## Adding and Subtracting Mixed Fractions

A Mixed Fraction is a whole number and a fraction combined:

To make it easy to add and subtract them, just convert to Improper Fractions first:

An Improper fraction has a top number larger than or equal to the bottom number:

Can you see that 1 3 4 is the same as 7 4 ?

In other words "one and three quarters" is the same as "seven quarters".

(You may like to read how to Convert from or to Mixed Fractions )

## Adding Mixed Fractions

- convert them to Improper Fractions
- then add them (using Addition of Fractions )
- then convert back to Mixed Fractions

## Example: What is 2 3 4 + 3 1 2 ?

Convert to Improper Fractions:

7 2 becomes 14 4 (by multiplying top and bottom by 2)

Convert back to Mixed Fractions:

When you get more experience you can do it faster like this example:

## Example: What is 3 5 8 + 1 3 4

Convert them to improper fractions:

Make same denominator: 7 4 becomes 14 8 (by multiplying top and bottom by 2)

## Subtracting Mixed Fractions

Just follow the same method, but subtract instead of add:

## Example: What is 15 3 4 − 8 5 6 ?

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## WORD PROBLEMS ON MIXED FRACTIONS

Total no. of miles she walked is

In the above mixed fractions, we have the denominators 3 and 5.

So, Linda walked 5 ¹¹⁄₁₅ miles in all.

No. of pizzas he had initially is

So, initially David had 3 ⁵⁄₁₄ pizzas.

Now, no. of acres of land that Mr. A has

In the above mixed fractions, we have the denominators 3 and 4.

Now, Mr. A has 2 ⁵⁄₁₂ acres of land.

No. of cups of nuts that Lily put in all is

So, Lily put 4 ⅔ cups of nuts in all.

No. of periods in all he played is

So, Rodayo played 3 ¼ periods in all.

No. of bags = Total no. of lbs./No of lbs. per bag

Because, we use division, we have to convert the given mixed numbers into improper fractions.

Total no. of pounds of flour is

Number of bags = (15/2) ÷ (3/2)

So, the number of bags that Mimi can make is 5.

Total weight of the fish they caught is

In the above mixed fractions, we have the denominators 4 and 5.

So, the total weight of the fish they caught is 5 ¹⁹⁄₂₀ kg.

No. of bottles of milk used is

In the above mixed fractions, we have the denominators 5 and 4.

So, no. of bottles of milk used is 1 ¹⁷⁄₂₀ .

= (2 + ²⁰⁄₂₀ + ¹⁰⁄₂₀ ) - 1 ¹⁷⁄₂₀

So, 1 ¹³⁄₂₀ bottles of milk Amy has left over.

Initially, the tank has 82 ¾ liters.

24 ⅘ liters were used -----> Subtract

The tank was filled with another 18 ¾ liters -----> Add

Then, the final volume of the water in tank is

= 82 ¹⁵⁄₂₀ - 24 ¹⁶⁄₂₀ + 18 ¹⁵⁄₂₀

= (82 - 24 + 18) + ( ¹⁵⁄₂₀ - ¹⁶⁄₂₀ + ¹⁵⁄₂₀ )

So, the final volume of water in the tank is 76 ⁷⁄₁₀ liters.

Initial stock of lemonade is 21 ½ liters.

No. of liters sold = Initial stock - closing stock

No. of liters sold = 21 ½ - 2 ⅝

No. of liters sold = 21 ⁴⁄₈ - 2 ⅝

No. of liters sold = (21 + ⁴⁄₈ ) - 2 ⅝

So, 18 ⅞ liters of lemonade was sold by the Trader.

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Analysis: To solve this problem, we will add two fractions with like denominators.

Answer: Rachel rode her bike for three-fifths of a mile altogether.

Analysis: To solve this problem, we will subtract two fractions with unlike denominators.

Answer: Stefanie swam one-third of a lap farther in the morning.

Answer: It took Nick three and one-fourth hours to complete his homework altogether.

Answer: Diego and his friends ate six pizzas in all.

