BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon102 Learners

Last updated on July 4th, 2025

Math Whiteboard Illustration

Addition and Subtraction of Fractions

Professor Greenline Explaining Math Concepts

A part of a whole number is known as a fraction. It has two sections, the top number is the numerator, while the bottom number is the denominator. To find the total value of a number, the processes of addition and subtraction of fractions are essential. In this topic, we are going to learn about the addition and subtraction of fractions.

Addition and Subtraction of Fractions for Indonesian Students
Professor Greenline from BrightChamps

What is Adding and Subtracting of Fractions?

To calculate the overall value of a number, the process of addition and subtraction of fractions involves checking if the fractions have common denominators. For example, Donald drinks 1½ liters of water in the morning and 1½ liters of water in the evening. To calculate how much water Donald drinks in a day, we use addition and subtraction of fractions.

 

In a fraction, the top number indicates how many parts are under consideration. The bottom number shows how many equal pieces the whole is divided into. For example, in the fraction 1/2, the numerator shows one part, while the denominator represents that the whole is divided into two equal parts.

Professor Greenline from BrightChamps

Rules for Adding and Subtracting of Fractions

The process of adding and subtracting fractions involves joining and removing parts of a whole, as defined by fractions. To perform these operations effectively, some rules should be followed.

 

Rules for Adding Fractions 

Confirm the denominators are equal: Check the bottom numbers in two fractions are the same. For example, 5⁄10 + 4⁄10 = 9⁄10. Here, the denominators are the same, 10. So, the calculation will be like this:
 5⁄10 + 4⁄10 = 5 + 4/10 =  9⁄10.

 

If denominators are different, find the common denominator: In the given fractions, if the denominators are not the same, then identify the least common denominator. To find the least common denominator, we have to list the multiples of the given denominators. For instance, 1⁄4 + 1⁄6. Here, both the denominators are different. So we have to list the multiples of 4 and 6. 

The multiples of 4 include 4, 8, 12, 16, 20, 24, …

The multiples of 6 include 6, 12, 18, 24, 30, …

Among the lists of multiples, 12 is the least common multiple. So 12 is the denominator. Now, we need to match the LCD with the fractions. 

1⁄4 = 1×3/4×3 = 3⁄12

1⁄6 = 1×2/6×2 = 2⁄12. Now we can add both fractions easily.
 
 3⁄12 + 2⁄12 = 5⁄12.

 

Combine mixed numbers: Convert mixed numbers into improper fractions. After that follow the addition method. For instance,
 
1 1⁄3 +2 2⁄3 

It becomes 4⁄3 + 8⁄3 = 12⁄3 = 4

 

Rules for Subtracting 

Subtract the numerators: If the given fractions have the same denominators, then subtract the numerators. For instance, the given fractions are 8⁄3 and 4⁄3.
8⁄3 - 4⁄3 = 4⁄3

 

Use the biggest numerators to subtract fractions: We get a negative result when the numerator is larger than the other fraction. For example,

4⁄3 - 8⁄3 = -4⁄3 

Here, 8⁄3 is the larger fraction.

 

Subtract the mixed numbers in a fraction: Change the mixed numbers into improper fractions and then follow the remaining steps. 

First, multiply the whole number with the denominator. Then add the numerator we will get the improper fraction. 
For instance, 

3 1⁄2 - 1 2⁄3 

(3 × 2) + 1 = 7/2 and 

(1 × 3) + 2 = 5/3

Subtract these two fractions:

7/2 - 5/3 

Next, we have to find the least common denominator of 2 and 3. The result is 6. Now we have to match the LCD (least common denominator) with the fractions. It becomes:

21⁄6 - 10⁄6 = 11⁄6 = 1 5⁄6 .

 

Addition of Fractions 

The addition of fractions is a simple operation in mathematics. It teaches us to sum the fractions that have the same or different denominators. If the denominators are same, we only need to add the numerators. If the denominators are different, we have to find the least common denominator. 

Take a look at this:

We can add 1⁄4 and 2⁄4:

1⁄4 + 2⁄4 = 3⁄4

Here, the denominators are the same. Next, we can move on to the next set of fractions.

 3⁄4 + 4⁄4 = 7⁄4.

This sequence illustrates how fractions with the same denominator increase progressively, starting from 1⁄4, 2⁄4, 3⁄4, 4⁄4, and so on. 

 

Subtraction of Fractions 

Subtraction of fractions involves the subtraction of two fractional values. With this, we can find the difference between two fractions. The common denominators will remain unchanged and the numerators will be subtracted. 

