103 LearnersLast updated on July 4th, 2025
Equivalent Fractions
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.
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.
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:
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Equivalent Fractions |
Equal Fractions |
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Indicate the same value, but have different numerators and denominators. |
Have the same numerator and denominator. |
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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. |
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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. |
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Obtained by dividing or multiplying the numerators and denominators by the same number. |
Since they are naturally the same, no calculations are required. |
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.
How to Find Equivalent Fractions?
To find the equivalent fractions, we multiply or divide both the numerator and denominator using the same number.
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.
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.
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
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.
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
Not Using the Same Number to Divide or Multiply
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
Misusing Cross-Multiplication
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
Multiplying or Dividing by Zero
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
Forgetting to Simplify the Fraction
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
Misinterpreting the Rules for Multiplication
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
Solved examples of Equivalent Fractions
Problem 1
Determine two equivalent fractions for 4/9
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.
Problem 2
Check if 5/10 and 7/14 are equivalent.
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.
Problem 3
Convert 3/8 to an equivalent fraction with denominator 24.
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.
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?
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.
Problem 5
Simplify 32/ 64 to its lowest terms.
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
FAQs on Equivalent Fractions
1.What do you mean by equivalent fractions?
2.Can we check if two fractions are equivalent?
3.What is the easiest way to generate equivalent fractions?
4.What is the significance of equivalent fractions?
5.How can we create infinite equivalent fractions?
6.How can children in Philippines use numbers in everyday life to understand Equivalent Fractions?
7.What are some fun ways kids in Philippines can practice Equivalent Fractions with numbers?
8.What role do numbers and Equivalent Fractions play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve Equivalent Fractions skills?
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.
Fun Fact
: She loves to read number jokes and games.
