MATH Worksheets 4 Kids

Child Login

  • Kindergarten
  • Number charts
  • Skip Counting
  • Place Value
  • Number Lines
  • Subtraction
  • Multiplication
  • Word Problems
  • Comparing Numbers
  • Ordering Numbers
  • Odd and Even
  • Prime and Composite
  • Roman Numerals
  • Ordinal Numbers
  • In and Out Boxes
  • Number System Conversions
  • More Number Sense Worksheets
  • Size Comparison
  • Measuring Length
  • Metric Unit Conversion
  • Customary Unit Conversion
  • Temperature
  • More Measurement Worksheets
  • Writing Checks
  • Profit and Loss
  • Simple Interest
  • Compound Interest
  • Tally Marks
  • Mean, Median, Mode, Range
  • Mean Absolute Deviation
  • Stem-and-leaf Plot
  • Box-and-whisker Plot
  • Permutation and Combination
  • Probability
  • Venn Diagram
  • More Statistics Worksheets
  • Shapes - 2D
  • Shapes - 3D
  • Lines, Rays and Line Segments
  • Points, Lines and Planes
  • Transformation
  • Quadrilateral
  • Ordered Pairs
  • Midpoint Formula
  • Distance Formula
  • Parallel, Perpendicular and Intersecting Lines
  • Scale Factor
  • Surface Area
  • Pythagorean Theorem
  • More Geometry Worksheets
  • Converting between Fractions and Decimals
  • Significant Figures
  • Convert between Fractions, Decimals, and Percents
  • Proportions
  • Direct and Inverse Variation
  • Order of Operations
  • Squaring Numbers
  • Square Roots
  • Scientific Notations
  • Speed, Distance, and Time
  • Absolute Value
  • More Pre-Algebra Worksheets
  • Translating Algebraic Phrases
  • Evaluating Algebraic Expressions
  • Simplifying Algebraic Expressions
  • Algebraic Identities
  • Quadratic Equations
  • Systems of Equations
  • Polynomials
  • Inequalities
  • Sequence and Series
  • Complex Numbers
  • More Algebra Worksheets
  • Trigonometry
  • Math Workbooks
  • English Language Arts
  • Summer Review Packets
  • Social Studies
  • Holidays and Events
  • Worksheets >
  • Pre-Algebra >
  • Fractions >

Fraction Word Problem Worksheets

Featured here is a vast collection of fraction word problems, which require learners to simplify fractions, add like and unlike fractions; subtract like and unlike fractions; multiply and divide fractions. 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

Represent and Simplify the Fractions: Type 1

Presented here are the fraction pdf worksheets based on real-life scenarios. Read the basic fraction word problems, write the correct fraction and reduce your answer to the simplest form.

  • Download the set

Represent and Simplify the Fractions: Type 2

Represent and Simplify the Fractions: Type 2

Before representing in fraction, children should perform addition or subtraction to solve these fraction word problems. Write your answer in the simplest form.

Adding Fractions Word Problems Worksheets

Adding Fractions Word Problems Worksheets

Conjure up a picture of how adding fractions plays a significant role in our day-to-day lives with the help of the real-life scenarios and circumstances presented as word problems here.

(15 Worksheets)

Subtracting Fractions Word Problems Worksheets

Subtracting Fractions Word Problems Worksheets

Crank up your skills with this set of printable worksheets on subtracting fractions word problems presenting real-world situations that involve fraction subtraction!

Multiplying Fractions Word Problems Worksheets

Multiplying Fractions Word Problems Worksheets

This set of printables is for the ardently active children! Explore the application of fraction multiplication and mixed-number multiplication in the real world with this exhilarating practice set.

Fraction Division Word Problems Worksheets

Fraction Division Word Problems Worksheets

Gift children a broad view of the real-life application of dividing fractions! Let them divide fractions by whole numbers, divide 2 fractions, divide mixed numbers, and solve the word problems here.

Related Worksheets

» Decimal Word Problems

» Ratio Word Problems

» Division Word Problems

» Math Word Problems

Become a Member

Membership Information

Privacy Policy

What's New?

Printing Help

Testimonial

Facebook

Copyright © 2024 - Math Worksheets 4 Kids

This is a members-only feature!

Happy Learning!

Corbettmaths

Adding Fractions Practice Questions

Click here for questions, click here for answers.

Addition, Adding

GCSE Revision Cards

adding and subtracting fractions problem solving questions

5-a-day Workbooks

adding and subtracting fractions problem solving questions

Primary Study Cards

adding and subtracting fractions problem solving questions

Privacy Policy

Terms and Conditions

Corbettmaths © 2012 – 2024

Fraction Worksheets

Conversion :: Addition :: Subtraction :: Multiplication :: Division

Conversions

Fractions - addition, fractions - subtraction, fractions - multiplication, fractions - division.

  • International
  • Schools directory
  • Resources Jobs Schools directory News Search

Adding and Subtracting Fraction Word Problems

Adding and Subtracting Fraction Word Problems

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

evh4

Last updated

16 June 2015

  • Share through email
  • Share through twitter
  • Share through linkedin
  • Share through facebook
  • Share through pinterest

docx, 18.11 KB

Creative Commons "Sharealike"

Your rating is required to reflect your happiness.

It's good to leave some feedback.

Something went wrong, please try again later.

Perfect for my year 7. Thank you for sharing.

Empty reply does not make any sense for the end user

excellent - just what I was looking for

roger_matthews

Helpful sheet for practicing wordy fraction questions. Answers can sometimes be simplified further.

Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch.

Not quite what you were looking for? Search by keyword to find the right resource:

Word Problems - Fraction Addition (same denominators)

Word Problems - Fraction Addition (same denominators) pic

Description:  This packet helps students practice doing word problems using addition of fractions with like denominators. Each page has a speed and accuracy guide, to help students see how fast and how accurately they should be doing these problems. After doing all 23 problems, students should be more comfortable doing these problems and have a clear understanding of how to solve them. 

Adam and Julie ordered a large pizza that was sliced into 8 pieces. Adam ate $\dfrac{2}{8}$ of the pizza. Julie ate $\dfrac{3}{8}$. How much pizza did they eat altogether? 

Practice problems require knowledge of how to add and subtract whole numbers.

adding and subtracting fractions problem solving questions

Ed Boost  - 3300 Overland Avenue, #202, Los Angeles, CA 90034 - Phone: 310.559.1991 - Fax: 323.345.6473 - edboost at edboost dot org

Smarter Kids, Better world

Copyright© 2024,

[FREE] Fun Math Games & Activities Packs

Always on the lookout for fun math games and activities in the classroom? Try our ready-to-go printable packs for students to complete independently or with a partner!

In order to access this I need to be confident with:

Addition and subtraction

Prime and composite numbers

Fractions operations

Here you will learn about fractions operations, including how to add, subtract, multiply and divide with fractions.

Students will first learn about fractions operations as part of number and operations in fractions in elementary school. They will continue to build on this knowledge in the number system in 6th grade and 7th grade.

What are fractions operations?

Fractions operations are when you add, subtract, multiply or divide with fractions.

For example,

Fractions Operations opening image

Adding and subtracting fractions

Adding and subtracting fractions means finding the sum or the difference of two or more fractions.

In order to do this, the fractions must have a common denominator (bottom number).

The numerator shows the number of parts out of the whole and the denominator shows how many equal parts the whole is divided into.

To add or subtract the numerators (top numbers) and keep the denominators the same.

Fractions Operations image 1

The equation is taking \, \cfrac{1}{8} \, away from \, \cfrac{4}{8} \, .

Since the denominators are the same, the parts are the same size.

You subtract to see how many parts are left: 4-1 = 3.

Fractions Operations image 2

There are 3 parts and the size is still eighths, so the denominator stays the same.

Fractions Operations image 3

When fractions have unlike denominators, create equivalent fractions with common denominators to solve.

Fractions Operations image 4

The parts are NOT the same size, since the denominators are different.

Use equivalent fractions to create a common denominator of 10.

Multiply the numerator and denominator of \, \cfrac{2}{5} \, by 2.

\cfrac{2 \, \times \, 2}{5 \, \times \, 2}=\cfrac{4}{10}

Fractions Operations image 5

Add to find how many parts there are in all: 2 + 4 = 6.

There are 6 parts and the size is still tenths, so the denominator stays the same.

Fractions Operations image 6

The sum could also be written as the equivalent fraction \, \cfrac{3}{5} \, .

Step-by-step guide: Adding fractions

Step-by-step guide: Subtracting fractions

Step-by-step guide: Adding and subtracting fractions

Multiplying and dividing fractions

Multiplying and dividing fractions means using multiplication and division to calculate with fractions. Fraction multiplication and division can be solved using models or an algorithm.

Fractions Operations image 7

Using models:

Fractions Operations image 8

In the model, \, \cfrac{2}{3} \, is yellow and \, \cfrac{1}{2} \, is blue.

The product is where the fractions overlap in green.

The model shows \, \cfrac{2}{3} \, of \, \cfrac{1}{2}, \, so \, \cfrac{1}{2} \times \cfrac{2}{3} = \cfrac{2}{6} \, .

Using the algorithm:

To multiply fractions , you multiply the numerators together, and multiply the denominators together:

\cfrac{1}{2} \, \times \, \cfrac{2}{3}=\cfrac{2}{6} \, .

You can also divide fractions with a model or an algorithm.

Fractions Operations image 9

Think of this equation as how many \, \cfrac{1}{4} \, fit into \, \cfrac{1}{2} \, .

In the model, \, \cfrac{1}{2} \, is orange and \, \cfrac{1}{4} \, is yellow.

To divide into equal groups, use the equivalent fraction \, \cfrac{2}{4} \, .

The quotient is the final fraction formed when \, \cfrac{2}{4} \, is put into a group of \, \cfrac{1}{4} \, .

Fractions Operations image 10

Two groups of \cfrac{1}{4} can be made, so \cfrac{1}{2} \div \cfrac{1}{4}=2.

KEEP the first fraction, FLIP the second fraction, CHANGE to multiplication.

\cfrac{1}{2} \div \cfrac{1}{4}

Keep the dividend (first fraction): \, \cfrac{1}{2}

Take the reciprocal of the divisor (flip the second fraction): \, \cfrac{1}{4} \rightarrow \cfrac{4}{1}

Change to multiplication: \, \cfrac{1}{2} \times \cfrac{4}{1}

Multiply the fractions: \, \cfrac{1}{2} \times \cfrac{4}{1}=\cfrac{4}{2} \, which simplifies to 2.

\cfrac{1}{2} \div \cfrac{1}{4}=2

Since \, \cfrac{1}{2} \, is larger than \, \cfrac{1}{4} \, , the answer makes sense.

A larger number divided by a smaller number, will have a quotient of greater than 1.

Notice that it is not necessary to create a common denominator to multiply and divide fractions when using the algorithm, like it is to add and subtract fractions.

Step-by-step guide: Multiplying fractions

Step-by-step guide: Dividing fractions

Step-by-step guide: Multiplying and dividing fractions

The algorithm for dividing fractions involves using the reciprocal .

When two numbers are multiplied by something other than 1, and have a product of 1, they are reciprocals.

This is also known as the multiplicative inverse.

Fractions Operations image 11.1

The reciprocal of all numbers can be found by writing the number as a fraction and then flipping it so that the numerator becomes the denominator and the denominator becomes the numerator.

Step-by-step guide: Reciprocal

Step-by-step guide: Multiplicative inverse

What are fractions operations?

Common Core State Standards

How does this relate to 4th grade math, 5th grade math, 6th grade math, and 7th grade math?

  • Grade 4 – Number and Operations – Fractions (4.NF.B.3a) Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
  • Grade 4 – Number and Operations – Fractions (4.NF.B.3c) Add and subtract mixed numbers with like denominators, for example, by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
  • Grade 4 – Number and Operations – Fractions (4.NF.B.4b) ​​Understand a multiple of \, \cfrac{a}{b} \, as a multiple of \, \cfrac{1}{b} \, , and use this understanding to multiply a fraction by a whole number.
  • Grade 5 – Number and Operations – Fractions (5.NF.A.1) Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, \, \cfrac{2}{3} + \cfrac{5}{4} = \cfrac{8}{12} + \cfrac{15}{12} = \cfrac{23}{12} \, . \; ( In general, \, \cfrac{a}{b} + \cfrac{c}{d} = \cfrac{(ad \, + \, bc)}{bd} \, . )
  • Grade 5 – Number and Operations – Fractions (5.NF.B.4b) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
  • Grade 6 – Number System (6.NS.A.1) Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

[FREE] Fraction Operations Check for Understanding Quiz (Grade 4 to 6)

[FREE] Fraction Operations Check for Understanding Quiz (Grade 4 to 6)

Use this quiz to check your grade 4 to 6 students’ understanding of fraction operations. 10+ questions with answers covering a range of 4th to 6th grade fraction operations topics to identify areas of strength and support!

How to use fractions operations

There are a lot of ways to use fractions operations. For more specific step-by-step guides, check out the fraction pages linked in the “What are fractions operations?” section above or read through the examples below.

Fractions operations examples

Example 1: adding fractions with like denominators.

Solve \, \cfrac{5}{8}+\cfrac{7}{8} \, .

Add or subtract the numerators (top numbers).

Fractions Operations example 1 image 1

Since the denominators are the same, the parts are the same size. You add to see how many parts there are in total: 5 + 7 = 12.

2 Write your answer as a fraction.

There are 12 parts, and the size is still eighths, so the denominator stays the same.

Fractions Operations example 1 image 2

\cfrac{12}{8} \, is an improper fraction and converts to the mixed number 1 \, \cfrac{4}{8} \, .

\cfrac{5}{8}+\cfrac{7}{8}=1 \cfrac{4}{8}

You can also write this answer as the equivalent mixed number \, 1 \cfrac{1}{2} \, .

Example 2: subtracting fractions with unlike denominators

Solve \cfrac{6}{10}-\cfrac{1}{3} \, .

Create common denominators (bottom numbers).

Since \, \cfrac{6}{10} \, and \, \cfrac{1}{3} \, do not have like denominators, the parts are NOT the same size.

Multiply the numerator and denominator by the opposite denominator to create equivalent fractions with common denominators.

\cfrac{6 \, \times \, 3}{10 \, \times \, 3}=\cfrac{18}{30} \quad and \quad \cfrac{1 \, \times \, 10}{3 \, \times \, 10}=\cfrac{10}{30}

Now use the equivalent fractions to solve: \, \cfrac{18}{30}-\cfrac{10}{30} \, .

Since the denominators are the same, the parts are the same size. You subtract to see how many parts are left: 18-10 = 8.

Fractions Operations example 2

Write your answer as a fraction.

There are 8 parts and the size is still thirtieths, so the denominator stays the same.

\cfrac{18}{30}-\cfrac{10}{30}=\cfrac{8}{30}

You can also write this answer as the equivalent fraction \, \cfrac{4}{15} \, .

Example 3: multiplying a mixed number by a fraction with the algorithm

Solve 1 \, \cfrac{11}{12} \times \cfrac{3}{4} \, .

Convert whole numbers and mixed numbers to improper fractions.

Convert the mixed number to an improper fraction.

Fractions Operations example 3

Multiply the numerators together.

\cfrac{23}{12} \times \cfrac{3}{4}=\cfrac{69}{}

Multiply the denominators together.

\cfrac{23}{12} \times \cfrac{3}{4}=\cfrac{69}{48}

If possible, simplify or convert to a mixed number.

The numerator is greater than the denominator, so the improper fraction can be converted to a mixed number.

\cfrac{69}{48}=1 \, \cfrac{21}{48}

The product can be simplified. 21 and 48 have a common factor of 3.

\cfrac{21 \, \div \, 3}{48 \, \div \, 3}=\cfrac{7}{16}

So, \, \cfrac{23}{12} \times \cfrac{3}{4}=\cfrac{69}{48} \, or 1 \, \cfrac{7}{16} \, .

Example 4: dividing a fraction by a fraction

Divide the numbers \, \cfrac{1}{12} \div \cfrac{1}{4} \, .

Take the reciprocal (flip) of the divisor (second fraction).

\cfrac{1}{4} \, → \, \cfrac{4}{1}

Change the division sign to a multiplication sign.

\cfrac{1}{12} \, \times \, \cfrac{4}{1}

Multiply the fractions together.

\cfrac{1}{12} \, \times \, \cfrac{4}{1}=\cfrac{4}{12}

\cfrac{4}{12}=\cfrac{1}{3}

This can also be solved with a model.

You can think of this equation as how many \, \cfrac{1}{4} \, fit into \, \cfrac{1}{12} \, .

