solve word problems involving addition and subtraction of fractions

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Dive into Fractions: How to Solve Addition and Subtraction Word Problems

Welcome back, budding mathematicians! Today, we'll explore a new exciting topic: word problems involving addition and subtraction of fractions. Don't let the term 'word problems' intimidate you. With some simple steps, you can tackle these like a pro.

Adding and Subtracting Fractions: A Refresher

Adding and subtracting fractions involves a little more than adding and subtracting whole numbers, but the concept is pretty straightforward. It revolves around the idea of finding a common denominator, which is a shared multiple of the denominators of the fractions involved.

Step-by-Step Guide: Adding and Subtracting Fractions in Word Problems

Step 1: understand the problem.

Read the problem carefully. Understand what is being asked and identify the fractions you will need to add or subtract.

Step 2: Find the Common Denominator

This is perhaps the trickiest part. The denominators of the fractions must be the same before you can add or subtract them. To find the common denominator, look for the least common multiple (LCM) of the denominators.

Step 3: Adjust the Fractions

Once you have the common denominator, adjust the fractions by multiplying the numerator and denominator by the same number so that the denominator matches the common denominator.

Step 4: Add or Subtract

Now, add or subtract the numerators of the fractions. The denominator remains the same.

Step 5: Simplify the Answer

After performing the operation, simplify your answer if possible. This may involve reducing the fraction to its lowest term.

Step 6: Write the Answer

Finally, write down your answer, making sure it correctly answers the question asked in the word problem.

Now, let’s see this process in action:

Ella has \(\frac{2}{3}\) of a chocolate bar left, and her friend Mia has \(\frac{1}{2}\) of a chocolate bar left. How much chocolate do they have together?

• Understand the problem: We need to add \(\frac{2}{3}\) and \(\frac{1}{2}\).
• Find the common denominator: The LCM of \(3\) and \(2\) is \(6\).
• Adjust the fractions: \(\frac{2}{3}\) becomes \(\frac{4}{6}\), and \(\frac{1}{2}\) becomes \(\frac{3}{6}\).
• Add the fractions: \(\frac{4}{6} + \frac{3}{6} = \frac{7}{6}\).
• Simplify the answer: \(\frac{7}{6}\) can be written as \(1\frac{1}{6}\).
• Write the answer: Ella and Mia have \(1\frac{1}{6}\) chocolate bars together.

Remember, the key to mastering word problems involving fractions is practice. So, roll up your sleeves and dive in!

by: Effortless Math Team about 9 months ago (category: Articles )

Effortless Math Team

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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 .

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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)

• Your answer should be
• a proper fraction, like 1 / 2 ‍   or 6 / 10 ‍  
• an improper fraction, like 10 / 7 ‍   or 14 / 8 ‍  

Word Problems – Add & Subtract Fractions

With our Word Problems – Add & Subtract Fractions lesson plan, students learn how to solve word problems that contain the addition or subtraction of fractions. Students solve problems and write their own word problems as a part of this lesson.

Included with this lesson are some adjustments or additions that you can make if you’d like, found in the “Options for Lesson” section of the Classroom Procedure page. One of the optional additions to this lesson is to have students create a poster that shows a variety of strategies that they can use to solve fraction word problems for adding and subtracting.

Description

Additional information, what our word problems – add & subtract fractions lesson plan includes.

Lesson Objectives and Overview: Word Problems – Add & Subtract Fractions teaches students how to interpret and solve word problems that require the addition or subtraction of fractions. At the end of the lesson, students will be able to solve fraction addition and subtraction problems using models and other strategies. This lesson is for students in 5th grade.

Classroom Procedure

Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the blue box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand. The only supplies needed for this lesson are the handouts. To prepare for this lesson ahead of time, you can pair students for the activity and copy the handouts.

Options for Lesson

Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. You can adjust the lesson activity by increasing or decreasing the number of problems, or by using the problems for a class quiz or test. An optional addition to this lesson is to have students create pictures and exchange them with other students to create fraction word problems. Students could also create a poster that shows a variety of strategies that they can use to solve fraction word problems for adding and subtracting.

Teacher Notes

The teacher notes page includes a paragraph with additional guidelines and things to think about as you begin to plan your lesson. This page also includes lines that you can use to add your own notes as you’re preparing for this lesson.

