BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon103 Learners

Last updated on July 4th, 2025

Math Whiteboard Illustration

Equivalent Fractions

Professor Greenline Explaining Math Concepts

Equivalent fractions are two or more different fractions that represent the same value. These fractions have different numerators and denominators, but represent the same value. For example, 1/2, 5/10, and 8/16 are all equivalent fractions as they simplify to 1/2. An equivalent fraction helps divide resources equally when sharing food or money. Let’s now learn more about the topic.

Equivalent Fractions for Thai Students
Professor Greenline from BrightChamps

What are Equivalent Fractions?

Equivalent fractions are different fractions that have the same value. When we multiply or divide both the numerator and denominator by the same non-zero number, we get equivalent fractions. It can be simplified to their lowest terms. For example, fractions such as 1/4, 2/8, 3/12, and 4/16 are equivalent because they can be simplified to 1/4.
 

Professor Greenline from BrightChamps

Differences Between Equivalent and Equal Fractions

Equivalent fractions and equal fractions are often confused. To understand them clearly, here are a few major differences between equivalent fractions and identical fractions:
 

 

Equivalent Fractions

Equal Fractions

Indicate the same value, but have different numerators and denominators.

Have the same numerator and denominator.

For example, 2/8, 3/12, and 4/16 are equivalent when simplified to 1/4.

3/6 and 3/6 are equal because they have the same numerator and denominator.

They can be visually represented as covering the same portion of a whole.

They appear to be the same because they have the same numerator and denominator.

Obtained by dividing or multiplying the numerators and denominators by the same number.

Since they are naturally the same, no calculations are required.

 

Professor Greenline from BrightChamps

How to Check Whether the Fractions are Equivalent or Not?

We use different methods to determine if the fractions are equivalent or not. Let’s learn each of them:

 

 

Making the denominators equal


In this method, we make the denominators equal by finding their LCM.
For a better understanding, here’s an example:


Check if 5/10 and 8/16 are equivalent.


Step 1: Find the LCM of 10 and 16 which equals 80

 


Step 2: Make the denominators the same by multiplying the numerator and denominator by appropriate numbers.
(5 × 8) / (10 × 8) = 40/80
(8 × 5) / (16 ×  5) = 40/80
Since both fractions are 40/80, they are equivalent.

 

 

Cross multiplication method

 


We cross-multiply the fractions and if the obtained results are the same, then the fractions are equivalent. Cross multiplication is done by multiplying the numerator of the first fraction with the denominator of the second fraction and vice versa. 
In the case of 58 and 1016, the cross multiplication is done like this:
5 × 16 = 80
8 × 10 = 80
Since both the products are the same, the fractions are equivalent.

 

 

Visual Method

 

This technique uses shapes that are divided into various parts to compare fractions visually. Here, the shaded portions of a whole represent whether they are equal or not.

 

In the image:

 

  • The first rectangle is divided into 3 parts, where only 1 part is shaded: 1/3.

 

  • The second rectangle is divided into 6 parts, where only 2 parts are shaded: 2/6

 

  • The third rectangle is divided into nine parts, where only 3 parts are shaded: 3/9

 

  • The fourth rectangle is divided into 12 parts, where only 4 are shaded: 4/12.

 

In the image, the shaded portions of the four rectangles represent the same value. So they are equivalent fractions.
 

Professor Greenline from BrightChamps

How to Find Equivalent Fractions?

To find the equivalent fractions, we multiply or divide both the numerator and denominator using the same number.
 

Professor Greenline from BrightChamps

Multiplication:

Here, we find the equivalent fractions for 3/8:
We multiply both the numerator and denominator using the same number:
Multiply by 2: 3  2 8   2  = 6/16
Multiply by 3:  3  3 8   3  = 9/24
Multiplying the numerator and denominator using the same number does not change the value of the fraction.
So, the equivalent fractions of 3/8 are 6/ 16 and 9/24.
 

Professor Greenline from BrightChamps

Division:

Let’s find equivalent fractions for 80/100:
To find equivalent fractions, we divide both the numerator and denominator by the same common factor. 
Dividing by 2: 80 ÷ 2 /100 ÷ 2  = 40/50 = 4/5
Dividing by 5: 80 ÷ 5 /100÷  5  = 16/20 = 4/5
Dividing by 10:80 ÷ 10 /100  ÷ 10  = 8/10 = 4/5
So, the equivalent fractions of 80/100 are 40/50, 16/20, and 8/10.

Professor Greenline from BrightChamps

Equivalent Fractions Chart

The equivalent fraction chart is an illustration that displays the equivalent fraction for each given quantity. Here, the corresponding fractions of 1, 1/3, 1/6, etc. are depicted in the chart below:

 

 

This chart shows that the equivalent fractions of 1/3 are: 2/6, 4/12, 8/24,... and so on 
 

Professor Greenline from BrightChamps

Real-life Applications of Equivalent Fractions

The concept of equivalent fractions can be applied and used in various fields. Here are a few real-life applications of equivalent fractions:

 

 

  • The concept is used to measure the amount of ingredients required for cooking. 

 

  • Learning equivalent fractions helps children in mental math, which can be applied when dealing with money.

 

  • These fractions are applied in construction when working with measurements in feet and inches.