In the model, \, \cfrac{1}{12} \, is yellow and \, \cfrac{1}{4} \, is orange.

To divide into equal groups, the fractional pieces need to be the same size.

Use \, \cfrac{1}{12} \, and \, \cfrac{3}{12} \, to solve.

The quotient is the final fraction formed when \, \cfrac{1}{12} \, is put into groups of \, \cfrac{3}{12} \, .

Fractions Operations example 4

One out of the three parts are filled, so \, \cfrac{1}{12} \div \cfrac{3}{12}=\cfrac{1}{3} \, .

Example 5: adding mixed numbers with unlike denominators

There are 2 \, \cfrac{1}{3} \, pounds of red apples and 4 \, \cfrac{1}{6} \, pounds of green apples.

How many pounds of apples are there in all?

Create an equation to model the problem.

2 \cfrac{1}{3}+4 \cfrac{1}{6}= \, ?

Add or subtract the whole numbers.

Fractions Operations example 5 image 1

Since \, \cfrac{1}{3} \, and \, \cfrac{1}{6} \, do not have like denominators, the parts are NOT the same size.

Use equivalent fractions to create a common denominator.

A common denominator of 6 can be used.

Multiply the numerator and denominator of \, \cfrac{1}{3} \, by 2 to create an equivalent fraction.

\cfrac{1}{3}=\cfrac{1 \, \times \, 2}{3 \, \times \, 2}=\cfrac{2}{6} \quad and \quad \cfrac{1}{6}

Add or subtract the fractions.

Since the denominators are the same, the parts are the same size. You add to see how many parts there are in total: 2 + 1 = 3.

Fractions Operations example 5 image 3

There are 3 parts, and the size is still sixths, so the denominator stays the same.

Fractions Operations example 5 image 4

Write your answer as a mixed number.

Add the whole number and fraction together.

Fractions Operations example 5 image 5

You can also write this answer as the equivalent mixed number 6 \, \cfrac{1}{2} \, .

There are 6 \, \cfrac{1}{2} \, pounds of apples in all.

Example 6: word problem dividing with fractions

Each seed needs \, \cfrac{1}{5} \, cup of soil. How many seeds can be planted with 11 cups of soil?

11 \div \cfrac{1}{5}= \, ?

Change any mixed numbers to an improper fraction.

Change 11 to an improper fraction.

11=\cfrac{11}{1}

Take the reciprocal (flip) of the divisor (second fractions).

\cfrac{1}{5} \, → \, \cfrac{5}{1}

\cfrac{11}{1} \times \cfrac{5}{1}

\cfrac{11}{1} \times \cfrac{5}{1}=\cfrac{55}{1}

If possible, simplify or convert to a mixed number (mixed fraction).

\cfrac{55}{1}=55

55 seeds can be planted with 11 cups of soil.

Teaching tips for fractions operations

  • Fraction work in lower grades emphasizes understanding through models, including area models and number lines. To support students in upper grades, always have digital or physical models available for students to use as they work with fractions operations.
  • Fraction worksheets can be useful when students are developing understanding around basic operations with fractions. However, when students have successful strategies and can flexibly operate, make the practice more engaging by using math games or real world projects that allow students to use fractions in a variety of situations.
  • Highlight patterns within and between the operations as students are learning and encourage them to look for patterns on their own. This will help students make sense of the algorithms used to operate with fractions and minimize conceptual errors.
  • Let students find reciprocal numbers on their own by consistently asking questions such as, “What number multiplied by 7 will have a product of 1 ?” Each time this is discussed, write these equations on an anchor chart and students will begin to see a pattern over time. Although worksheets can serve a purpose and help with skill and test prep practice, having students discover and make sense of mathematical concepts is more meaningful for building long lasting understanding.

Easy mistakes to make

Fractions Operations image 12

  • Forgetting how to find the reciprocal of a whole number Whole numbers can be written as an improper fraction and then the numerator and denominator of the improper fraction can be flipped to find the reciprocal of the whole number. For example, 16 can be written as \, \cfrac{16}{1} \, and the reciprocal is \, \cfrac{1}{16} \, .

Practice fractions operations questions

1. Solve \, \cfrac{5}{9}+\cfrac{2}{9} \, .

GCSE Quiz False

Since the denominators are the same, the parts are the same size. You add to see how many parts there are in total: 5 + 2 = 7.

There are 7 parts and the size is still ninths, so the denominator stays the same.

Fractions Operations practice question 1 image 2

\cfrac{5}{9}+\cfrac{2}{9}=\cfrac{7}{9}

2. Solve \, 2 \, \cfrac{3}{10}-1 \, \cfrac{4}{5} \, .

The equation is taking \, 1 \cfrac{4}{5} \, away from \, 2 \cfrac{3}{10} \, .

Start with the fractions. Since \, \cfrac{3}{10} \, and \, \cfrac{4}{5} \, do not have like denominators, the parts are NOT the same size.

Use equivalent fractions to create a common denominator. Both denominators are multiples of 10.

\cfrac{3}{10} \quad and \quad \cfrac{4 \, \times \, 2}{5 \, \times \, 2}=\cfrac{8}{10}

Now use the equivalent fraction to solve: 2 \, \cfrac{3}{10}-1 \, \cfrac{8}{10}

However, there are not enough parts to take 8 away from 3.

You can break one of the wholes into \cfrac{10}{10} \, …

Fractions Operations practice question 2 image 1

Now you can solve 1 \, \cfrac{13}{10}-1 \, \cfrac{8}{10}.

You subtract to see how many parts are left: 13-8 = 5.

Fractions Operations practice question 2 image 2

There are 5 parts and the size is still tenths, so the denominator stays the same.

Fractions Operations practice question 2 image 3

\cfrac{13}{10}-\cfrac{8}{10}=\cfrac{5}{10}

Subtract the whole numbers.

Fractions Operations practice question 2 image 4

1 \, \cfrac{13}{10}-1 \, \cfrac{8}{10}=\cfrac{5}{10}

You can also write this answer as the equivalent fraction \, \cfrac{1}{2} \, .

3. Solve \, \cfrac{1}{4} \times \cfrac{2}{5} \, .

To solve using a model, draw a rectangle. Divide one side into fourths.

Fractions Operations practice question 3 image 1

Divide the other side into fifths.

Fractions Operations practice question 3 image 2

Shade in \, \cfrac{1}{4} \, with yellow and \, \cfrac{2}{5} with blue.

Fractions Operations practice question 3 image 3

The model shows \, \cfrac{2}{5} \, of \, \cfrac{1}{4} \, , so \, \cfrac{1}{4} \times \cfrac{2}{5}=\cfrac{2}{20} \, , because there are 2 green squares and the whole has 20 squares in total.

The product can be simplified. Both 2 and 20 have a factor of 2, so they can be divided by 2 :

\, \cfrac{2 \, \div \, 2}{20 \, \div \, 2}=\cfrac{1}{10} \, .

So, \, \cfrac{1}{4} \times \cfrac{2}{5}=\cfrac{2}{20} \; or \; \cfrac{1}{10}

4. Solve \, 2 \, \cfrac{1}{6} \div 1 \, \cfrac{2}{3} \, . Write the quotient in lowest terms.

Change the mixed numbers to improper fractions:

Fractions Operations practice question 4

Keep the dividend (first fraction): \, \cfrac{13}{6}

Take the reciprocal of the divisor (flip the second fraction): \, \cfrac{5}{3} → \cfrac{3}{5}

Change to multiplication: \, \cfrac{13}{6} \times \cfrac{3}{5}

Multiply the fractions: \, \cfrac{13}{6} \times \cfrac{3}{5}=\cfrac{39}{30}

Change back into a mixed number: \, \cfrac{39}{30}=1 \, \cfrac{9}{30}

Simplify: \, \cfrac{9 \, \div \, 3}{30 \, \div \, 3}=\cfrac{3}{10} \, , so the answer in lowest terms is \, 1 \, \cfrac{3}{10} \, .

5. Rashad is cutting a 12 \, ft rope into smaller \, \cfrac{2}{3} \, ft pieces. How many smaller pieces of rope will he have?

8 smaller pieces of rope

12 smaller pieces of rope

18 smaller pieces of rope

\cfrac{24}{3} smaller pieces of rope

Use the equation \, 12 \div \cfrac{2}{3}= \, ?

Draw 12 wholes and break them up into thirds.

