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How to divide whole numbers by fractions

Want to find out how to divide whole numbers by fractions? We've provided a step-by-step guide of how to divide whole numbers by fractions to teach you everything you need to know.

Step 1: Find the reciprocal of the fractions

To do this, we switch the numerator and the denominator. For example, to divide 56 by 8/9 , we first find the reciprocal of 8/9.

Step 2: Multiply whole number with reciprocal

Multiply the whole number with the reciprocal. So, we have:

Step 3: Cancel common factors

Cancel out common factors from the numerator and denominator then simplify the product. We can only cancel common factors from the denominator and either the whole number or numerator.

This means that 56 divided by 8/9 is equal to 63.

Examples of dividing fractions by whole numbers

Q1) Divide the following whole numbers and fractions. a. 144÷ 2/3 b. 625÷ 25/27

Find the reciprocal of the divisor (fraction after ÷).

Reciprocal of 2/3=3/2 Reciprocal of 25/27=27/25

Once we have the reciprocal, multiply the whole number with the reciprocal. 144÷ 2/3 625÷ 25/27

=144× 3/2 =625× 27/25

Find common factors that can be cancelled between the denominator and either the whole number or numerator. Simplify and find the product.

144÷ 2/3 625÷ 25/27

=144× 3/2 =625× 27/25

=72× 3/1 =25× 27/1 =216 =675

Hence, we have the following quotients. 144÷ 2/3=216 625÷ 25/27=675

Q2) John is planning to join a 10-k marathon and as part of his preparation, he intends to walk a total of 9/10 km every day. How many days would it take him to cover 45 km in total?

To find the number of days that it will for John to cover 45 km, we divide 45 by 9/10: 45 ÷ 9/10

Multiply 45 by the reciprocal of 9/10. 45 × 10/9

Cancel common factors and multiply the remaining factors. 45 ÷ 9/10 =45 × 10/9 =5 × 10/1=50

This means that it will take John 50 days to cover 45 km.