choose the “Dec” choice. 5. Press the “ENTER” button. 6. The calculator will show “0.5”. Changing Decimals to Fractions If it’s good to convert a decimal to a fraction, you need to use the next steps: 1. Enter the decimal into the calculator. 2. Press the “MATH” button. 3. Choose the “Frac” choice. 4. Choose the “Dec” choice. 5. Press the “ENTER” button. For instance, to transform 0.5 to a fraction, you’ll enter the next steps into the calculator: 1. Enter “0.5”. 2. Press the “MATH” button. 3. Choose the “Frac” choice. 4. Choose the “Dec” choice. 5. Press the “ENTER” button. 6. The calculator will show “1/2”. Changing Blended Numbers to Fractions If it’s good to convert a blended quantity to a fraction, you need to use the next steps: 1. Enter the blended quantity into the calculator. 2. Press the “MATH” button. 3. Choose the “Frac” choice. 4. Choose the “Combine” choice. 5. Press the “ENTER” button. For instance, to transform 1 1/2 to a fraction, you’ll enter the next steps into the calculator: 1. Enter “1 1/2”. 2. Press the “MATH” button. 3. Choose the “Frac” choice. 4. Choose the “Combine” choice. 5. Press the “ENTER” button. 6. The calculator will show “3/2”. Changing Fractions to Blended Numbers If it’s good to convert a fraction to a blended quantity, you need to use the next steps: 1. Enter the fraction into the calculator. 2. Press the “MATH” button. 3. Choose the “Frac” choice. 4. Choose the “Combine” choice. 5. Press the “ENTER” button. For instance, to transform 3/2 to a blended quantity, you’ll enter the next steps into the calculator: 1. Enter “3/2”. 2. Press the “MATH” button. 3. Choose the “Frac” choice. 4. Choose the “Combine” choice. 5. Press the “ENTER” button. 6. The calculator will show “1 1/2”. Utilizing Fractions to Remedy Ratio Issues Introduction Ratios are used to check two or extra values. They are often expressed as a fraction, decimal, or p.c. For instance, the ratio of boys to women in a classroom may be written as 3:4, 0.75, or 75%. Fractions are a typical approach to specific ratios, particularly when the values aren’t entire numbers. Utilizing the TI-84 Plus to Remedy Ratio Issues The TI-84 Plus can be utilized to unravel quite a lot of ratio issues. To enter a fraction, press the “2nd” key adopted by the “alpha” key. Then, use the arrow keys to navigate to the “frac” choice. Enter the numerator and denominator of the fraction, separated by a “/”. For instance, to enter the fraction 3/4, press 2nd alpha, then use the arrow keys to navigate to “frac”. Then, enter 3 (numerator) and 4 (denominator), separated by a “/”. Fixing a Ratio Downside To unravel a ratio drawback utilizing the TI-84 Plus, comply with these steps: Enter the ratio as a fraction. Arrange an equation to characterize the issue. Remedy the equation for the unknown worth. Instance Suppose you may have a recipe that calls for two cups of flour to three cups of sugar. You wish to make a half batch of the recipe. How a lot flour and sugar do you want? Answer: Enter the ratio as a fraction: 2/3 Arrange an equation to characterize the issue: 2/3 = x/y Remedy the equation for the unknown worth: x = 1 and y = 1.5 Subsequently, you want 1 cup of flour and 1.5 cups of sugar to make a half batch of the recipe. Superior Ratio Issues The TI-84 Plus may also be used to unravel extra superior ratio issues. For instance, you need to use the calculator to: Discover the unit charge of a ratio Examine ratios Remedy proportions Unit Fee The unit charge of a ratio is the ratio of 1 unit of the primary amount to at least one unit of the second amount. To search out the unit charge of a ratio, divide the primary amount by the second amount. For instance, suppose you may have a ratio of 12 miles to three hours. The unit charge of this ratio is 12 miles / 3 hours = 4 miles per hour. Evaluating Ratios To match ratios, you need to use the next guidelines: Two ratios are equal if they’ve the identical worth. If the primary ratio is bigger than the second ratio, then the primary amount is bigger than the second amount. If the primary ratio is lower than the second ratio, then the primary amount is lower than the second amount. Proportions A proportion is an equation that states that two ratios are equal. Proportions can be utilized to unravel quite a lot of issues, akin to discovering lacking values or fixing phrase issues. To unravel a proportion, cross-multiply and resolve for the unknown worth. For