Division of a Fraction by a Whole Number

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

If

Division of Fraction Math

represent 1

The shaded

Division of Fraction Math 1

portion represents

1 ÷ 2 or ½ of 1 or 1 × ½ = ½

and

Division of Fraction Math 2

represents ½ ÷ 3 or ½ of 1/3 = 1/3 × ½ = 1/6

Therefore, the rules for the division of a fractional number by a whole number is Fraction ÷ Whole number = Fraction × Reciprocal of whole number.

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

For Example:

1. 1/3 ÷ 3

Here 1/3 is the fraction and 3 is the whole number.

[Replace ‘÷’ by ‘×’ sign.

Replace the whole number ‘3’ by its reciprocal ‘1/3’].

= 1/3 × 1/3

= (1 × 1)/(3 × 3)

= 1/9



2. 4/7 ÷ 9

[Replace ‘÷’ by ‘×’ sign.

Replace the whole number ‘9’ by its reciprocal ‘1/9’].

= 4/7 × 1/9

= (4 × 1)/(7 × 9)

= 4/63



3. 1 2/5 ÷ 2

= (1 × 5 + 2)/5 ÷ 2

= 7/5 ÷ 2

[Replace ‘÷’ by ‘×’ sign.

Replace the whole number ‘2’ by its reciprocal ‘1/2’].

= 7/5 × 1/2

= (7 × 1)/(5 × 2)

= 7/10



4. 2 1/7 ÷ 15

= (2 × 7 + 1)/7 ÷ 15

= 15/7 ÷ 15

[Replace ‘÷’ by ‘×’ sign.

Replace the whole number ‘15’ by its reciprocal ‘1/15’].

= 15/7 × 1/15

Division of a Fraction by a Whole Number




= 1/7



5. 19/5 ÷ 37

[Replace ‘÷’ by ‘×’ sign.

Replace the whole number ‘37’ by its reciprocal ‘1/37’].

= 19/5 × 1/37

= (19 × 1)/(5 × 37)

= 19/185



6. 212/8 ÷ 4

= (21 × 8 + 2)/8 ÷ 4

= 170/8 ÷ 4

[Replace ‘÷’ by ‘×’ sign.

Replace the whole number ‘4’ by its reciprocal ‘1/4’].

= 170/8 × 1/4

= (170 × 1)/(8 × 4)

= 170/32

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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