Equivalent Fractions
2026-02-28 12:41 Diff
https://brightchamps.com/en-us/math/numbers/equivalent-fractions

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.