Fractions Operations practice question 5 image 1

Create groups of \, \cfrac{2}{3} \, .

Fractions Operations practice question 5 image 2

There are 18 groups of \, \cfrac{2}{3} \, .

Rashad will have 18 pieces of smaller rope.

6. A recipe calls for 3 \, \cfrac{1}{4} \, cups of strawberries. If Tyler has 5 \, \cfrac{5}{8} \, cups of strawberries, how many will he have left after he makes 1 recipe?

2 \, \cfrac{3}{8} cups

2 \, \cfrac{4}{4} cups

8 \, \cfrac{7}{8} cups

8 \, \cfrac{6}{12} cups

Use the equation 5 \cfrac{5}{8}-3 \cfrac{1}{4}= \, ?

Start with the fraction.

Since \, \cfrac{5}{8} \, and \, \cfrac{1}{4} \, do not have like denominators, the parts are NOT the same size.

A common denominator of 8 can be used.

Multiply the numerator and denominator of \, \cfrac{1}{4} \, by 2 to create an equivalent fraction.

\cfrac{5}{8} \quad and \quad \cfrac{1}{4}=\cfrac{1 \, \times \, 2}{4 \, \times \, 2}=\cfrac{2}{8}

You subtract to see how many parts there are in total: 5-2 = 3.

Fractions Operations explanation image 1

There are 2 parts and the size is still eighths, so the denominator stays the same.

Fractions Operations explanation image 2

There will be \, 2 \cfrac{3}{8} \, cups of strawberries left.

Fractions operations FAQs

No, although using these operations will create different denominators and numerators, as long as they are multiplied or divided by the same thing, the value of the fraction will remain the same.

No, unless the question specifies the lowest terms, it is valid to answer without using the least common denominator (LCD). However, as students progress in their understanding of fractions, it is a good idea to encourage them to practice this skill. Also be mindful of standard expectations, as they may vary from state to state.

Yes, just like any other type of number, to solve multistep problems correctly, the order of operations must be followed.

The multiplicative inverse of a number is the reciprocal. For any integer, that is the number written as the numerator over a denominator of 1. For any rational number, that is switching the numerator and denominator.

The next lessons are

  • Algebraic expression
  • Converting fractions decimals and percents
  • Interpret a fraction as division
  • Multiplicative inverse and reciprocals
  • Adding and subtracting fraction word problems

Still stuck?

At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.

Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.

One on one math tuition

Find out how we can help your students achieve success with our math tutoring programs .

[FREE] Common Core Practice Tests (Grades 3 to 6)

Prepare for math tests in your state with these Grade 3 to Grade 6 practice assessments for Common Core and state equivalents.

40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!

Privacy Overview

SplashLearn

Addition and Subtraction of Fraction: Methods, Examples, Facts, FAQs

What is addition and subtraction of fractions, methods of addition and subtraction of fractions, addition and subtraction of mixed numbers, solved examples on addition and subtraction of fractions, practice problems on addition and subtraction of fractions, frequently asked questions on addition and subtraction of fractions.

Addition and subtraction of fractions are the fundamental operations on fractions that can be studied easily using two cases:

  • Addition and subtraction of like fractions (fractions with same denominators)
  • Addition and subtraction of unlike fractions (fractions with different denominators)

A fraction represents parts of a whole. For example, the fraction 37 represents 3 parts out of 7 equal parts of a whole. Here, 3 is the numerator and it represents the number of parts taken. 7 is the denominator and it represents the total number of parts of the whole.

Adding and subtracting fractions is simple and straightforward when it comes to like fractions. In the case of unlike fractions, we first need to make the denominators the same. Let’s take a closer look at both these cases.

Related Games

Add Decimal Fractions Using Equivalence Game

Before adding and subtracting fractions, we first need to make sure that the fractions have the same denominators. 

When the denominators are the same, we simply add the numerators and keep the denominator as it is. To add or subtract unlike fractions, we first need to learn how to make the denominators alike. Let’s learn how to add fractions and how to subtract fractions in both cases.

Related Worksheets

1 and 2 more within 10: Horizontal Addition Worksheet

Addition and Subtraction of Like Fractions

The rules for adding fractions with the same denominator are really simple and straightforward. 

Let’s learn with the help of examples and visual bar models.

Addition of Like Fractions

Here are the steps to add fractions with the same denominator:

Step 1: Add the numerators of the given fractions. 

Step 2: Keep the denominator the same. 

Step 3: Simplify.          

$\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$  …$c \neq 0$

Example 1: Find $\frac{1}{4} + \frac{2}{4}$ .

$\frac{1}{4} + \frac{2}{4} = \frac{1 + 2}{4} = \frac{3}{4}$

We can visualize this addition using a bar model:

Visual representation of the fractions

Example 2: $\frac{1}{8} + \frac{3}{8} = \frac{1 + 3}{8} = \frac{4}{8} = \frac{1}{2}$

Visual model of addition of like fractions

Subtraction of Like Fractions

Here are the steps to subtract fractions with the same denominator:

Step 1: Subtract the numerators of the given fractions. 

Step 3: Simplify. 

$\frac{a}{c}\;-\;\frac{b}{c} = \frac{a \;-\; b}{c}$ …$c \neq 0$

Example 1: Find $\frac{4}{6} \;-\; \frac{1}{6}$.

$\frac{4}{6}\;-\;\frac{1}{6} = \frac{4-1}{6} = \frac{3}{6} = \frac{1}{2}$

Subtracting fractions with the same denominators

Addition and Subtraction of Unlike Fractions

Addition and subtraction of fractions with unlike denominators can be a little bit tricky since the denominators are not the same. So, we need to first convert the unlike fractions into like fractions. Let’s look at a few ways to do this!

Addition of Unlike Fractions

We can make the denominators the same by finding the LCM of the two denominators. Once we calculate the LCM, we multiply both the numerator and the denominator with an appropriate number so that we get the LCM value in the denominator. 

Example: $\frac{3}{5} + \frac{3}{2}$

Step 1: Find the LCM (Least Common Multiple) of the two denominators.

The LCM of 5 and 2 is 10.

Step 2: Convert both the fractions into like fractions by making the denominators same.  

$\frac{3 \times 2}{5 \times 2} = \frac{6}{10}$  

$\frac{3 \times 5}{2 \times 5} = \frac{15}{10}$

Step 3: Add the numerators. The denominator stays the same.

$\frac{6}{10} + \frac{15}{10} = \frac{21}{10}$

Step 4: Convert the resultant fraction to its simplest form if the GCF of the numerator and denominator is not 1. 

In this case, GCF (21,10) $= 1$

The fraction $\frac{21}{10}$ is already in its simplest form. 

Thus, $\frac{3}{5} + \frac{3}{2} = \frac{21}{10}$

Subtraction of Unlike Fractions

Let’s learn how to subtract fractions when denominators are not the same. To subtract unlike fractions, we use the LCM method. The process is similar to what we discussed in the previous example.

Example: $\frac{5}{6} \;-\; \frac{2}{9}$

Step 1: Find the LCM of the two denominators.

LCM of 6 and $9 = 18$

Step 2: Convert both the fractions into like fractions by making the denominators same.

$\frac{5 \times 3}{6 \times 3} = \frac{15}{18}$   

$\frac{2 \times 2}{9 \times 2} = \frac{4}{18}$

Step 3: Subtract the numerators. The denominator stays the same.

$\frac{15}{18} \;-\; \frac{4}{18} = \frac{11}{18}$

In this case, the GCF (11,18) $= 1$

So, it is already in its simplest form. 

Thus, $\frac{5}{6}\;-\; 29 = \frac{11}{18}$

A mixed number is a type of fraction that has two parts: a whole number and a proper fraction. It is also known as a mixed fraction. Any mixed number can be written in the form of an improper fraction and vice-versa. 

Adding and subtracting mixed fractions is done by converting mixed numbers into improper fractions .

Addition and Subtraction of Mixed Fractions with Same Denominators

The steps of adding and subtracting mixed numbers with the same denominators are the same. The only difference is the operation.

Step 1: Convert the given mixed fractions to improper fractions.

Step 2: Add/Subtract the like fractions obtained in step 1.

Step 3: Reduce the fraction to its simplest form.

Step 4: Convert the resulting fraction into a mixed number.