Answer: The Cocozzelli family took one-half more days to drive home.

Answer: The warehouse has 21 and one-half meters of tape in all.

Answer: The electrician needs to cut 13 sixteenths cm of wire.

Analysis: To solve this problem, we will subtract a mixed number from a whole number.

Answer: The carpenter needs to cut four and seven-twelfths feet of wood.

- Add fractions with like denominators.
- Subtract fractions with like denominators.
- Find the LCD.
- Add fractions with unlike denominators.
- Subtract fractions with unlike denominators.
- Add mixed numbers with like denominators.
- Subtract mixed numbers with like denominators.
- Add mixed numbers with unlike denominators.
- Subtract mixed numbers with unlike denominators.

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Home / United States / Math Classes / 5th Grade Math / Problem Solving using Fractions

## Problem Solving using Fractions

## Table of Contents

## What are Fractions?

- Fractions with like and unlike denominators
- Operations on fractions
- Fractions can be multiplied by using
- Let’s take a look at a few examples

## Solved Examples

A fraction in which the numerator is less than the denominator value is called a proper fraction.

For example , \(\frac{3}{4}\) , \(\frac{5}{7}\) , \(\frac{3}{8}\) are proper fractions.

Eg \(\frac{9}{4}\) , \(\frac{8}{8}\) , \(\frac{9}{4}\) are examples of improper fractions.

We express improper fractions as mixed numbers.

For example , 5\(\frac{1}{3}\) , 1\(\frac{4}{9}\) , 13\(\frac{7}{8}\) are mixed fractions.

## Fractions with Like and Unlike Denominators

\(\frac{1}{3}\) and \(\frac{1}{4}\) are unlike fractions as they both have a different denominator.

## Operations on Fractions

We can perform addition, subtraction, multiplication and division operations on fractions.

## Fractions can be Multiplied by Using:

## Let’s Take a Look at a Few Examples

Addition and subtraction using common denominator

( \(\frac{1}{6} ~+ ~\frac{2}{5}\) )

\(\frac{1}{6} ~+ ~\frac{2}{5}\)

( \(\frac{5}{2}~-~\frac{1}{6}\) )

Examples of Multiplication and Division

(\(\frac{1}{6}~\times~\frac{2}{5}\))

(\(\frac{2}{5}~÷~\frac{1}{6}\))

= (\(\frac{2 ~\times~ 5}{6~\times~ 1}\)) [Multiplying dividend with the reciprocal of divisor]

= (\(\frac{2 ~\times~ 6}{5 ~\times~ 1}\))

Example 1: Solve \(\frac{7}{8}\) + \(\frac{2}{3}\)

\(\frac{7}{8}\) + \(\frac{2}{3}\)

Example 2: Solve \(\frac{11}{13}\) – \(\frac{12}{17}\)

\(\frac{11}{13}\) – \(\frac{12}{17}\)

Example 3: Solve \(\frac{15}{13} ~\times~\frac{18}{17}\)

Multiply the numerators and multiply the denominators of the 2 fractions.

\(\frac{15}{13}~\times~\frac{18}{17}\)

= \(\frac{15~~\times~18}{13~~\times~~17}\)

Example 4: Solve \(\frac{25}{33}~\div~\frac{41}{45}\)

Divide by multiplying the dividend with the reciprocal of the divisor.

\(\frac{25}{33}~\div~\frac{41}{45}\)

= \(\frac{25~\times~45}{33~\times~41}\)

= \(\frac{7}{8}\) + \(\frac{3}{7}\)

= \(\frac{73}{56}~-~\frac{10}{11}\)

First \(\frac{15}{8}\) l needs to be converted to milliliters.

\(\frac{15}{8}\)l into milliliters = \(\frac{15}{8}\) x 1000 = 1875 ml

The number of oranges required for 1875 m l of juice = \(\frac{1875}{25}\) ml = 75 oranges

= \(\frac{1875}{200}~=~9\frac{3}{8}\) cups

Money made on selling 9 cups = 9 x 64 = 576 cents

Hence she makes 576 cents from her juice stand.