instance, to unravel the proportion 2/3 = x/6, cross-multiply to get 2 * 6 = 3 * x. Then, resolve for x to get x = 4. Utilizing Fractions to Estimate Values The TI-84 Plus calculator can be utilized to estimate values of fractions. This may be useful for getting a fast approximation of a price with out having to carry out a protracted division calculation. To estimate a price of a fraction, comply with these steps: Enter the fraction into the calculator. Press the “enter” key. The calculator will show the decimal worth of the fraction. For instance, to estimate the worth of 1/2, enter 1/2 into the calculator and press the “enter” key. The calculator will show the decimal worth 0.5. Utilizing Fractions to Estimate Values with a Bigger Quantity within the Denominator (instance: 40) When the denominator of a fraction is a big quantity, it may be troublesome to estimate the worth of the fraction. Nonetheless, there are just a few strategies that can be utilized to get approximation. One technique is to make use of the “fraction button” on the calculator. This button is situated on the primary display screen of the calculator, and it appears like a fraction with a line by it. To make use of the fraction button, comply with these steps: Press the “fraction button”. Enter the numerator of the fraction. Press the “enter” key. Enter the denominator of the fraction. Press the “enter” key. The calculator will show the decimal worth of the fraction. For instance, to estimate the worth of 1/40, press the “fraction button”, enter 1, press the “enter” key, enter 40, and press the “enter” key. The calculator will show the decimal worth 0.025. One other technique for estimating the worth of a fraction with a big denominator is to make use of the “desk” perform on the calculator. This perform can be utilized to create a desk of values for the fraction. To make use of the “desk” perform, comply with these steps: Press the “2nd” key after which the “desk” key. Enter the equation for the fraction. Press the “enter” key. Enter the beginning worth for the unbiased variable. Press the “enter” key. Enter the ending worth for the unbiased variable. Press the “enter” key. Enter the step worth for the unbiased variable. Press the “enter” key. The calculator will show a desk of values for the fraction. For instance, to create a desk of values for the fraction 1/40, enter 1/40 into the calculator, press the “enter” key, enter 0 into the calculator, press the “enter” key, enter 100 into the calculator, press the “enter” key, and enter 10 into the calculator. The calculator will show a desk of values for the fraction 1/40, as proven within the following desk: x y 0 0.025 10 0.25 20 0.5 30 0.75 40 1 As you may see from the desk, the worth of 1/40 is roughly 0.025. It is a good approximation, regardless that the denominator of the fraction is comparatively massive. Utilizing Fractions to Characterize Chance Fractions can be utilized to characterize likelihood. Chance is a measure of the chance that an occasion will happen. It’s expressed as a quantity between 0 and 1, the place 0 signifies that the occasion is unattainable and 1 signifies that the occasion is definite. For instance, the likelihood of rolling a 6 on a die is 1/6, as a result of there may be one consequence out of six potential outcomes that can lead to a 6. Fractions may also be used to check chances. For instance, the likelihood of rolling a 6 on a die is bigger than the likelihood of rolling a 1, as a result of there may be one consequence out of six potential outcomes that can lead to a 6, however just one consequence out of six potential outcomes that can lead to a 1. Utilizing Fractions to Remedy Chance Issues Fractions can be utilized to unravel likelihood issues. Listed below are some examples: What’s the likelihood of drawing a crimson card from a deck of 52 playing cards? There are 26 crimson playing cards in a deck of 52 playing cards. So the likelihood of drawing a crimson card is 26/52 = 1/2. What’s the likelihood of rolling a 6 on a die after which rolling a 2? The likelihood of rolling a 6 on a die is 1/6. The likelihood of rolling a 2 on a die is 1/6. The likelihood of rolling a 6 after which rolling a 2 is (1/6) * (1/6) = 1/36. What’s the likelihood of getting heads on a coin toss after which tails on the second coin toss? The likelihood of getting heads on a coin toss is 1/2. The likelihood of getting tails on a coin toss is 1/2. The likelihood of getting heads after which tails is (1/2) * (1/2) = 1/4. Utilizing Fractions to Characterize Percentages Fractions can be utilized to characterize percentages. A proportion is a means of expressing a quantity as a fraction of 100. For instance, 50% is identical as 50/100 = 1/2. Fractions may also be used to transform percentages to decimals. To transform a proportion to a decimal, divide the proportion by 100. For instance, 50% is identical as 50/100 = 0.5. Utilizing Fractions to Remedy Share Issues Fractions can be utilized to unravel proportion issues. Listed below are some examples: What’s 25% of 100? 