WORD PROBLEMS – ADD & SUBTRACT FRACTIONS LESSON PLAN CONTENT PAGES

Adding/subtracting word problems.

The Word Problems – Add & Subtract Fractions lesson plan includes three pages of content. The lesson begins by stating that while students have solved many addition and subtraction problems, they often find word problems difficult because they aren’t sure whether they’re supposed to add or subtract. Luckily, there are keywords that we can use to identify the right operation. The lesson reviews some common keywords for addition and subtraction. Addition keywords include plus, sum, total, in all , and added to . Subtraction keywords include minus, difference, change, take away , and less than .

Some other strategies that students may already be familiar with for solving word problems are drawing pictures, making charts or lists, and taking notes. We can also use these same strategies to help solve word problems that include the addition or subtraction of fractions!

Add & Subtract Fraction Word Problems

Solving word problems with fractions is not very different from solving word problems with whole numbers. The primary difference is that most of the numbers are fractions! The lesson provides an example problem about pizza to illustrate this. The example problem uses the phrase in all, which tells us that it’s an addition problem, and that we must add together all of the pieces of pizza that Ryan ate. He ate 1/4 of one pizza and 1/8 of another. 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. An unreasonable answer could have a result that’s less than one of the addends. It’s important to remember that the results must be reasonable. We can also use mental math to add, subtract, or create equations that help us solve the problem.

The lesson then delves into two more example problems. The first is a subtraction problem that we can solve using a similar method to the first example (find the common denominator and solve). However, the third example is one that can be solved using mental math, since there’s already a common denominator.

There are many different methods and strategies that we can use to solve word problems with fractions, like identifying keywords, drawing pictures, and more!

WORD PROBLEMS – ADD & SUBTRACT FRACTIONS LESSON PLAN WORKSHEETS

The Word Problems – Add & Subtract Fractions lesson plan includes three worksheets: an activity worksheet, a practice worksheet, and a homework assignment. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.

CREATING PROBLEMS ACTIVITY WORKSHEET

Students will work with a partner to complete the activity. They will create two addition, two subtraction, and two mixed fraction word problems, They should make sure to use keywords that will help other students solve their problems, and will create an answer key to accompany their problems.

Students can work either alone or in groups for this activity if you’d prefer.

COFFEE SHOP PRACTICE WORKSHEET

The practice worksheet asks students to read and solve word problems that require them to add or subtract. They will solve five of these problems and will then create a word problem using the provided picture.

WORD PROBLEMS – ADD & SUBTRACT FRACTIONS HOMEWORK ASSIGNMENT

For the homework assignment, students will use the provided chart to answer five word problems.

Worksheet Answer Keys

This lesson plan includes answer keys for the practice worksheet and the homework assignment. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.

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Fraction Addition And Subtraction: Word Problems

Description.

Objective:  Solve word problems involving addition and subtraction of  fractions.

As students move into problem solving in Lesson 19, they create tape diagrams or number lines to represent and solve fraction addition and subtraction word problems. These problems bridge students into work with mixed numbers, which follows the Mid-Module Assessment.

There may be cases when our downloadable resources contain hyperlinks to other websites. These hyperlinks lead to websites published or operated by third parties. UnboundEd and EngageNY are not responsible for the content, availability, or privacy policies of these websites.

• Grade 4 Mathematics Module 5, Topic D, Lesson 19

Prerequisites

• 4.NF.B.3.A ,
• 4.NF.B.3.B ,
• CCSS Standard:

Related Guides and Multimedia

Our professional learning resources include teaching guides, videos, and podcasts that build educators' knowledge of content related to the standards and their application in the classroom.

There are no related guides or videos. To see all our guides, please visit the Enhance Instruction section here .

Curriculum  /  Math  /  4th Grade  /  Unit 5: Fraction Operations  /  Lesson 4

Fraction Operations

Lesson 4 of 21

Criteria for Success

Tips for teachers, anchor tasks.

Problem Set

Target Task

Additional practice.

Solve word problems that involve the addition and subtraction of fractions where the total is less than or equal to one.

Common Core Standards

Core standards.

The core standards covered in this lesson

Number and Operations—Fractions

4.NF.B.3.D — Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

The essential concepts students need to demonstrate or understand to achieve the lesson objective

• Make sense of a three-act task and persevere in solving it (MP.1).
• Solve one-, two-, and multi-step word problems that involve the addition and subtraction of fractions less than or equal to 1 (MP.4).