## What is a mixed fraction?

## How will you add fractions with unlike denominators?

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## How to Solve Fraction Questions in Math

Last Updated: February 24, 2023 References Approved

## Doing Calculations with Fractions

- For example, if you need to add 1/2 and 2/3, start by determining a common multiple. In this case, the common multiple is 6 since both 2 and 3 can be converted to 6. To turn 1/2 into a fraction with a denominator of 6, multiply both the numerator and denominator by 3: 1 x 3 = 3 and 2 x 3 = 6, so the new fraction is 3/6. To turn 2/3 into a fraction with a denominator of 6, multiply both the numerator and denominator by 2: 2 x 2 = 4 and 3 x 2 = 6, so the new fraction is 4/6. Now, you can add the numerators: 3/6 + 4/6 = 7/6. Since this is an improper fraction, you can convert it to the mixed number 1 1/6.
- On the other hand, say you're working on the problem 7/10 - 1/5. The common multiple in this case is 10, since 1/5 can be converted into a fraction with a denominator of 10 by multiplying it by 2: 1 x 2 = 2 and 5 x 2 = 10, so the new fraction is 2/10. You don't need to convert the other fraction at all. Just subtract 2 from 7, which is 5. The answer is 5/10, which can also be reduced to 1/2.

## Practicing the Basics

## Fraction Calculator, Practice Problems, and Answers

## Community Q&A

- Take the time to carefully read through the problem at least twice so you can be sure you know what it's asking you to do. ⧼thumbs_response⧽ Helpful 0 Not Helpful 0
- Check with your teacher to find out if you need to convert improper fractions into mixed numbers and/or reduce fractions to their lowest terms to get full marks. ⧼thumbs_response⧽ Helpful 0 Not Helpful 0
- To take the reciprocal of a whole number, just put a 1 over it. For example, 5 becomes 1/5. ⧼thumbs_response⧽ Helpful 0 Not Helpful 0

## You Might Also Like

- ↑ https://www.sparknotes.com/math/prealgebra/fractions/terms/
- ↑ https://www.bbc.co.uk/bitesize/articles/z9n4k7h
- ↑ https://www.mathsisfun.com/fractions_multiplication.html
- ↑ https://www.mathsisfun.com/fractions_division.html
- ↑ https://medium.com/i-math/the-no-nonsense-straightforward-da76a4849ec
- ↑ https://www.youtube.com/watch?v=PcEwj5_v75g
- ↑ https://sciencing.com/solve-math-problems-fractions-7964895.html

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## Fraction Word Problems - Mixed Numbers

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Step 1. Is it a problem in addition or subtraction?

Step 2. Do you need to find a common denominator?

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## Fraction Word Problem Worksheets

Represent and Simplify the Fractions: Type 1

Represent and Simplify the Fractions: Type 2

Adding Fractions Word Problems Worksheets

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## Fractions Calculator

## Calculator Use

To do math with mixed numbers (whole numbers and fractions) use the Mixed Numbers Calculator .

## Math on Fractions with Unlike Denominators

There are 2 cases where you need to know if your fractions have different denominators:

## How to Add or Subtract Fractions

- Find the least common denominator
- You can use the LCD Calculator to find the least common denominator for a set of fractions
- For your first fraction, find what number you need to multiply the denominator by to result in the least common denominator
- Multiply the numerator and denominator of your first fraction by that number
- Repeat Steps 3 and 4 for each fraction
- For addition equations, add the fraction numerators
- For subtraction equations, subtract the fraction numerators
- Convert improper fractions to mixed numbers
- Reduce the fraction to lowest terms

## How to Multiply Fractions

## How to Divide Fractions

- Rewrite the equation as in "Keep, Change, Flip"
- Keep the first fraction
- Change the division sign to multiplication
- Flip the second fraction by switching the top and bottom numbers

## Fraction Formulas

The formulas for multiplying and dividing fractions follow the same process as described above.