Example 1: $2\frac{1}{5} + 1\frac{3}{5}$

$2\frac{1}{5} = \frac{(5 \times 2) + 1}{5} = \frac{11}{5}$

$1\frac{3}{5} = \frac{(5 \times 1) + 3}{5} = \frac{8}{5}$

Thus, $2\frac{1}{5} + 1\frac{3}{5} = \frac{11}{5} + \frac{8}{5} = \frac{19}{5}$

Converting $\frac{19}{5}$ into a mixed number, we get

$\frac{19}{5} = 3\frac{4}{5}$

Example 2: $2\frac{1}{5} + 1\frac{3}{5} = \frac{11}{5} \;-\; \frac{8}{5} = \frac{3}{5}$

Addition and Subtraction of Mixed Fractions with Unlike Denominators

Step 2: Convert both the fractions into like fractions by finding the least common denominator.

Step 3: Add the fractions. (or subtract the fractions.)

Step 4: Reduce the fraction if possible or convert back to a mixed number 

Let us understand the addition of mixed numbers with unlike denominators with the help of an example.

Example 1: Find the value of $1\frac{3}{5} + 2\frac{1}{2}$.

Convert the given mixed fractions to improper fractions.

$1\frac{3}{5} = \frac{8}{5}$ and $2\frac{1}{2} = \frac{5}{2}$

Step 2: Convert both the fractions into like fractions by making the denominators the same.

Here, LCM of 5 and 2 is 10.

Thus, $\frac{8 \times 2}{5 \times 2} = \frac{16}{10}$ and $\frac{5\times 5}{2 \times 5} = \frac{25}{10}$

Step 3: Add the fractions by adding the numerators.

$\frac{16}{10} + \frac{25}{10} = \frac{41}{10}$

Step 4: Convert back into a mixed number. 

Thus, $\frac{41}{10}$ will become  $4\frac{1}{10}$

Therefore, $1\frac{3}{5} + 2\frac{1}{2} =  4\frac{1}{10}$

Here’s an example for subtraction. It follows the same steps.

Example 2 : $6\frac{1}{2} \;-\; 1\frac{3}{4}$

Step 1: Convert the mixed numbers into improper fractions.

     $6\frac{1}{2} \;-\; 1\frac{3}{4} = \frac{13}{2} \;-\; \frac{7}{4}$

Step 2: Make the denominators equal.

LCM of 2 and 4 is 4. 

   $\frac{13 \times 2}{2 \times 2} = \frac{26}{4}$ 

Step 3: Subtract the fractions.

        $\frac{26}{4} \;-\;  \frac{7}{4} = \frac{19}{4}$

Step 4: Convert the fraction as a mixed number.

            $\frac{19}{4}  = 4\frac{3}{4}$  

Thus, $6\frac{1}{2} \;-\; 1\frac{3}{4}  =   4\frac{3}{4}$  

Facts about Addition and Subtraction of Fractions

  • We cannot add or subtract fractions without converting them into like fractions.
  • Like fractions are fractions that have the same denominator, and unlike fractions are fractions that have different denominators.
  • Equivalent fractions are two different fractions that represent the same value.
  • The LCD (least common denominator) of two fractions is the LCM of the denominators.

In this article, we have learned about addition and subtraction of fractions (like fractions, unlike fractions, mixed fractions), methods of addition and subtraction of these fractions along with the steps. Let’s solve some examples on adding and subtracting fractions to understand the concept better.

  • Solve: $\frac{2}{4} + \frac{1}{4}$ .

Solution: 

Here, the denominators are the same.

Thus, we add the numerators by keeping the denominators as it is.

$\frac{2}{4} + \frac{1}{4} = \frac{2 + 1}{4}$ 

$\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$

2. Find the sum of the fractions $\frac{3}{5}$ and $\frac{5}{2}$ by using the LCM method.

$\frac{3}{5}$ and $\frac{5}{2}$ are unlike fractions.

The LCM of 2 and 5 is 10.

Thus, we can write

$\frac{3}{5} + \frac{5}{2} = \frac{3 \times 2}{5 \times 2} + \frac{5 \times 5}{2 \times 5}$

$= \frac{6}{10} + \frac{25}{10}$

            $= \frac{6}{10} + \frac{25}{10}$

            $= \frac{31}{10}$

Thus, $\frac{3}{5} + \frac{5}{2} =  \frac{31}{10}$

3. Find $\frac{4}{16} + \frac{5}{8}$.

Solution:  

To add two fractions with different denominators, we first need to find the LCM of the denominators.

The LCM of 16 and 8 is 16.

$\frac{4}{16} + \frac{5}{8} = \frac{4 \times 1}{16\times 1} + \frac{5 \times 2}{8 \times 2}$ 

            $= \frac{10}{16} + \frac{4}{16}$ 

            $= \frac{14}{16}$

$= \frac{7}{8}$

4. From a rope $12\frac{1}{2}$ ft. long, a $7 \frac{6}{8}\;-$ ft-long piece is cut off. Find the length of the remaining rope.

Total length of the rope $= 12\frac{1}{2}$ ft.

Length of the rope that was cut off $= 7 \frac{6}{8}$ ft. 

The length of the remaining rope $= 12\frac{1}{2} \;-\; 7 \frac{6}{8}$

$12\frac{1}{2} \;-\; 7 \frac{6}{8} = \frac{25}{2} \;-\; \frac{62}{8}$

         $= \frac{25 \times 4}{2 \times 4} \;-\; \frac{62 \times 1}{8\times 1}$

         $= \frac{100}{8} \;-\; \frac{62}{8}$

         $= \frac{38}{8}$

         $= \frac{19}{4}$

Converting it into a mixed fraction, $\frac{19}{4}$ becomes $4 \frac{3}{4}$.

Thus, the length of the remaining rope is $4\frac{3}{4}$ ft.

Attend this quiz & Test your knowledge.

Find $\frac{2}{4} + \frac{2}{4}$.

$\frac{7}{24} + \frac{5}{16} =$, what is the least common denominator of $\frac{1}{2}$ and $\frac{1}{3}$, $\frac{3}{6} \;-\; \frac{1}{6} =$, what equation does the following figure represent.

Addition and Subtraction of Fraction: Methods, Examples, Facts, FAQs

How do we add and subtract negative fractions?

Negative fractions are simply fractions with a negative sign. The steps to add and subtract the negative fractions remain the same. We need to follow the rules for addition/subtraction with negative signs.

How can we convert an improper fraction into a mixed number?

To convert an improper fraction into a mixed number, we divide the numerator by the denominator. The denominator stays the same. The quotient represents the whole number part. The remainder represents the numerator of the mixed number.

Example: $\frac{14}{3} = 4\; \text{R}\; 2$

Quotient $= 4$

Remainder $= 2$

$\frac{14}{3} = 4\frac{2}{3}$

How do we divide two fractions?

To divide one fraction by another, we multiply the first fraction by the reciprocal of the second fraction.

$\frac{A}{B} \div \frac{C}{D} = \frac{A}{B} \times \frac{D}{C}$

For example, $\frac{1}{2} \div \frac{3}{5} = \frac{1}{2} \times \frac{5}{3} = \frac{5}{6}$

What are the rules of adding and subtracting fractions?

  • Before adding or subtracting, we check if the fractions have the same denominator.
  • If the denominators are equal, then we add/subtract the numerators keeping the common denominator.
  • If the denominators are different, then we make the denominators equal by using the LCM method. Once the fractions have the same denominator, we can add/subtract the numerators keeping the common denominator as it is.

How do we add and subtract fractions with whole numbers?

  • Convert the whole number to a fraction. To do this, give the whole number a denominator of 1.
  • Convert to fractions of like denominators. 
  • Add/subtract the numerators. Now that the fractions have the same denominators, you can treat the numerators as a normal addition/subtraction problem.

RELATED POSTS

  • Cube Numbers – Definition, Examples, Facts, Practice Problems
  • Volume of Hemisphere: Definition, Formula, Examples
  • CPCTC: Definition, Postulates, Theorem, Proof, Examples
  • Dividend – Definition with Examples
  • Reflexive Property – Definition, Equality, Examples, FAQs

Math & ELA | PreK To Grade 5

Kids see fun., you see real learning outcomes..

Watch your kids fall in love with math & reading through our scientifically designed curriculum.

