Division of a Whole Number by a Fraction

We will discuss here about division of a whole number by a fraction.

Look at the collection of circles. It has 8 circles.

Collection of Circles

How many two’s are there in 8?

How many two’s are there in 8? So we find there are 4 two in 8.

Now what does the following statement mean?

How many halves are there in 8? To find this, let us divide each of the 8 circles into halves.

Circles into Halves

We find there are 16 halves in 8

So, the answer is 8 ÷ ½ = 16

i.e. = 8 ÷ ½ = 8 × 2/1 = 8 × 2/1 = 16

Therefore, the rules for the division of a whole number by a fractional number is

Whole Number ÷ Fraction = Whole Number × Reciprocal of Fraction.

Hence, we conclude that to divide whole number by a fractional number, we multiply the whole number by multiplicative inverse of the fractional number.

Note: Wherever mixed numbers are used first change them into improper fractions.

For Example:

1. 4 ÷ 1/3

[We know, Whole Number × Reciprocal of Fraction]

Reciprocal of Fraction of ‘1/3’ is ‘3’

= 4 × 3

= 12



2. 16 ÷ 2/5

Reciprocal of Fraction of ‘2/5’ is ‘5/2’

= 16 × 5/2

= (16 × 5)/2

Division of a Whole Number by a Fraction




= 8 × 5

= 40



3. 24 ÷ 1 3/5

= 24 ÷ (1 × 5 + 3)/5

= 24 ÷ 8/5

Reciprocal of Fraction of ‘8/5’ is ‘5/8’

= 24 × 5/8




= 3 × 5

= 15



4. 49 ÷ 7/3

Reciprocal of Fraction of ‘7/3’ is ‘3/7’

= 49 × 3/7




= 7 × 3

= 21



5. 11 9/9 ÷ 12/7

= (11 × 9 + 9)/9 ÷ 12/7

= 108/9 ÷ 12/7

Reciprocal of Fraction of ‘12/7’ is ‘7/12’

= 108/9 × 7/12





= 7



6. 91 ÷ 91/34

Reciprocal of Fraction of ‘91/34’ is ‘34/91’

= 91 × 34/91




= 34

Multiplication is Repeated Addition.

Multiplication of Fractional Number by a Whole Number.

Multiplication of a Fraction by Fraction.

Properties of Multiplication of Fractional Numbers.

Multiplicative Inverse.

Worksheet on Multiplication on Fraction.

Division of a Fraction by a Whole Number.

Division of a Fractional Number.

Division of a Whole Number by a Fraction.

Properties of Fractional Division.

Worksheet on Division of Fractions.

Simplification of Fractions.

Worksheet on Simplification of Fractions.

Word Problems on Fraction.

Worksheet on Word Problems on Fractions.




5th Grade Numbers Page

5th Grade Math Problems

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