## Adding Fractions

The formula for adding fractions is:

## Subtracting Fractions

The formula for subtracting fractions is:

## Multiplying Fractions

The formula for multiplying fractions is:

## Dividing Fractions

The formula for dividing fractions is:

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## 2.3.2: Subtracting Fractions and Mixed Numbers

## Learning Objectives

- Subtract fractions with like and unlike denominators.
- Subtract mixed numbers without regrouping.
- Subtract mixed numbers with regrouping.
- Solve application problems that require the subtraction of fractions or mixed numbers.

## Introduction

## Subtracting Fractions

If you subtract 3 pieces, you can see below that \(\ \frac{7}{12}\) of the cake remains.

\(\ \frac{10}{12}-\frac{3}{12}=\frac{7}{12}\)

## Subtracting Fractions with Like Denominators

\(\ \frac{6}{7}-\frac{1}{7}=\frac{5}{7}\)

\(\ \frac{5}{9}-\frac{2}{9}=\frac{1}{3}\)

\(\ \frac{1}{5}-\frac{1}{6}=\frac{1}{30}\)

\(\ \frac{5}{6}-\frac{1}{4}=\frac{7}{12}\)

\(\ \frac{2}{3}-\frac{1}{6}\) Subtract and simplify the answer.

- \(\ \frac{1}{3}\)
- \(\ \frac{3}{6}\)
- \(\ \frac{5}{6}\)
- \(\ \frac{1}{2}\)
- Incorrect. Find a least common denominator and subtract; then simplify. The correct answer is \(\ \frac{1}{2}\).
- Incorrect. Simplify the fraction. The correct answer is \(\ \frac{1}{2}\).
- Incorrect. Subtract, don’t add, the fractions. The correct answer is \(\ \frac{1}{2}\)
- Correct. \(\ \frac{4}{6}-\frac{1}{6}=\frac{3}{6}=\frac{1}{2}\)

## Subtracting Mixed Numbers

\(\ 6 \frac{4}{5}-3 \frac{1}{5}=3 \frac{3}{5}\)

\(\ 8 \frac{1}{3}-4 \frac{2}{3}=3 \frac{2}{3}\)

\(\ 7 \frac{1}{2}-2 \frac{1}{3}=5 \frac{1}{6}\)

\(\ 9 \frac{4}{5}-4 \frac{2}{3}\)

Subtract. Simplify the answer and write it as a mixed number.

- \(\ \frac{2}{15}\)
- \(\ 5 \frac{2}{15}\)
- \(\ 4 \frac{7}{15}\)
- Incorrect. Subtract the whole numbers, too. The correct answer is \(\ 5 \frac{2}{15}\).
- Correct. \(\ 9-4=5\); \(\ \frac{4}{5}-\frac{2}{3}=\frac{12}{15}-\frac{10}{15}=\frac{2}{15}\). Combining them gives \(\ 5 \frac{2}{15}\).
- Incorrect. Subtract, don’t add, the fractions. The correct answer is \(\ 5 \frac{2}{15}\).
- Incorrect. Subtract the fractions as well as the whole numbers. The correct answer is \(\ 5 \frac{2}{15}\).

## Subtracting Mixed Numbers with Regrouping

Now, you can write an equivalent problem to the original:

\(\ 6 \frac{7}{6}-3 \frac{5}{6}\)

Then, you just subtract like you normally subtract mixed numbers:

\(\ \frac{7}{6}-\frac{5}{6}=\frac{2}{6}=\frac{1}{3}\)

So, the answer is \(\ 3 \frac{1}{3}\).

\(\ 7 \frac{1}{5}-3 \frac{1}{4}=3 \frac{19}{20}\)

\(\ 8-4 \frac{2}{5}=3 \frac{3}{5}\)

- Subtract 1 from the whole number part of the mixed number being subtracted.
- Add that 1 to the fraction part to make an improper fraction. For example: \(\ 7 \frac{2}{3}=6+\frac{3}{3}+\frac{2}{3}=6 \frac{5}{3}\)
- Then, subtract as with any other mixed numbers.

Alternatively, you can change both numbers to improper fractions and then subtract.