Suggestions for teachers to help them teach this lesson

Let students work on each problem in the Problem Set independently and circulate to see whether students are solving correctly. If not, come back together to discuss how/what to draw on a tape diagram, then allow them to try again on their own. 

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Act 1: Watch the following video:  A Delicious Mix .

a.   What do you notice? What do you wonder?

b.   What fraction of each kind of candy is in the bag?

Guiding Questions

3 Act: A Delicious Mix by Catherine Castillo is made available on Ms Castillos Math . Accessed July 17, 2018, 11:39 a.m..

Act 2: Use the following information to solve.

Act 3: Reveal the answer.

Was your answer reasonable? Why or why not?

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

• How many students played either soccer or basketball in #2? What role does the word “or” serve in this problem? 
• I think the answer to #4 is $${{7\over8}}$$ . Do you agree or disagree with me? Why? 
• How did you decide what the possible mass of the music and art books was in #7(b)? 
• What was the total amount of toppings, in gallons, in #8? What is another way to represent this amount? 

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Solve. Show or explain your work.

Gauvain had $$5\over 6$$  yard of ribbon. He used $$3\over 6$$  to tie a bow on a gift. How much ribbon did he have left?

Of the books Ayala read this year, $$1\over 12$$  were science fiction books and  $$7\over 12$$ were mysteries. What fraction of the books were neither science fiction nor mysteries?

Student Response

An example response to the Target Task at the level of detail expected of the students.

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Answer keys for Problem Sets and Extra Practice Problems are available with a Fishtank Plus subscription.

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Topic A: Building, Adding, and Subtracting Fractions Less Than or Equal to 1

Decompose fractions as a sum of unit fractions and as a multiple of a unit fraction.

4.NF.B.3.B 4.NF.B.4.A

Decompose fractions as a sum of fractions with the same denominator in more than one way.

Add and subtract fractions within 1 with the same units.

4.NF.B.3.A 4.NF.B.3.C

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Topic B: Building, Adding, and Subtracting Fractions Less Than 2

Decompose non-unit fractions less than 2 as a sum of unit fractions, as a sum of non-unit fractions, and as a whole number times a unit fraction.

Add and subtract fractions that require regrouping where the total is less than 2. 

Add two fractions where one denominator is a multiple of the other using the denominators 2, 3, 4, 5, 6, 8, 10, and 12.

Topic C: Building, Adding, and Subtracting Fractions Greater Than or Equal to 2

Decompose and compose non-unit fractions greater than two as a sum of unit fractions, as a sum of non-unit fractions, and as a whole number times a unit fraction. 

Convert fractions greater than 1 to mixed numbers.

4.NF.B.3.B 4.NF.B.3.C

Convert mixed numbers to fractions greater than 1.

Compare and order fractions greater than 1 using various methods.

Add fractions and mixed numbers where the total is greater than or equal to 2.

Subtract fractions and mixed numbers where the total is greater than or equal to 2.

Add and subtract mixed numbers using a variety of mental strategies.

Solve word problems involving addition and subtraction of fractions.

Topic D: Multiplication of Fractions

Multiply a whole number by a fraction.

Multiply a whole number by a mixed number.

Solve word problems involving multiplication of fractions.

Solve word problems involving addition, subtraction, and multiplication of fractions.

4.NF.B.3.D 4.NF.B.4.C

Topic E: Line Plots

Make a line plot (dot plot) representation to display a data set of measurements in fractions of a unit.

Solve problems using information presented in line plots.

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Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result $2/5 + 1/2 = 3/7$, by observing that $3/7 < 1/2$.

Fraction Two-Step Word Problems - Mixed Numbers Worksheets

Related Topics & Worksheets: Adding Fractions Worksheet Fraction Games

Objective: I can solve two-step word problems involving addition and subtraction of mixed numbers.

“Fraction Word Problems” Worksheets: Fraction Word Problems (Add, Subtract) 2-Step Fraction Word Problems (Add, Subtract)

1-Step Mixed Number Word Problems (Add, Subtract) 2-Step Mixed Number Word Problems (Add, Subtract)

Solving mixed number word problems involves applying arithmetic operations to mixed numbers in real-world situations.