For example, 

5⁄8 - 3⁄8 = 2⁄8

We can simplify 2⁄8 as 1⁄4. Take a look at this too:

 3⁄4 - 2⁄4 = 1⁄4 or 

3⁄4 - 1⁄4 = 2⁄4

2/4 = 1/2 

Professor Greenline from BrightChamps

Tips and Tricks for Adding and Subtracting of Fractions

Performing addition and subtraction of fractions is sometimes tricky. Here are some of the tips and tricks to calculate the fractions using addition or subtraction:

 

Identify the least common denominator: If we get fractions that have different denominators, we have to figure out the LCD. It will help to make the process more simple and easier. LCD can be found by listing the multiples of denominators. 

 

Convert mixed numbers into improper fractions: It will help to reduce mistakes and the process more easier. While using improper fractions over mixed numbers, we can easily complete the task.

 

Simplify the fractions: If we get 4⁄8, it can be simplified into 1⁄2. It provides consistency and accuracy in calculations. Also, it avoids complications and helps to compare the values.

 

Be careful about the negative results: We get a negative result when the numerator is larger than the other fraction. Carefully handle the signs to avoid wrong results.

Max from BrightChamps Saying "Hey"

Addition and Subtraction of Fractions Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Calculate the value of 2⁄10 + 5⁄10.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

7⁄10 is the value we get when we add 2⁄10 and 5⁄10.

Explanation

Here, the denominators are same, it is 10. So, we can sum up the numerators.

2 + 5 = 7

Hence, the result is 7⁄10.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

What is the value of 4⁄6 - 3⁄2?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

-5⁄6 is the value.

Explanation

Here, the denominators are different. So we need to find the least common denominator (LCD). The LCD of 6 and 2 is 6.

Now, we need to write the fractions according to the LCD. 

 4⁄6 remains the same. 3⁄2 will be written as:

3⁄2 = 3 × 3 / 2  × 3 = 9⁄6

Now, we can subtract the fractions:

4⁄6 - 9⁄6 = -5⁄6.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

John collected a jar of honey and used 4⁄9 of the honey. After one week, he used 2⁄9 more. How much of the jar is filled with honey now?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

2⁄3 of the jar is filled with honey.

Explanation

9 is the denominator. So we need to add the numerators, 4 and 2.

4 + 2 = 6. Therefore, 4⁄9 + 2⁄9 = 6/9

6/9th of the jar is filled with honey. 6⁄9 can be simplified to 2⁄3. So 2⁄3 of the jar is filled now.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

Find 7⁄9 - 4⁄9.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The value is 1⁄3.

Explanation

9 is the denominator of both the fractions. Now, we need to subtract the numerators, i.e., 7 and 4.

7 - 4 = 3

 7⁄9 - 4⁄9 = 3⁄9

3⁄9 is the value we get by subtracting 7⁄9 and 4⁄9.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Find 1 1⁄2 + 2 1⁄3.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

3 5⁄6

Explanation

These fractions are mixed numbers. So we have to convert it into improper fractions. 

1 1⁄2 = 3⁄2 

2 1⁄3 = 7⁄3 

Next, we have to find the LCD. 6 is the least common denominator. 
3⁄2 = 9⁄6
7⁄3 = 14⁄6 

Now we can add the fractions:

9⁄6 + 14⁄6 = 23⁄6 

We can simplify 23⁄6 to 3 5⁄6.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQs on Addition and Subtraction of Fractions

1.What do you mean by a fraction?

Math FAQ Answers Dropdown Arrow

2.If fractions have the same denominator, does it change when adding or subtracting them?

Math FAQ Answers Dropdown Arrow

3.What is LCD?

Math FAQ Answers Dropdown Arrow

4.What are the rules of addition and subtraction of fractions?

Math FAQ Answers Dropdown Arrow

5.How can children in Indonesia use numbers in everyday life to understand Addition and Subtraction of Fractions?

Math FAQ Answers Dropdown Arrow

6.What are some fun ways kids in Indonesia can practice Addition and Subtraction of Fractions with numbers?

Math FAQ Answers Dropdown Arrow

7.What role do numbers and Addition and Subtraction of Fractions play in helping children in Indonesia develop problem-solving skills?

Math FAQ Answers Dropdown Arrow

8.How can families in Indonesia create number-rich environments to improve Addition and Subtraction of Fractions skills?

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important Glossaries for Addition and Subtraction of Fractions

  • Fraction: It is a part of a whole number. A fraction has a denominator and a numerator. For example, 5⁄6 is a fraction.

 

  • Numerator: It is a part of a fraction. The numerator is the top number. It represents how many parts we have. For instance, 7⁄30 where 7 is the numerator and defines 7 parts is considered out of 30.

 

  • Denominator: It refers to total parts in a whole number. In a fraction, a denominator is the bottom number. For instance, 7⁄30 where 30 is the denominator and defines the whole is counted into 30 parts. 

 

  • Least common denominator: LCD refers to the least common denominator of a fraction. If the given fractions have different denominators we will find the LCD. After that rewrite the fractions then add or subtract them. 
Math Teacher Background Image
Math Teacher Image

Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Max, the Girl Character from BrightChamps

Fun Fact

: She loves to read number jokes and games.

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom