Equivalent Fractions
Equivalent Fractions
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A fraction is a number stated as a quotient with a numerator divided by a denominator into mathematical terms. A simple fraction is made up of two parts: an integer numerator and a non-zero integer denominator. Equivalent fractions are those with different numerators and denominators but their fractional values are the same. 5/10  and 7/14, for example, are similar fractions because they are both equal to 1 / 2 when simplified. Each fraction represents a part of a whole. If two or more fractions are equal to the same fraction when simplified, they are said to be equivalent.

Improper Fractions

There are three types of fractions,

  • Proper fraction,
  • Improper fraction, and
  • Mixed fraction.
  • Proper Fraction
  • When the value in the numerator is smaller than the value in the denominator it is a proper fraction. For example ⅗, ⅚, ⅞, are all proper fractions.
  • Improper Fraction

If the numerator is equal to greater than the denominator it is called the improper fraction. For example 8/5, 7/7, 9/4 are all improper fractions.

  • Mixed Fraction

When a whole number and a fraction are together then it is a mixed fraction. For example, 2 ¾,5 ⅓,4 ⅖ are mixed fractions.

How to Find Equivalent Fractions?

There are two ways in which you can find the Equivalent Fractions

  • Multiplication Method
  • Division Method

1. Multiplication Method

Step 1: Multiply both the numerator and denominator of a fraction by the same whole number.

Step 2: If you multiply the top and bottom of the fraction by the same number, you will not change the value of the fraction.

Example on Equivalent Fractions

Find fractions equivalent to ⅖ by multiplying the numerator and denominator by the same whole number


Multiplying the numerator and denominator by 3


Multiplying the numerator and denominator by 4


Multiplying the numerator and denominator by 5


Multiplying the numerator and denominator by 6


Therefore these are all equivalent fractions:

2/5,  6/15, 8/20, 10/25 ,12/30

In the lowest terms, all of these fractions equal 2/5.

2. Division Method

Step 1: Divide the numerator and denominator of any fraction by the same number to find the equivalent fraction.

Example: Find an equivalent fraction of 60/90.


2 is a common factor of 60 and 90.

Thus, 60/90=



= 30/45

Again, 3 is a common factor of 30 and 45.




= 10/15

Here, 5 is a common factor of 10 and 15.

Thus, 10/15=



= 2/3

Therefore, a few equivalent fractions of 60/190 are 30/45, 10/15, 2/3,

Understanding Improper Fractions with Examples

Converting Mixed Fractions to Improper Fractions

To convert a mixed fraction to an improper fraction, follow these steps:

  1.  The whole number part is multiplied by the denominator.
  2.  Add that to the numerator
  3. Add the result to the denominator.

Example: Convert 4  to an improper fraction.

Solution: In multiplying the whole number by the denominator, you get:

4 × 5 = 20

Add that to the numerator:

20 + 3 = 23

Then write that result above the denominator:

∴ Fraction 4  = 23/5

Converting Improper Fractions to Mixed  Fractions

In order to  convert an improper fraction to a mixed fraction, follow these steps:

  1. Divide the numerator by the denominator.
  2. Write down the whole number answer
  3. Then write down any remainder above the denominator.

Example: Convert to a mixed fraction.


Divide 13 by 5 the remainder will be 3 and the quotient will be 2

First, write down the quotient  2 and then write down the remainder (3) above the denominator (5).

∴ Fraction   = 2

If you want to learn more about equivalent fractions and improper fractions visit Cuemath.

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