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227 LearnersLast updated on December 2, 2025
Equivalent Fractions
Equivalent fractions are two or more different fractions that represent the same value. These fractions have different numerators and denominators, but they 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 its lowest terms. For example, fractions such as \({1\over4}, {2\over8}, {3\over12}, \) and \(4\over16\) are equivalent because they can be simplified to \(1\over4\).
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 equal fractions:
| Equivalent Fractions | Equal Fractions |
| Indicate the same value, but have different numerators and denominators. | Have the same numerator and denominator. |
|
For example, and are equivalent when simplified to . |
and 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 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 \(5\over10 \) and \( 8\over 16\) 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.
\({{(5 × 8)} \over {(10 × 8)}} = {40\over 80}\)
\({{(8 × 5)} \over {(16 × 5)}} = {40\over 80}\)
Since both fractions are \(40\over 80\), they are equivalent.
Determining the decimal form of both Fractions
To check if two or more fractions are equivalent, one method is to convert each fraction to decimal form. If the decimal values are the same, then the fractions are equivalent. If they are not equal, then the fractions are not comparable.
Check if \({2 \over 5}, {4 \over 10}, {\text { and }}, {6 \over 15}\)are equivalent fractions.
Converting each fraction to its decimal form:
\({2 \over 5}= 0.4 \)
\({4 \over 10}= 0.4 \)
\({6\over 15} = 0.4 \)
As the three fractions give the same decimal value, they are equivalent fractions.
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 \(5\over 8 \) and \(10\over 16\), cross multiplication is done like this:
\(5 × 16 = 80\)
\(8 × 10 = 80\)
Since both 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: \(1\over 3\).
- The second rectangle is divided into 6 parts, where only 2 parts are shaded: \(2 \over 6\).
- 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: \(4 \over 12\).
In the image, the shaded portions of the four rectangles represent the same value. So they are equivalent fractions.
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How to Find Equivalent Fractions?
Equivalent fractions are formed by multiplying or dividing both the numerator and the denominator of a fraction by the same non-zero number. To find equivalent fractions, we perform the same operation on both the numerator and the denominator. There are two primary methods:
- Multiplying the Numerator and Denominator by the Same Number
- Dividing the Numerator and Denominator by the Same Number
Multiplying the Numerator and Denominator by the Same Number
To find the equivalent fractions, we multiply the numerator and the denominator by the same whole number. For example, let’s find what fractions are equivalent to \(2 \over 3\)?
To find the equivalent fraction, we multiply both 2 and 3 by the same number.
\({2 \over 3} × {2\over 2} = {4\over 6} \)
\({2 \over 3} × {3\over 3} = {6\over9} \)
\({2 \over 3} × {4\over 4} = {8\over 12} \)
\({2 \over 3} × {5\over 5} = {10\over 15} \)
So, the equivalent fractions of \( {2\over 3}\) are \( {4\over 6}, {6\over 9}, {8\over 12}, {\text { and }}{10\over 15}\)
Dividing the Numerator and Denominator by the Same Number
Another method to find equivalent fractions is by dividing both the numerator and the denominator by the same common factor. This process, also known as simplifying a fraction, helps us find the simplest form of a fraction while listing all equivalent fractions.
For example, how to find equivalent fractions for \(72\over 108\)?
To find the equivalent fraction of \(72 \over 108\), start by identifying the common factors of 72 and 108
Dividing 72 and 108 by 2:
\({72\over 108 }÷ {2\over 2} = {36\over 54 } \)
Dividing by 2:
\( {36\over 54 } ÷ {2\over 2} = {18 \over 27} \)
Dividing by 3:
\( {18 \over 27} ÷ {3\over 3} = {6\over 9} \)
Dividing by 3:
\({6\over 9} ÷ {3\over 3} = {2 \over 3}\)
So, the equivalent fractions of \(72 \over 108\) are \( {36 \over 54}, {18 \over 27}, {6 \over 9}, {\text { and }}{2 \over 3}\)
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.
Tips and Tricks to Master Equivalent Fraction
Learning what equivalent fractions are helps students understand how fractions can represent the same value in different forms. Here are some tips and tricks to master equivalent fractions.
- Always apply the same operation to both the numerator and the denominator. Multiply both to find the bigger equivalent fraction and divide both to see the simplified fraction.
- Use cross-multiplication to check if two fractions are equivalent. If cross products match, they are equal.
- Parents can encourage children to draw fraction bars or circles, as visuals make understanding faster and more precise.
- Teachers can regularly assign an equivalent fractions worksheet to improve skills through structured practice.
- Teachers can use concrete models such as paper folding, fraction strips, or counters to help students visualize equivalence.
- Use visual tools like fraction walls or number lines to see how different fractions can represent the same value clearly.
- Students can use the equivalent fractions calculator to determine whether their answer is correct.
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.
\({3\over 8} × 2 = {6\over8}\) (Incorrect)
Solution: Ensure that the numerator and denominator are multiplied or divided by the same number. For example, \({3 × 2 \over 8 × 2 }= {6\over 16}\).
Mistake 2
Misusing Cross-Multiplication.
Students sometimes forget that cross-multiplication results in different products. For example, using cross-multiplication to check if \(4\over 5\) and \(6\over 18\) are equivalent:
\(4 × 18 = 72, 5 × 6 = 30\). So, we conclude that cross-multiplication is not applicable to check the equivalent fractions.
If 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 is not equal to 30.
Mistake 3
Multiplying or Dividing by Zero.
Some students tend to multiply or divide by zero, while finding equivalent fractions.
Example: \({3 \times 0 \over 8 \times 0 }\)
Dividing any number by zero is undefined.
Mistake 4
Forgetting to Simplify the Fraction.
Another common mistake is not simplifying the fraction when 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 \({1\over3} + {1\over3} = {2\over6}\). This is wrong, as the correct answer is \(2 \over 3\). It is important to remember that we should have a common denominator while adding or subtracting fractions.
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 \(1\over 2\) 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.
Solved examples of Equivalent Fractions
Problem 1
Determine two equivalent fractions for 4/9
Two equivalent fractions for \(4 \over 9\) are \(8\over18 \) and \(12\over27\).
Explanation
To find two equivalent fractions, we multiply both the numerator and denominator using the same number:
Let’s multiply by 2:
\({4 × 2 \over 9 × 2} = {8\over18} \)
Now, multiply by 3:
\({4 × 3 \over 9 × 3} = {12\over27}\)
So, the two equivalent fractions for \(4\over9\) are \(8\over18\) and \(12 \over 27\).
Problem 2
Check if 5/10 and 7/14 are equivalent.
\(5 \over 10\) and \(7 \over 14 \) 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 \({{3\over 8}}\) into \( 9\over 24\), which is equivalent to \({{3\over 8}} \).
Explanation
To obtain a denominator of 24, we look for the number that multiplies with 8 to become 24:
\(8 × 3 = 24\)
Now, we multiply the numerator by the same number:
\({3 × 3 \over 8 × 3} = {9\over 24}\)
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?
\( 1\over3\).
Explanation
We simplify the given fraction:
The GCD of 5 and 15 is 5.
Now, both the numerator and denominator are divided by 5:
\({5 ÷ 5 \over 15 ÷ 5} = {1\over3}\)
The fraction can be simplified into \(1\over3\) which means you ate \(1\over3\) of the cake.
Problem 5
Simplify 32/ 64 to its lowest terms.
\({32\over64} = {1\over2 }\)
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:
\({{32 ÷ 32 \over 64 ÷ 32 }} = {{1\over2}} \)
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?
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.