Steps to Solve Mixed Number Word Problems:

• Carefully read the word problem to understand what it is asking. Identify the quantities, units of measurement, and any other relevant details.
• Determine what information is given in the problem and what is known. Identify the different steps or components of the problem.
• Identify what the problem is asking you to find. This may involve finding intermediate values or the final solution.
• Decide on a strategy to solve the problem. This may involve breaking the problem into smaller steps, converting mixed numbers to improper fractions, performing arithmetic operations, or applying other problem-solving techniques.
• Follow your plan and perform the necessary calculations to solve each step of the problem. Use arithmetic operations such as addition, subtraction, multiplication, and division as needed.
• After solving each step, check your answer to ensure it makes sense and matches the problem’s requirements. Re-read the problem to verify that you have answered each part correctly.
• Clearly state your final answer in the context of the problem. Use proper units and labels if applicable.

Printable Mixed Number Word Problems

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Mixed Number Word Problem Worksheets .

(Answers on the second page.) Mixed Number Word Problems Worksheet #1 Mixed Number Word Problems Worksheet #2 Mixed Number Word Problems Worksheet #3

Online Fraction Word Problems

Solve the following word problems. Irene bought 7 3 / 8 m of cloth. Molly bought 1 / 2 m less than Irene. a. How many metres of cloth did Molly buy? b. How many metres of cloth did they buy altogether? Jasmine cooked 1 5 / 6 kg of rice. Alice cooked 5 / 8 kg more than Jasmine. a. How many kg of rice did Alice cook? b. How many kg of rice did they cook together? Jonathan had 8 5 / 6 m of string. Matthew bought 5 / 9 m more than Jonathan. a. How many metres of string did Matthew buy? b. How many metres of string did they buy altogether? Harold prepared 4 3 / 7 litres of drinks for a party. Dan also prepared drinks and he prepared 1 1 / 2 litres less than Harold. What is the total volume of drinks that Harold and Dan prepared altogether? Jeremy collected 12 3 / 4 kg of newspaper for recycling. Brian collected 3 2 / 5 kg more than Jeremy. Find the total mass of newspaper that Jeremy and Brian collected together. Henry has 7 3 / 5 metres of rope, and Sam has a rope that is 1 1 / 6 metres shorter than Henry’s. What is the total length of rope that Henry and Sam have altogether? Ryan collected 3 2 / 5 kg of mangoes and 5 2 / 3 kg of guavas from his orchard. His son also collected some fruits, and his son’s collection was 1 3 / 4 kg less than the total weight of the fruits that Ryan collected. Find the total mass of all the fruits that Ryan and his son collected altogether. Suzie bought 1 1 / 4 kg of lettuce and 1 2 / 3 kg of spinach. Then, she bought a bunch of bananas that was 2 / 3 kg heavier than the total weight of the vegetables that she bought. What was the total weight of the bananas and vegetables in kg? 20 1/3 litres of drinks were prepared for a school basketball match. The players drank 9 1 / 2 litres during the first half of the game. In the second half, the players drank 1 3 / 5 less than in the first half. What is the volume of drinks left at the end?

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Adding and Subtracting Fraction Word Problems

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

16 June 2015

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Subtracting Fractions Word Problems Worksheets

Thumb through our printable subtracting fractions word problems worksheets and discover a treasure of fun, realistic scenarios. Our pdf prepping tools, with included answer keys, are well-chosen for grade 3 through grade 6 students. Task young learners with reading, understanding, and solving an array of fraction subtraction word problems. Deftly find the difference between two like fractions, two unlike fractions, mixed numbers, and more. Go after our free subtracting fractions word problems worksheet!

Subtracting Fractions with Whole Numbers Word Problems

Perk up your math sessions with this section of our subtracting fractions word problems worksheets. Have kids determining the difference between fractions and whole numbers in real life with nuance and flair!

• Download the set

Subtracting Like Fractions Word Problems

Pride yourself on your subtraction on fractions skills! The interactive scenarios in our pdf word problems worksheets for 3rd grade, 4th grade, and 5th grade make subtracting like fractions a rewarding affair!

Subtracting Unlike Fractions Word Problems

Enhance problem-solving skills with these fraction subtraction word problems worksheets. Young learners read and solve word problems involving fractions with different denominators with accuracy.