Parents, try for free Teachers, use for free

Banner Image

Home

Reading & Math for K-5

  • Kindergarten
  • Learning numbers
  • Comparing numbers
  • Place Value
  • Roman numerals
  • Subtraction
  • Multiplication
  • Order of operations
  • Drills & practice
  • Measurement
  • Factoring & prime factors
  • Proportions
  • Shape & geometry
  • Data & graphing
  • Word problems
  • Children's stories
  • Leveled Stories
  • Context clues
  • Cause & effect
  • Compare & contrast
  • Fact vs. fiction
  • Fact vs. opinion
  • Main idea & details
  • Story elements
  • Conclusions & inferences
  • Sounds & phonics
  • Words & vocabulary
  • Reading comprehension
  • Early writing
  • Numbers & counting
  • Simple math
  • Social skills
  • Other activities
  • Dolch sight words
  • Fry sight words
  • Multiple meaning words
  • Prefixes & suffixes
  • Vocabulary cards
  • Other parts of speech
  • Punctuation
  • Capitalization
  • Cursive alphabet
  • Cursive letters
  • Cursive letter joins
  • Cursive words
  • Cursive sentences
  • Cursive passages
  • Grammar & Writing

Breadcrumbs

  • Word Problems
  • Addition & subtraction of fractions

Introduction to Fractions Workbook

Download & Print Only $5.90

Adding & subtracting fractions word problems

Word problem worksheets: addition & subtraction of fractions.

Below are three versions of our grade 4 math worksheet on adding and subtracting fractions and mixed numbers.  All fractions have like denominators.  Some problems will include irrelevant data so that students have to read and understand the questions, rather than simply recognizing a pattern to the solutions.  These worksheets are pdf files .

adding and subtracting fractions problem solving questions

These worksheets are available to members only.

Join K5 to save time, skip ads and access more content. Learn More

More word problem worksheets

Explore all of our math word problem worksheets , from kindergarten through grade 5.

What is K5?

K5 Learning offers free worksheets , flashcards  and inexpensive  workbooks  for kids in kindergarten to grade 5. Become a member  to access additional content and skip ads.

Our members helped us give away millions of worksheets last year.

We provide free educational materials to parents and teachers in over 100 countries. If you can, please consider purchasing a membership ($24/year) to support our efforts.

Members skip ads and access exclusive features.

Learn about member benefits

This content is available to members only.

  • Forgot Password?

Addition and Subtraction of Fractions

While adding and subtracting fractions , we need to check whether the fractions have the same denominators or different denominators and then the calculation starts. Let us learn more about the addition and subtraction of fractions in this article.

How to Add and Subtract Fractions?

Addition and subtraction of fractions is done using similar rules in which the denominators are checked before the addition or subtraction starts. After the denominators are checked, we can add or subtract the given fractions accordingly. The denominators are checked in the following way.

  • If the denominators of the given fractions are the same, we add or subtract only the numerators and we retain the denominator.
  • If the denominators are different, we convert the fractions to like fractions so that the denominators become the same, and then we add or subtract, whatever is required.

Let us learn about these in the following sections.

Adding and Subtracting Fractions with Like Denominators

The process for adding and subtracting fractions with like denominators is quite simple because we just need to work with the numerators.

Adding Fractions with Like Denominators

Let us add the fractions 1/5 and 2/5 using rectangular models. In this case, both the fractions have the same denominators. These fractions are called like fractions . The following figure represents both the fractions in the same model.

  • 1/5 indicates that 1 out of 5 parts are shaded yellow.
  • 2/5 indicates that 2 out of 5 parts are shaded blue.

Adding Fractions with like Denominators - Addition and subtraction of fractions

Out of the 5 parts, 3 parts are shaded. In the fractional form, this can be represented as 3/5.

Now, let us add the fractions with like denominators in numerical terms. In this case, we need to add 1/5 + 2/5. Let us use the following steps to understand the addition.

  • Step 1: Add the numerators of the given fractions. Here, the numerators are 1 and 2, so it will be 1 + 2 = 3
  • Step 2: Retain the same denominator. Here, the denominator is 5.
  • Step 3: Therefore, the sum of 1/5 + 2/5 = (1 + 2)/5 = 3/5

It should be noted that we use the same method for subtracting fractions.

Subtracting Fractions with Like Denominators

Let us subtract the fractions 2/5 and 1/5 using rectangular models. We will represent 2/5 in this model by shading 2 out of 5 parts. We will further shade out 1 part from our shaded parts of the model which would represent removing 1/5.

Subtracting Fractions with Same Denominators - Addition and subtraction of fractions

We are now left with 1 part in the shaded parts of the model.

Now, let us subtract the fractions with like denominators in numerical terms. In this case, we need to subtract 2/5 - 1/5. Let us understand the procedure using the following steps.

  • Step 1: We will subtract the numerators of the given fractions. Here, the numerators are 2 and 1, so it will be 2 - 1 = 1
  • Step 3: Therefore, the difference of 2/5 - 1/5 = (2 - 1)/5 = 1/5

Adding and Subtracting Fractions with Unlike Denominators

For adding and subtracting fractions with unlike denominators, we need to convert the unlike fractions to like fractions by writing their equivalent fractions in such a way that their denominators become the same. Let us understand this with the help of an example.

Example: Add 1/5 + 1/3

Solution: For adding unlike fractions we need to use the following steps

  • Step 1: Find the Least Common Multiple (LCM) of the denominators. Here, the LCM of 5 and 3 is 15.
  • Step 2: Convert the given fractions to like fractions by writing the equivalent fractions for the respective fractions such that their denominators remain the same. Here, it will be \(\frac {1}{5}\)×\(\frac {3}{3}\)=\(\frac {3}{15}\)
  • Step 3: Similarly, an equivalent fraction of 1/3 with denominator 15 is \(\frac {1}{3}\)×\(\frac {5}{5}\)=\(\frac {5}{15}\)
  • Step 4: Now, that we have converted the given fractions to like fractions we can add the numerators and retain the same denominator. This will be 3/15 + 5/15 = 8/15
  • Subtracting Fractions with Unlike Denominators

For subtracting unlike fractions, we follow the same steps as we did for the addition of unlike fractions. Let us understand this with the help of an example.

Example: Subtract 5/6 - 1/3

Solution: For subtracting unlike fractions we need to use the following steps.

  • Step 1: Find the Least Common Multiple (LCM) of the denominators. Here, the LCM of 6 and 3 is 6.
  • Step 2: Convert the given fractions to like fractions by writing the equivalent fractions for the respective fractions such that their denominators remain the same. Here, it will be \(\frac {5}{6}\)×\(\frac {1}{1}\)=\(\frac {5}{6}\)
  • Step 3: Similarly, an equivalent fraction of 1/3 with denominator 6 is \(\frac {1}{3}\)×\(\frac {2}{2}\)=\(\frac {2}{6}\)
  • Step 4: Now, that we have converted the given fractions to like fractions we can subtract the numerators and retain the same denominator. This will be 5/6 - 2/6 = 3/6. This can be further reduced to 1/2

Adding and Subtracting Mixed Fractions

Adding and subtracting mixed fractions is done by converting the mixed fractions to improper fractions and then the addition or subtraction is done as per the requirement. Let us understand these with the help of the following examples.

Example: Add the mixed fractions: \(2\dfrac{1}{4}\) + \(1\dfrac{3}{4}\)

Solution: First let us convert the mixed fractions to improper fractions.

  • Step 1: Convert the given mixed fractions to improper fractions. So, \(2\dfrac{1}{4}\) will become 9/4; and \(1\dfrac{3}{4}\) will become 7/4
  • Step 2 : Add the fractions by adding the numerators because the denominators are the same. This will be 9/4 + 7/4= 16/4.
  • Step 3: Reduce the fraction, if required. This will become, 16/4 = 4. Therefore, \(2\dfrac{1}{4}\) + \(1\dfrac{3}{4}\) = 4.

Now, let us understand the subtraction of mixed fractions using the same method.

Example: Subtract the mixed fractions: \(5\dfrac{1}{3}\) - \(2\dfrac{1}{3}\)

  • Step 1: Convert the given mixed fractions to improper fractions. So, \(5\dfrac{1}{3}\) will become 16/3; and \(2\dfrac{1}{3}\) will become 7/3
  • Step 2 : Subtract the fractions by subtracting the numerators because the denominators are the same. This will be 16/3 - 7/3 = 9/3
  • Step 3: Reduce the fraction, if required. This will become, 9/3 = 3. Therefore, \(5\dfrac{1}{3}\) - \(2\dfrac{1}{3}\) = 3

Adding and Subtracting Fractions with Whole Numbers

Adding and subtracting fractions with whole numbers can be done using the following method. Let us understand this using an example.