\(\ 15-13 \frac{1}{4}\) Subtract. Simplify the answer and write as a mixed number.

- \(\ 2 \frac{1}{4}\)
- \(\ 28 \frac{1}{4}\)
- \(\ 1 \frac{3}{4}\)
- \(\ 2 \frac{3}{4}\)
- Incorrect. This is the answer to \(\ 15 \frac{1}{4}-13\). The fraction has to be subtracted from the 15. The correct answer is \(\ 1 \frac{3}{4}\).
- Incorrect. Subtract, don’t add, the quantities. The correct answer is \(\ 1 \frac{3}{4}\).
- Correct. \(\ 14 \frac{4}{4}-13 \frac{1}{4}=1 \frac{3}{4}\)
- Incorrect. Subtract 1 from the whole number when rewriting it as a mixed number. The correct answer is \(\ 1 \frac{3}{4}\).

## Subtracting Fractions and Mixed Numbers to Solve Problems

Sherry has \(\ 2 \frac{5}{8}\) yards of blue print fabric left over.

Pilar ran \(\ 1 \frac{7}{8}\) miles more than Farouk.

Jose used \(\ \frac{1}{6}\) of a can more paint than Mike.

- \(\ 22 \frac{5}{12}\) inches
- \(\ 15 \frac{1}{12}\) inches
- \(\ 15\) inches
- \(\ 14 \frac{11}{12}\) inches
- Incorrect. Subtract, don’t add, the fractions. The correct answer is \(\ 14 \frac{11}{12}\) inches.
- Incorrect. Subtract \(\ \frac{2}{3}-\frac{3}{4}\), not \(\ \frac{3}{4}-\frac{2}{3}\). The correct answer is \(\ 14 \frac{11}{12}\) inches.
- Incorrect. Subtract the fractions as well as the whole numbers in the mixed numbers. The correct answer is \(\ 14 \frac{11}{12}\) inches.
- Correct. \(\ 17 \frac{20}{12}-3 \frac{9}{12}=14 \frac{11}{12}\)

## improper fraction/mixed number word problems

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Learn about mixed fractions using our free math solver with step-by-step solutions. Skip to main content. Microsoft Math Solver. Solve Practice Download. ... Type a math problem. Type a math problem. Solve. Examples. 3 \frac{ 3 }{ 7 } 4 \frac{ 15 }{ 32 } 1 \frac{ 1 }{ 2 } +3 \frac{ 4 }{ 5 } ...

That is why it is called a "mixed" fraction (or mixed number). Names. We can give names to every part of a mixed fraction: Three Types of Fractions. There are three types of fraction: Mixed Fractions or Improper Fractions. We can use either an improper fraction or a mixed fraction to show the same amount. For example 1 34 = 74, as shown here:

To add mixed fractions: convert them to Improper Fractions then add them (using Addition of Fractions) then convert back to Mixed Fractions Like this: Example: What is 2 3 4 + 3 1 2 ? Convert to Improper Fractions: 2 3 4 = 11 4 3 1 2 = 7 2 Common denominator of 4: 11 4 stays as 11 4 7 2 becomes 14 4 (by multiplying top and bottom by 2) Now Add:

Mixed Numbers Calculator (also referred to as Mixed Fractions): This online calculator handles simple operations on whole numbers, integers, mixed numbers, fractions and improper fractions by adding, subtracting, dividing or multiplying. The answer is provided in a reduced fraction and a mixed number if it exists.

To convert a mixed fraction into an improper fraction, first, we multiply the denominator of the proper fraction by the whole number attached to it and then we add the numerator. For example, 3 1 / 2 is a mixed fraction. Multiply 2 and 3, 2×3 = 6 Add 6 and 1 (numerator) = 6+1 = 7 Hence, 31/2 = 7/2 How to add mixed fractions?

