Last updated on July 4th, 2025
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 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.
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. |
We use different methods to determine if the fractions are equivalent or not. Let’s learn each of them:
In this method, we make the denominators equal by finding their LCM.
For a better understanding, here’s an example:
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 shaded portions of the four rectangles represent the same value. So they are equivalent fractions.
To find the equivalent fractions, we multiply or divide both the numerator and denominator using the same number.
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.
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.
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
The concept of equivalent fractions can be applied and used in various fields. Here are a few real-life applications of 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:
Determine two equivalent fractions for 4/9
Two equivalent fractions for 4/9 are 8/18 and 12/27.
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.
Check if 5/10 and 7/14 are equivalent.
5/10 and 7/14 are equivalent fractions.
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.
Convert 3/8 to an equivalent fraction with denominator 24.
We convert 3/8 into 9/24, which is equivalent to 3/8.
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.
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?
1/3
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.
Simplify 32/ 64 to its lowest terms.
32/64 = 1/2
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
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.
: She loves to read number jokes and games.