Example: Add 7/4 + 5

Solution: Let us add 7/4 + 5 using the following steps.

  • Step 1: Write the whole number in the form of a fraction. In this case the whole number is 5 which can be written as 5/1. So, now we need to add 7/4 + 5/1
  • Step 2: Now, find the LCM of the denominators and convert the given fractions to like fractions. Here the LCM of 4 and 1 is 4. And after converting them to like fractions we get, (7 × 1)/(4 × 1) + (5 × 4)/(1 × 4) = 7/4 + 20/4
  • Step 3: Add the numerators while the denominator remains the same. Here, 7/4 + 20/4 = 27/4 = \(6\dfrac{3}{4}\)

Now, let us understand the subtraction of a fraction from a whole number with the help of the following example.

Example: Subtract 6 - 3/5

Solution: Let us subtract 6 - 3/5 using the following steps.

  • Step 1: Write the whole number in the form of a fraction. In this case the whole number is 6 which can be written as 6/1. So, now we need to subtract 6/1 - 3/5
  • Step 2: Now, find the LCM of the denominators and convert the given fractions to like fractions. Here the LCM of 1 and 5 is 5. And after converting them to like fractions we get, (6 × 5)/(1 × 5) - (3 × 1)/(5 × 1) = 30/5 - 3/5
  • Step 3: Subtract the numerators while the denominator remains the same. Here, 30/5 - 3/5 = 27/5 = \(5\dfrac{2}{5}\)

Important Notes on Adding and Subtracting Fractions

  • For adding and subtracting like fractions, we can directly work with the numerators while the denominators remain the same.
  • For adding and subtracting unlike fractions, never add or subtract the numerators and denominators directly. Convert them to like fractions and then add or subtract.

☛ Related Topics

  • Adding Fractions
  • Subtraction of Fractions
  • Multiplying Fractions
  • Division of Fractions
  • Adding Fractions with Unlike Denominators
  • Like Fractions Calculator
  • Fractions Calculator

Adding and Subtracting Fractions Examples

Example 1: Find the sum of 1/7 + 3/7 Solution: The given fractions are like fractions so we will add the numerators and retain the same denominator.

1/7 + 3/7 = (1 + 3)/7 = 4/7

Therefore, the sum is 4/7

Example 2: Subtract 2/3 - 2/5 Solution: The given fractions are unlike fractions. So, we need to find the LCM of the denominators and convert 2/5 and 2/3 to equivalent fractions of the same denominator and then subtract.

LCM of (3, 5) = 15

\(\begin{align} &= \left(\frac {2}{3} \times \frac {5}{5} \right) - \left(\frac {2}{5} \times \frac {3}{3} \right) \\ &= \frac {10}{15} - \frac {6}{15} \\ &= \frac {4}{15} \end{align}\)

Therefore, the difference is 4/15

Example 3: State true or false with respect to adding and subtracting fractions.

a.) 4/5 + 3/5 = 7/5

b.) 7/8 - 2/8 = 9/8 Solution:

a.) True, 4/5 + 3/5 = 7/5

b.) False, 7/8 - 2/8 = 5/8

go to slide go to slide go to slide

adding and subtracting fractions problem solving questions

Book a Free Trial Class

Practice Questions on Addition and Subtraction of Fractions

go to slide go to slide

FAQs on Addition and Subtraction of Fractions

For adding and subtracting fractions , we first need to check the denominators. If the denominators are the same, we simply add or subtract the numerators and retain the same denominator. In the case of unlike fractions, when the denominators are not the same, we convert the unlike fractions to like fractions by finding the LCM of the denominators. This helps in writing their respective equivalent fractions and then they are added or subtracted, as required.

How to Add and Subtract Fractions with Different Denominators?

In order to add and subtract fractions with different denominators, we need to convert the fractions to like fractions so that the denominators become the same. Once the denominators are the same, we can add or subtract the numerators. In order to convert the given fractions to like fractions, we need to find the LCM of the denominators and then write their respective equivalent fractions. The equivalent fractions with the same denominators can then be added or subtracted, as the case may be.

How to Add and Subtract Fractions with Whole Numbers?

For adding and subtracting fractions with whole numbers we use the following method.

  • Write the whole number in the form of a fraction by writing 1 as its denominator. For example, if we need to add 8/7 + 5, we will write the whole number in the form of a fraction. In this case the whole number is 5 which can be written as 5/1. So, now we need to add 8/7 + 5/1. We will find the LCM of the denominators and convert the given fractions to like fractions. Here the LCM of 7 and 1 is 7. And after converting them to like fractions we get, (8 × 1)/(7 × 1) + (5 × 7)/(1 × 7) = 8/7 + 35/7 = 43/7 = \(6\dfrac{1}{7}\)
  • The same method will be used for subtraction, for example, if we need to subtract 7 - 2/5, we will write the whole number 7 as 7/1 and then subtract. This will make it 7/1 - 2/5. We will find the LCM of the denominators and convert the given fractions to like fractions. Here the LCM of 5 and 1 is 5. And after converting them to like fractions we get, (7 × 5)/(1 × 5) - (2 × 1)/(5 × 1) = 35/5 - 2/5 = 33/5 = \(6\dfrac{3}{5}\)

How to Add and Subtract Fractions with Mixed Numbers?

To add and subtract fractions with mixed numbers, we convert the mixed numbers to improper fractions . Now, if they are like fractions, we can simply add or subtract the numerators and retain the same denominator. For adding or subtracting unlike fractions, we convert them to like fractions. We find the LCM of the denominators and convert the addends to their equivalent fractions and add them in the same way as we add like fractions.

What are the Rules for Adding and Subtracting Fractions?

The basic rules for adding and subtracting fractions are given below:

  • We need to check if the denominators of the fractions are same or different.
  • If the denominators are the same, we can simply add or subtract the numerators.
  • If the denominators are not the same, we need to convert them to like fractions and then we add or subtract.

Transum Shop  ::  Laptops aid Learning  ::  School Books  ::  Tablets  ::  Educational Toys  ::  STEM Books

Menu Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Level 9 Mixed Numbers Help More

This is level 1: adding two fractions with the same denominators. Give your answers as single fractions in their lowest terms. You can earn a trophy if you get at least 9 correct and you do this activity online .

This is Fractions level 1. You can also try: Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Level 9 You can also try the Mixed Numbers exercises: Level 1 Level 2 Level 3 Level 4

Apple

For Students:

  • Times Tables
  • TablesMaster
  • Investigations
  • Exam Questions

Transum.org is a proud supporter of the kidSAFE Seal Program

For Teachers:

  • Starter of the Day
  • Shine+Write
  • Random Names
  • Maths Videos
  • Laptops in Lessons
  • Online Teaching
  • Class Admin
  • Create An Account
  • About Transum
  • Privacy Policy

©1997-2024 WWW.TRANSUM.ORG

© Transum Mathematics 1997-2024 Scan the QR code below to visit the online version of this activity.

This is a QR Code

https://www.Transum.org/go/?Num=341

Description of Levels

Close

Level 1 - Adding two fractions with the same denominators.

Level 2 - Adding two fractions with a common denominator.

Level 3 - Adding two fractions with random denominators.

Level 4 - Subtracting two fractions with the same denominators.

Level 5 - Subtracting two fractions with a common denominator.

Level 6 - Subtracting two fractions with random denominators.

Level 7 - Multiplying two fractions.

Level 8 - Dividing one fraction by another.

Level 9 - Mixed fraction calculations.

Mixed Numbers exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Reminder Video

You may also want to use a calculator to check your working. See Calculator Workout skill 10.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Close

FREE Math Success Workshop: Adding, Subtracting, Multiplying, and Dividing Fractions

Thursday, february 15, 2024.

Girl with backpack and books in front a wall of math symbols

The LAVC Academic Resource Center offers FREE weekly online and in-person Math Success Workshop Series. These weekly sessions will help you review some basic but key concepts, so you can succeed in your math class! If it’s been a while since you took a math class, or if math was never your favorite subject, these workshops are for you!

Topic: Adding, Subtracting, Multiplying, and Dividing Fractions Date & Time: Thursday, February 15 from 1 p.m.-2:30 p.m. Locations: Hybrid - Online & LARC 212 (Library & Academic Resource Center, 2nd Floor) ( view map )

LAVC Tutoring Services & Schedule Info

For more information, please contact the Academic Resource Center at @email or (818) 947-2922.