25% is identical as 25/100 = 1/4. So 25% of 100 is (1/4) * 100 = 25. What’s the proportion of 20 that’s 5? To search out the proportion of 20 that’s 5, divide 5 by 20 after which multiply by 100. So the proportion of 20 that’s 5 is (5/20) * 100 = 25%. What’s 12% of fifty? 12% is identical as 0.12. So 12% of fifty is 0.12 * 50 = 6. Utilizing Fractions in Actual-World Conditions Fractions are utilized in quite a lot of real-world conditions. Listed below are some examples: Cooking: Fractions are used to measure elements in recipes. Development: Fractions are used to measure distances and angles. Finance: Fractions are used to calculate rates of interest and percentages. Drugs: Fractions are used to measure dosages of treatment. Science: Fractions are used to measure portions akin to temperature and quantity. 41. Utilizing Fractions to Remedy Sensible Issues Along with the examples given above, fractions may also be used to unravel quite a lot of different sensible issues. Listed below are just a few examples: Mixing paint: If you wish to combine two totally different colours of paint, you need to use fractions to find out how a lot of every colour to make use of. For instance, if you wish to combine 1/2 gallon of crimson paint with 1/4 gallon of blue paint, you would want to make use of 2/3 gallon of crimson paint and 1/3 gallon of blue paint. Dividing a pizza: If you wish to divide a pizza evenly amongst a bunch of individuals, you need to use fractions to find out how a lot of the pizza every particular person ought to get. For instance, if you wish to divide a pizza evenly amongst 4 folks, you would want to chop the pizza into 4 equal slices. Calculating reductions: If you wish to calculate a reduction, you need to use fractions to find out how a lot of the unique worth you’ll pay. For instance, if you wish to calculate a ten% low cost, you would want to multiply the unique worth by 0.9. Conclusion Fractions are a flexible mathematical instrument that can be utilized to unravel quite a lot of issues. By understanding tips on how to use fractions, you may make your life simpler and extra environment friendly. Utilizing Fractions to Calculate Quantity The TI-84 Plus calculator can be utilized to calculate the amount of quite a lot of objects, together with rectangular prisms, cylinders, cones, and spheres. Fractions can be utilized in any of those calculations. To make use of the calculator to calculate the amount of an object utilizing fractions, comply with these steps: 1. Enter the scale of the thing. For an oblong prism, enter the size, width, and peak. For a cylinder, enter the radius and peak. For a cone, enter the radius and peak. For a sphere, enter the radius. 2. Enter the method for the amount of the thing. The method for the amount of an oblong prism is V = lwh. The method for the amount of a cylinder is V = πr²h. The method for the amount of a cone is V = (1/3)πr²h. The method for the amount of a sphere is V = (4/3)πr³. 3. Exchange the variables within the method with the values you entered in step 1. For instance, in case you are calculating the amount of an oblong prism with a size of 5, a width of three, and a peak of two, you’ll enter the next method into the calculator: “` V = 5 * 3 * 2 “` 4. Consider the expression. The calculator will show the amount of the thing. For instance, when you entered the method from step 3 into the calculator, the calculator would show the next end result: “` V = 30 “` The amount of the oblong prism is 30 cubic models. Listed below are some examples of tips on how to use fractions to calculate the amount of objects utilizing the TI-84 Plus calculator: Object Formulation Instance Consequence Rectangular prism V = lwh V = (1/2) * 3 * 4 V = 6 Cylinder V = πr²h V = π * (1/2)² * 3 V = (3π)/4 Cone V = (1/3)πr²h V = (1/3)π * (1/4)² * 5 V = (5π)/48 Sphere V = (4/3)πr³ V = (4/3)π * (2/3)³ V = (32π)/27 Utilizing Fractions to Calculate Weight Fractions are a typical approach to characterize elements of a complete. They can be utilized to calculate weight, amongst different issues. To make use of fractions to calculate weight, it’s good to know the next: The load of the entire object The fraction of the thing that you just wish to calculate the load of After you have this info, you need to use the next method to calculate the load of the fraction: “` Weight of fraction = Weight of entire object * Fraction “` For instance, when you have a 10-pound bag of rice and also you wish to calculate the load of half of the bag, you’ll use the next method: “` Weight of half bag = 10 kilos * 1/2 = 5 kilos “` You may as well use fractions to check weights. For instance, when you have a 5-pound bag of sugar and a 3-pound bag of flour, you need to use the next method to check their weights: “` Weight of sugar / Weight of flour = 5 kilos / 3 kilos = 1.67 “` Because of this the sugar is 1.67 occasions heavier than the flour. 48. Instance: Calculating the Weight of a Fraction of a Watermelon Suppose you may have a watermelon that weighs 12 kilos. You wish to calculate the load of half of the watermelon. You should use the next method: “` Weight of half watermelon = 12 kilos * 1/2 = 6 kilos “` Subsequently, half of the watermelon weighs 6 kilos. 121: How To Use Fractions On Ti 84 Plus Fractions may be entered into the TI-84 Plus in quite a lot of methods. 1) utilizing the Fraction template (Math > Templates > Fraction), 2) by urgent the “ALPHA” key adopted by the “” key (which produces the fraction bar), or 3) by utilizing the “MATH” key adopted by the “NUM” key (which produces quite a lot of fraction codecs). As soon as a fraction has been entered, it may be utilized in calculations similar to another quantity. Listed below are some examples of tips on how to enter fractions into the TI-84 Plus: To enter the fraction 1/2, press the “MATH” key adopted by the “NUM” key, then choose the “1/x” choice. To enter the fraction 3/4, press the “ALPHA” key adopted by the “” key, then enter “3/4”. To enter the fraction 5/6, press the “Math” key adopted by the “Templates” key, then choose the “Fraction” template. Enter the numerator (5) and denominator (6) of the fraction. As soon as a fraction has been entered, it may be utilized in calculations similar to another quantity. For instance, so as to add the fractions 1/2 and three/4, press the “1/2” key, then press the “+” key, then press the “3/4” key. The TI-84 Plus will return the reply, which is 5/4. To multiply the fractions 1/2 and three/4, press the “1/2” key, then press the “*” key, then press the “3/4” key. The TI-84 Plus will return the reply, which is 3/8. Fractions may also be transformed to decimals by urgent the “MATH” key adopted by the “NUM” key, then deciding on the “FracDec” choice. Folks Additionally Ask About 121: How To Use Fractions On Ti 84 Plus How do you simplify fractions on a TI 84 Plus? To simplify a fraction on a TI-84 Plus, press the “MATH” key adopted by the “NUM” key, then choose the “Simplify” choice. The TI-84 Plus will simplify the fraction and return the reply. How do you exchange a fraction to a decimal on a TI 84 Plus? To transform a fraction to a decimal on a TI-84 Plus, press the “MATH” key adopted by the “NUM” key, then choose the “FracDec” choice. The TI-84 Plus will convert the fraction to a decimal and return the reply. How do you add fractions on a TI 84 Plus? So as to add fractions on a TI-84 Plus, press the “MATH” key adopted by the “NUM” key, then choose the “FracAdd” choice. The TI-84 Plus will add the fractions and return the reply. How do you subtract fractions on a TI 84 Plus? To subtract fractions on a TI-84 Plus, press the “MATH” key adopted by the “NUM” key, then choose the “FracSub” choice. The TI-84 Plus will subtract the fractions and return the reply. How do you multiply fractions on a TI 84 Plus? To multiply fractions on a TI-84 Plus, press the “MATH” key adopted by the “NUM” key, then choose the “FracMult” choice. The TI-84 Plus will multiply the fractions and return the reply. How do you divide fractions on a TI 84 Plus? To divide fractions on a TI-84 Plus, press the “MATH” key adopted by the “NUM” key, then choose the “FracDiv” choice. The TI-84 Plus will divide the fractions and return the reply.