Mixed fraction word problems Add / subtract / multiply / divide fractions These word problems provide additional practice with fractions and the 4 basic operations. Mixing word problems and including unneeded data are ways to encourage students to carefully read and think about the questions. Worksheet #1 Worksheet #2 Worksheet #3 Worksheet #4

Step 1: Let's use shapes to represent the mixed number three and one-half. Step 2: Solution: In example 1, we used shapes to help us solve the problem. Let's look at example 2. Example 2: A school bell rings every half-hour. If it just rang, then how many times will it ring in in the next nine and one-half hours?

Fraction word problems with the 4 operations These word problems involve the 4 basic operations ( addition, subtraction, multiplication and division) on fractions. Mixing word problems encourages students to read and think about the questions, rather than simply recognizing a pattern to the solutions.

Mixed Fractions Worksheets. A mixed fraction is a fraction, but it consists of two parts: an integer part and a right fractional part. In math, the mixer forms mixed fractions from a pure fraction with one or more whole quantities. If an appropriate fraction is added to a total amount, then the quantity becomes a fraction. Therefore, the ...

WORD PROBLEMS ON MIXED FRACTIONS Problem 1 : Linda walked 2 ⅓ miles on the first day and 3 ⅖ miles on the next day. How many miles did she walk in all? Solution : Total no. of miles she walked is = 2⅓ + 3⅖ In the above mixed fractions, we have the denominators 3 and 5. LCM of (3, 5) = 15.

Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having unlike denominators. Solution: Answer: The electrician needs to cut 13 sixteenths cm of wire. Example 9: A carpenter had a piece of wood that was 15 feet in length.

Fractions can be Multiplied by Using: 1. Tape diagrams 2. Area models 3. Repeated addition 4. Unit fractions 5. Multiplication of numerators, and multiplication of denominators of the two fractions. Division operations on fractions can be performed using a tape diagram and area model.

Doing Calculations with Fractions 1 Add fractions with the same denominator by combining the numerators. To add fractions, they must have the same denominator. If they do, simply add the numerators together. [2] For instance, to solve 5/9 + 1/9, just add 5 + 1, which equals 6. The answer, then, is 6/9 which can be reduced to 2/3. 2

Mixed Number Calculator. With this online mixed fraction calculator (or mixed number calculator) with whole numbers and fractions you can easily add mixed fractions, subtract mixed. If you're looking for someone to help you with your assignments, you've come to the right place. At Get Assignment, we're here to help you get the grades you deserve.

Objective: I can solve one-step word problems involving addition and subtraction of mixed numbers (mixed fractions). Follow these steps to solve the mixed numbers word problems. Step 1. Is it a problem in addition or subtraction? Step 2. Do you need to find a common denominator?

With a mixed number, we need to first convert it to an improper fraction, or a fraction with a flair for off-color jokes. Wait, no, it's a fraction with a larger numerator than denominator....

The fraction word problems include proper fraction, improper fraction, and mixed numbers. Solve each word problem and scroll down each printable worksheet to verify your solutions using the answer key provided. Thumb through some of these word problem worksheets for free! Represent and Simplify the Fractions: Type 1

To perform math operations on mixed number fractions use our Mixed Numbers Calculator. This calculator can also simplify improper fractions into mixed numbers and shows the work involved. If you want to simplify an individual fraction into lowest terms use our Simplify Fractions Calculator .

Since the fractions have a like denominator, subtract the numerators. 11 3 = 32 3. Write the answer as a mixed number. Divide 11 by 3 to get 3 with a remainder of 2. 81 3 − 42 3 = 32 3. Since addition is the inverse operation of subtraction, you can check your answer to a subtraction problem with addition.

improper fraction/mixed number word problems Subject: Mathematics Age range: 7-11 Resource type: Worksheet/Activity 35 reviews File previews doc, 29.5 KB Differentiated word problems for improper fractions and mixed number. Hope it helps. Creative Commons "Sharealike" Report this resource to let us know if it violates our terms and conditions.

Learn about fractions using our free math solver with step-by-step solutions.

Problems increase in difficulty across all 90 pages in these sets. Purchase all 9 sets in our Level 1 Warm-Ups bundle. These exercises offer a mixed review of basic concepts & processes, similar to all standardized tests. Emphasize test-taking strategies and enrich your curriculum with this supplement!