July 25, 2024


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Equivalent Fractions

Teaching Equivalent Fractions - TeachableMath

Are the fractions 4/5 and 36/45 equal? At first glance, you might answer that both the fractions are different. However, if you find out the values of both the fractions, you will get to know that both the fractions have equal values. The fractions that have different values of numerator and denominator, but the resultant of which comes out to be equivalent are called equivalent fractions

Examples of equivalent fractions are 1/2 and 1000/2000, 3/4 and 9/16, etc.

Why Equivalent Fractions are Always the Same?

The equivalent fractions are always the same because when we divide or multiply both the numerator and denominator with the same number, we are always left with the same fraction value.

Rule to Remember 

Change the denominator using multiplication or division. And the same will be applied to the numerator.

For Example: 

1 × 22 × 2 = 24 = 2 × 24 × 2 = 48

18 ÷ 336 ÷ 3 = 612 = 6 ÷ 312 ÷ 3 = 2 ÷ 24 ÷ 2 = 12

Improper Fraction

The fractions in which the value of the denominator is smaller than the value of the numerator are called improper fractions. If the value of the numerator is equal to the value of the denominator, then also it is called an improper fraction. The improper fractions can be converted into mixed fractions to make them look more presentable. Examples of improper fractions are 13/4, 56/6, 78/6, 43/2, etc. Learn more about this topic at cuemath.

How Do You Convert Improper Fractions into Mixed Fractions?

Following are the steps to convert improper fractions into mixed fractions:

  • Carry the operation of division using the numerator and the denominator of the improper fractions.
  • The numerator will be treated as the dividend and the denominator will be treated as the divisor of the improper fraction.
  • Remember, While dividing improper fractions, the remainder will never be equal to zero.
  • Arrange the quotient, the remainder, and the divisor in the manner given below to write the improper fraction in the form of a mixed fraction: 

Quotient RemainderDivisor.

How To Convert Mixed Fractions into Improper Fractions?

Following are  the steps  to convert mixed fractions into improper fractions:

  • A mixed fraction will be given to you. Perform the operation of multiplication and then addition using the values of the mixed fraction. 
  • Multiply the divisor with the quotient and then add the remainder value to the product. 
  • Hence, the improper fraction value will be obtained.

Conversion of Improper Fractions Into  Mixed Fractions Example

  1. Convert 55/2 into a mixed fraction.


We will divide 33 by 2. The values obtained after division will be as follows: 

Quotient = 11, Remainder = 10, Divisor = 2. 

We will arrange these values in the form of a mixed fraction.

Thus, the required answer will be 11102

Conversion of Mixed Fractions Into Improper Fractions Example

  1. Convert 26½ into an improper fraction.


We will multiply the divisor with the quotient. That means 2 will be multiplied with 26. We will get the product 52

After the operation of multiplication, we will then add the 52 obtained in the previous step with the remainder. Hence, the value of the numerator will be ( 52 + 1 = 53)

Thus, the required answer will be 53/2.