Subtracting Mixed Numbers Word Problems | Like Denominators

Do nothing by halves! Get kids going all out to subtract mixed numbers having same denominators! The key to solving these problems is finding the difference between the whole number parts and fractions separately.

Subtracting Mixed Numbers Word Problems | Unlike Denominators

Add bells and whistles to your fraction subtraction practice with our printables. Grade 4, grade 5, and grade 6 kids find the LCM of different denominators and obtain the difference between two mixed numbers.

Related Worksheets

» Subtracting Like Fractions

» Subtracting Unlike Fractions

» Subtracting Mixed Numbers

» Subtracting Fractions from Whole Numbers

» Fraction Word Problems

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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.

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

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:

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

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 $\frac{4}{6} \;-\; \frac{1}{6}$.

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

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.

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.

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Word Problems Involving Addition and Subtraction

Word problems involving addition and subtraction are discussed here step by step.

There are no magic rules to make problem solving easy, but a systematic approach can help to the problems easily. 

Word problems based on addition are broadly of two types: (a) When objects of two or more collections are put together.  For example:

Amy has 20 lemon sweets and 14 orange sweets. What is the total number of sweets Amy has?  (b) When an increase in number takes place. 

For example:

Victor has 14 stamps. His friend gave him 23 stamps. How many stamps does Victor have in all? The key words used in problems involving addition are:

s um; total; in all; all together.

Word problems based on subtraction are of several types: (a) Partitioning : Take away, remove, given away.

(b) Reducing : Find out how much has been given away or how much remains.

(c) Comparison : More than / less than.

(d) Inverse of addition : How much more to be added. The key words to look out for in a problem sum involving subtraction are: take away; how many more ; how many less ; how many left ; greater ; smaller.

1. The girls had 3 weeks to sell tickets for their play. In the first week, they sold 75 tickets. In the second week they sold 108 tickets and in the third week they sold 210 tickets. How may tickets did they sell in all? Tickets sold in the first week = 75

Tickets sold in the second week = 108

Tickets sold in the third week = 210

Total number of tickets sold = 75 + 108 + 210 = 393

Answer: 393 tickets were sold in all.

2. Mr. Bose spent $450 for petrol on Wednesday. He spent $125 more than that on Thursday. How much did he spend on petrol on those two days. This problem has to be solved in two steps.

Step 1: Money spent for petrol on Thursday

450 + 125 = $575 Step 2: Money spent for petrol on both days

450 + 575 = $1025

Examples on word problems on addition and subtraction:

1. What is the sum of 4373, 4191 and 3127? Solution: The numbers are arranged in columns and added.

Therefore, sum =11,691

2. What is the difference of 3867 and 1298?

Solution: The numbers are arranged in columns and subtracted:

Therefore, difference = 2569

3. Subtract 4358 from the sum of 5632 and 1324. Solution: Sum of 5632 and 1324

Difference of 6956 and 4358

Therefore, 2598 is the answer.

4. Find the number, which is

(i) 1240 greater than 3267.

(ii) 1353 smaller than 5292. Solution: (i) The number is 1240 more than 3267

Therefore, the number = 3267 + 1240 or = 4507 (ii) The number is 1353 less than 5292

= 5292 – 1353 or

5. The population of a town is 16732. If there are 9569 males then find the number of females in the town. Solution:

6. In a factory there are 35,675 workers. 10,750 workers come in the first shift, 12,650 workers in the second shift and the rest come in the third shift. How many workers come in the third shift? Solution: Number of workers coming in the first and second shift

= 10750 + 12650 = 23400

Therefore, number of workers coming in the third shift = 35675 - 23400 = 12275

Related Concept

● Word Problems on Addition

● Subtraction

● Check for Subtraction and Addition

● Word Problems Involving Addition and Subtraction

● Estimating Sums and Differences

● Find the Missing Digits

● Multiplication

● Multiply a Number by a 2-Digit Number

● Multiplication of a Number by a 3-Digit Number

● Multiply a Number

● Estimating Products

● Word Problems on Multiplication

● Multiplication and Division

● Terms Used in Division

● Division of Two-Digit by a One-Digit Numbers

● Division of Four-Digit by a One-Digit Numbers

● Division by 10 and 100 and 1000

● Dividing Numbers

● Estimating the Quotient

● Division by Two-Digit Numbers

● Word Problems on Division

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