LACCD encourages persons with disabilities to participate in its programs and activities. Please allow 10 days if you anticipate on needing any type of accommodation or have questions about the physical or virtual access provided, contact the LAVC Academic Resource Center at (818) 947-2922 or email @email as soon as possible, but no later than ten (10) business days prior to the event.

Link copied to clipboard

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Course: 4th grade   >   Unit 8

Fraction word problem: piano.

  • Fraction word problem: pizza
  • Fraction word problem: spider eyes
  • Add and subtract fractions word problems (same denominator)

Want to join the conversation?

  • Upvote Button navigates to signup page
  • Downvote Button navigates to signup page
  • Flag Button navigates to signup page

Great Answer

Video transcript

IMAGES

  1. Adding and Subtracting Fractions Worksheets with Answer Key

    adding and subtracting fractions problem solving questions

  2. Mastery in maths

    adding and subtracting fractions problem solving questions

  3. Adding Subtracting Fractions Worksheets

    adding and subtracting fractions problem solving questions

  4. Free Fraction Worksheets Adding Subtracting Fractions

    adding and subtracting fractions problem solving questions

  5. 4th Grade Adding And Subtracting Fractions Word Problems Worksheets

    adding and subtracting fractions problem solving questions

  6. How to Solve Word Problems Involving the Addition or Subtraction of

    adding and subtracting fractions problem solving questions

VIDEO

  1. Subtracting Fractions with Like Denominators 7/23/2023

  2. Adding and Subtracting Fractions

  3. Addition of Fraction

  4. Add and subtract fractions

  5. FRACTIONS

  6. ADVANCED FRACTION MATH PROBLEMS / MATH TUTORIAL

COMMENTS

  1. Education.com Official Site

    The most comprehensive library of free printable worksheets & digital games for kids. Get thousands of teacher-crafted activities that sync up with the school year.

  2. Add and subtract fractions

    Unit test About this unit It's time to tackle fractions! From common denominators to unlike denominators, this unit will teach you everything you need to know to add and subtract them confidently. Get ready to show those fractions who's boss! Strategies for adding and subtracting fractions with unlike denominators Learn

  3. Fraction Word Problems Worksheets

    Featured here is a vast collection of fraction word problems, which require learners to simplify fractions, add like and unlike fractions; subtract like and unlike fractions; multiply and divide fractions. The fraction word problems include proper fraction, improper fraction, and mixed numbers.

  4. Fraction Addition and Subtraction: Problems with Solutions

    Difficult Fraction Addition and Subtraction: Problems with Solutions Problem 1 Calculate the sum of the fractions: \displaystyle \frac {1} {5}+\frac {2} {5} 51 + 52 \displaystyle \frac {2} {5} 52 \displaystyle \frac {1} {5} 51 \displaystyle \frac {3} {10} 103 \displaystyle \frac {3} {5} 53 Problem 2

  5. Adding Fractions Practice Questions

    Adding Fractions Practice Questions - Corbettmaths Adding Fractions Practice Questions Click here for Questions . Click here for Answers . Addition, Adding The Corbettmaths Practice Questions on Adding Fractions

  6. Fraction Worksheets

    Worksheet Simplify Fractions Mixed to Improper Fractions Improper to Mixed Fractions Fractions - Addition Worksheet Example Fractions (Same Denominator) 1 5 + 2 5 Unit Fractions 1 3 + 1 9 Easy Proper Fractions 3 8 + 2 7 Harder Proper Fractions 7 12 + 15 25 Easy Mixed Fractions 1 2 3 + 2 1 4 Harder Mixed Fractions 1 7 9 + 3 5 11

  7. Adding and Subtracting Fraction Word Problems

    Here are some word-based questions for solving problems involving the addition and subtraction of fractions. Feedback greatly appreciated!

  8. Add and subtract fractions

    Start Not started Decompose fractions Get 5 of 7 questions to level up! Practice Not started Adding and subtracting fractions with like denominators Learn Adding fractions with like denominators

  9. Add & Subtract Fractions Word Problems

    Mixed numbers word problems. These word problems require simple addition and subtraction of fractions and mixed numbers. Only fractions with like denominators are considered. Worksheet #1 Worksheet #2 Worksheet #3 Worksheet #4. Worksheet #5 Worksheet #6.

  10. Word Problems

    First, we have to find the common denominator, 8, and then add the fractions together using the new fractions (2/8 and 1/8). All in all, he ate 3/8ths of the pizza. Pictures would also be helpful to solve this problem. We know this answer is correct because it's a reasonable answer to the problem - he ate three pieces.

  11. IXL

    Skill plans. IXL plans. Virginia state standards. Textbooks. Test prep. Awards. Improve your math knowledge with free questions in "Add and subtract fractions with like denominators: word problems" and thousands of other math skills.

  12. Word Problems

    13 practice problems and an answer key. Description: This packet helps students practice doing word problems using addition of fractions with like denominators. Each page has a speed and accuracy guide, to help students see how fast and how accurately they should be doing these problems.

  13. Fractions Operations

    Adding and subtracting fractions. Adding and subtracting fractions means finding the sum or the difference of two or more fractions. In order to do this, the fractions must have a common denominator (bottom number). The numerator shows the number of parts out of the whole and the denominator shows how many equal parts the whole is divided into.

  14. Grade 4 Fractions Worksheets

    Free 4th grade fractions worksheets including addition and subtraction of like fractions, adding and subtracting mixed numbers, completing whole numbers, improper fractions and mixed numbers, comparing and ordering fractions and equivalent fractions. No login required.

  15. Addition and Subtraction of Fraction: Methods, Facts, Examples

    Frequently Asked Questions on Addition and Subtraction of Fractions What Is Addition and Subtraction of Fractions? Addition and subtraction of fractions are the fundamental operations on fractions that can be studied easily using two cases: Addition and subtraction of like fractions (fractions with same denominators)

  16. PDF Fractions in Real World (Addition and Subtraction)

    Fractions can be used to solve real world problems. By adding or subtracting fractions, we can find unknown measurements, currency, and more. One important concept that we must master is solving for missing or unknown fractions, by constructing a block model. Examples: Find the value of 🖤.

  17. IXL

    Skill plans. IXL plans. Virginia state standards. Textbooks. Test prep. Awards. Improve your math knowledge with free questions in "Add and subtract fractions with unlike denominators: word problems" and thousands of other math skills.

  18. Adding & subtracting fractions word problems

    Word problem worksheets: Addition & subtraction of fractions. Below are three versions of our grade 4 math worksheet on adding and subtracting fractions and mixed numbers. All fractions have like denominators. Some problems will include irrelevant data so that students have to read and understand the questions, rather than simply recognizing a pattern to the solutions.

  19. Addition and Subtraction of Fractions

    Solution: First let us convert the mixed fractions to improper fractions. Step 1: Convert the given mixed fractions to improper fractions. So, 2 1 4 2 1 4 will become 9/4; and 13 4 1 3 4 will become 7/4. Step 2: Add the fractions by adding the numerators because the denominators are the same.

  20. Subtracting fractions with unlike denominators

    Course: 5th grade > Unit 4 Lesson 3: Adding and subtracting fractions with unlike denominators Adding fractions with unlike denominators introduction Adding fractions with unlike denominators Add fractions with unlike denominators Subtracting fractions with unlike denominators introduction Subtracting fractions with unlike denominators

  21. Fractions

    A series of self-marking exercises on adding, subtracting, multiplying and dividing fractions. This is level 1: adding two fractions with the same denominators. Give your answers as single fractions in their lowest terms. You can earn a trophy if you get at least 9 correct. This is Fractions level 1.

  22. FREE Math Success Workshop: Adding, Subtracting, Multiplying, and

    FREE Math Success Workshop: Adding, Subtracting, Multiplying, and Dividing Fractions ... and Dividing Fractions Date & Time: Thursday, February 15 from 1 p.m.-2:30 p.m. Locations: Hybrid - Online & LARC 212 ... Please allow 10 days if you anticipate on needing any type of accommodation or have questions about the physical or virtual ...

  23. Fraction word problem: piano (video)

    And if you wanted to work it out mathematically, you just have to do the same thing to the numerator and the denominator. So let's divide the numerator and the denominator by 2, because they are both divisible by 2. That's actually their greatest common factor. So 2 divided by 2 is 1. 4 divided by 2 is 2.