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Fractions and Decimals

    Division of Fractions

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7th class > Fractions and Decimals > Division of Fractions

Division of Fractions

John has a paper strip of length 6 cm. He cuts this strip in smaller strips of length 2 cm each. You know that he would get 6 ÷ 2 = strips.

John cuts another strip of length 6 cm into smaller strips of length 32 cm each. How many strips will he get now? He will get 6 ÷ 32 strips.

A paper strip of length 152 cm can be cut into smaller strips of length 32 cm each to give 152 ÷ pieces. So, we are required to divide a whole number by a fraction or a fraction by another fraction. Let us see how to do that.

Let us find, 3 ÷ 14. This is nothing but the number of 14 parts obtained when each of the 3 whole, are divided into 14 equal parts = (From below figure)

Observe also that, 3 × 41 = 3 × 4 = . Thus, 3÷ 14 = 3 × 41 =

Take the fraction number: 21. What should be the number multiplied to 21 to get a product equal to 1? .

Similarly, for 31 how to get a product of 1? we multiply 31 with .

The non-zero numbers whose product with each other is 1, are called the reciprocals of each other.

So reciprocal of 59 is .

What is the receiprocal of 19? and 27 ?

Instruction

Will the reciprocal of a proper fraction be again a proper fraction?
Will the reciprocal of an improper fraction be again an improper fraction?
Therefore, we can say that: 1 ÷ 12 = 1 × 21 = 1 × reciprocal of .
3 ÷ 14 = 3 × 41 = 3 × reciprocal of .
3 ÷ 12 = 3 × = 3 × reciprocal of .
2 ÷ 34 = 2 × reciprocal of = 2 × .
5 ÷ 29 = 5 × reciprocal of = 5 ×

Thus, to divide a whole number by any fraction, multiply that whole number by the reciprocal of that fraction.

While dividing a whole number by a mixed fraction, first convert the mixed fraction into improper fraction and then solve it.

Try these

(i) Find 4 ÷ 2 25

Instruction

4÷225

  • We have 4 ÷ 225=
  • We first convert the mixed fraction into improper which gives us
  • Taking the reciprocal for the division
  • Simplifying
  • Therefore, we have found the answer.

Instruction

Find : (i) 7 ÷ 25
7 ÷ 25 = 7 × =
(ii) 6 ÷ 47 = 6 × =
(iii) 2 ÷ 89 = 2 × =
(iv) 6 ÷ 5 13 = 6 × =
(iv) 7 ÷ 2 47 = 7 × =

(i) What will be 34 ÷ 3?

As you can see, we have shaded 34 part of a circle. Now if that 34th part of the circle is divided into 3 equal parts, how much will each part be? You can move the 3 parts and see that they are of the circle.

Imagine a circle divided into 4 equal parts. If 34 of the circle is shaded, you have 3 out of 4 parts shaded.

Now, divide this shaded 34 of the circle into 3 equal parts.

To find out how much each part is, you divide the shaded 34 by 3. This can be represented mathematically as:

34 ÷ 3 = 34 × 13 =

Instruction

34÷3

  • We take the reciprocal of 3 which is
  • Thus, 34÷3 =
  • Multiplying and simplifying
  • We have found the answer

(i) We can now find 85 ÷ 23?

Instruction

85÷23

  • We take the reciprocal of 23 which is
  • Thus, 85×32 =
  • Simplifying we get, the fraction is
  • We have found the answer

(ii)We can now find 13 ÷ 65?

Instruction

13÷65

  • We take the reciprocal of 65 which is
  • Thus, 13×56 =
  • We have found the answer

TRY THESE

Instruction

Find: 35 ÷ 12
35 ÷ 12 = 35 × reciprocal of 12 = 35 ×
35 × 21 =

Instruction

Find: 12 ÷ 35
12 ÷ 35 = 12 × reciprocal of 35 = 12 ×
12 × 53 =

While dividing mixed fractions by whole numbers, convert the mixed fractions into improper fractions.

Instruction

Find: 2 12 ÷ 35
= 52 × reciprocal of 35 = ×
52 × 53 =

Instruction

Find: 5 16 ÷ 92
= × reciprocal of 92 = ×
316 × 29 =