# Division of a Whole Number by a Fraction

This topic discusses about division of a whole number by a fraction. In this we have to divide the whole number that is positive integers including zero by a fractional number. When dividing a whole number by a fraction we actually multiply the whole number by the multiplicative inverse or reciprocal of the fraction. After that the steps are same as we do in multiplication. That is the numerator is multiplied by another numerator and denominator by another denominator that is Product of the numerators/ product of the denominators. Then the answer is changed into lowest terms (if possible) and the final answer is expressed in mixed fraction (if it is an improper fraction) or in proper fraction.

Here are few examples to illustrate division of whole numbers by a fraction:

1. 250 ÷ 50/8

= 250 × 8/50 [reciprocal of 50/8]

= (250 × 8)/50 [Product of numerators and denominator]

= 2000/50

= (2000 ÷ 50)/(50 ÷50) [Changing into lowest terms]

= 40

2. 343 ÷ 49/3

= 343 × 3/49 [Reciprocal of 49/3]

= (343 × 3)/49 [Product of numerators and denominator]

= 1029/49

= (1029 ÷ 49)/(49 ÷49) [Changing into lowest terms]

= 21

3. 156 ÷ 8/3

= 156 × 3/8 [Reciprocal of  8/3]

= (156 × 3)/8 [Product of numerators and denominator]

= 468/8

= (468 ÷ 4)/(8 ÷4) [Changing into lowest terms]

= 117/2

= 58 1/2

4. 16 ÷ 4/3

= 16 × 3/4 [Reciprocal of  4/3]

= (16 × 3)/4 [Product of numerators and denominator]

= 48/4

= (48 ÷4)/(4 ÷4) [Changing into lowest terms]

= 12

5. 96 ÷ 6/5

= 96 × 5/6 [Reciprocal of  6/5]

= (96 × 5)/6 [Product of numerators and denominator]

= 480/6

= (480 ÷6)/(6 ÷6) [Changing into lowest terms]

= 80

6. 108 ÷ 9/12

= 108 × 12/9 [Reciprocal of  9/12]

= (108 × 12)/9 [Product of numerators and denominator]

= 1296/9

= (1296 ÷9)/(9 ÷9) [Changing into lowest terms]

= 144

7. 324 ÷ 36/12

= 324 × 12/36 [Reciprocal of  36/12]

= (324 × 12)/36 [Product of numerators and denominator]

= 3888/36

= (3888 ÷ 36)/(36 ÷ 36) [Changing into lowest terms]

= 108

8. 256 ÷ 18/12

= 256 × 12/18 [Reciprocal of  18/12]

= (256 × 12)/18 [Product of numerators and denominator]

= 3072/18

= (3072 ÷ 6)/(18 ÷ 6) [Changing into lowest terms]

= 512/3

It is an improper fraction hence should be changed into mixed fraction

= 170 2/3

9. 1424 ÷ 15/3

= 1424 × 3/15 [Reciprocal of  15/3]

= (1424 × 3)/15 [Product of numerators and denominator]

= 4272/15

= (4272 ÷ 3)/(15 ÷ 3) [Changing into lowest terms]

= 1424/5

It is an improper fraction hence should be changed into mixed fraction

= 284 4/5

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