We will discuss here about division of a whole number by a fraction.
Look at the collection of circles. It has 8 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.
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
= 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.
● 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.
● Worksheet on Word Problems on Fractions.
5th Grade Numbers Page
5th Grade Math Problems
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