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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