 

  • Students can use equivalent fractions in time management. For example, 30 minutes equals 1/2 hour.

 

  • Children are able to share their food fairly with their friends. For example, cutting a cake into 6 equal pieces allows 6 people to share the cake.
     
Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in Equivalent Fractions

Students tend to make some mistakes when working with equivalent fractions. Such errors can be avoided with proper understanding. Here’s a list of common mistakes and ways to avoid them:
 

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Not Using the Same Number to Divide or Multiply

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Students often forget to multiply or divide both numerator and denominator by the same number.
3/8 × 2 = 6/8 (Incorrect)
Solution: Ensure that the numerator and denominator are multiplied or divided by the same number. For example, 3 x 2 / 8 x 2  = 6/16.

Mistake 2

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Misusing Cross-Multiplication
 

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Students sometimes forget that cross-multiplication results in different products.
For example, using cross-multiplication to check if 4/5 and 6/18 are equivalent:
4 × 18 = 72, 5 × 6 = 30. So, they conclude that cross-multiplication is not applicable to check the equivalent fractions.
If the cross-multiplication does not give equal products, we can conclude that the fractions are not equivalent. In this case, the fractions are not equivalent because 72 not equals to 30.
 

Mistake 3

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Multiplying or Dividing by Zero

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Some students tend to multiply or divide by zero while finding equivalent fractions. 
Example: 3 x 0 / 8 x 0  
 Anything dividing by zero is undefined.
 

Mistake 4

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Forgetting to Simplify the Fraction

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Another common mistake is that students may not simplify the fraction when further simplification is possible. This can lead to errors in the final answer.
Solution: Always write the fraction in its simplest form. This can be done by dividing the fraction by the greatest common divisor (GCD).
 

Mistake 5

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Misinterpreting the Rules for Multiplication
 

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Students tend to ignore the rules for addition and subtraction, and just add or subtract numerators or denominators. This will cause an error in the final answer.
For example, they may write 1/3 + 1/3 = 2/6. This is wrong as the correct answer is 2/3.
It is important to remember that we should have a common denominator while adding or subtracting fractions
 

arrow-right
Max from BrightChamps Saying "Hey"

Solved examples of Equivalent Fractions

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

Problem 1

Determine two equivalent fractions for 4/9

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

Two equivalent fractions for 4/9 are 8/18 and 12/27.
 

Explanation

To find two equivalent fractions, we multiply both the numerator and denominator using the same number:
Let’s multiply by 2:
4 x 2 / 9 x 2  = 8/18
Now, multiply by 3:
4 x 3 / 9 x  3  = 12/27
So, the two equivalent fractions for 4/9 are 8/18 and 12/27.
 

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

Problem 2

Check if 5/10 and 7/14 are equivalent.

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

5/10 and 7/14 are equivalent fractions.
 

Explanation

To check if the given fractions are equivalent, we cross-multiply them:
5 × 14 = 70
7 × 10 = 70
Here, both products are equal, so we can confirm that they are equivalent.
 

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

Problem 3

Convert 3/8 to an equivalent fraction with denominator 24.

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

We convert 3/8 into 9/24, which is equivalent to 3/8.
 

Explanation

To obtain a denominator of 24, we look for the number that makes 8 into 24:
8 ×  3 = 24
Now, we multiply the numerator by the same number:
3 x 3 / 8 x  3  = 9/24
Therefore, 9/24 is equivalent to 3/8.
 

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

Problem 4

You have 15 pieces of cake, and you eat 5 pieces. The fraction of cake you ate is 5/15. What portion have you eaten?

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

 1/3
 

Explanation

We simplify the given fraction:
The GCD of 5 and 15 is 5.
Now, both the numerator and denominator are divided by 5:
5 ÷ 5 / 15 ÷ 5  = 1/3
The fraction can be simplified into 1/3 which means you ate 1/3 of the cake.
 

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

Problem 5

Simplify 32/ 64 to its lowest terms.

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

32/64 = 1/2 
 

Explanation

We express the given fraction in its simplest form using the steps mentioned below:
Find the GCD:
The GCD of 32 and 64 is 32
Division:
Now, we divide both numerator and denominator by their GCD:
32 ÷ 32 / 64 ÷  32  = 1/2
 

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

FAQs on Equivalent Fractions

1.What do you mean by equivalent fractions?

Math FAQ Answers Dropdown Arrow

2.Can we check if two fractions are equivalent?

Math FAQ Answers Dropdown Arrow

3.What is the easiest way to generate equivalent fractions?

Math FAQ Answers Dropdown Arrow

4.What is the significance of equivalent fractions?

Math FAQ Answers Dropdown Arrow

5.How can we create infinite equivalent fractions?

Math FAQ Answers Dropdown Arrow

6.How can children in Thailand use numbers in everyday life to understand Equivalent Fractions?

Math FAQ Answers Dropdown Arrow

7.What are some fun ways kids in Thailand can practice Equivalent Fractions with numbers?

Math FAQ Answers Dropdown Arrow

8.What role do numbers and Equivalent Fractions play in helping children in Thailand develop problem-solving skills?

Math FAQ Answers Dropdown Arrow

9.How can families in Thailand create number-rich environments to improve Equivalent Fractions skills?

Math FAQ Answers Dropdown Arrow
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