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Fraction as Division

Fraction as division is also known as fraction as quotient.

Can you divide a smaller number by a bigger number?

We have learnt how to divide a bigger number by a smaller number.

We know that 12 ÷ 4 = 3.

If you have 12 chocolates and these are distributed equally to 4 children, then each one gets 3 chocolates. If 8 chocolates are distributed to 4 children, the share of each one is 2 chocolates, because 842. When we equally distribute 4 chocolates to 4 children, then each one gets 1 chocolate.

What do you observe from this? The number of children is the same, but the number of chocolates is decreasing. Also, when the number of chocolates is decreasing, then the share for each one is decreasing.

$1 Chocolate$

Let us consider the following situation, where there is only 1 chocolate and it is to be distributed equally among 4 children.

The chocolate can be divided into 4 equal parts and 1 part can be given to each child.

$1/4 Fraction$

Here, no child is getting 1 whole chocolate, rather each one is only getting a part of the 1 whole chocolate. The share of each one is $\frac{1}{4}$, as there are four equal parts and each one is getting one part.

$\frac{1}{4}$ is the result obtained when 1 is divided by 4.

Let us consider the another situation, in which there are 3 chocolates in a packet and these chocolates are to be distributed equally to 4 children.

$3 Chocolates$

This can be done in the following way:

1. Divide each of the three chocolates into 4 equal parts.

$Three Chocolates into 4 Equal Parts$

2. Count the total numbers of parts (pieces) obtained, here 12 parts.

$12 Parts of Chocolate$

3. Divide these 12 parts among 4 children equally.

$Divide 12 Parts Among 4 Children$

4. Each child gets 3 parts after division, i.e., 3 parts out of 4 of a chocolate. In other words, each child gets 3/4 of a chocolate.

Now, the above description is represented in a tabular form as follows:

$Number of chocolates divided equally to 4 children$

Now, we can say that it is possible to divide a smaller number by a bigger number. The result in these cases is not a whole number, it is only a part of a whole or a fraction.

So, $\frac{1}{4}$ is the same as 1 ÷ 4,

$\frac{3}{4}$ is the same as 3 ÷ 4.

Examples on Fraction as division

If 8 biscuits are distributed between 2 children equally, then each of them will get 8 ÷ 2 = 4 biscuits.

If 4 biscuits are distributed between 2 children equally, then each of them will get 4 ÷ 2 = 2 biscuits.

If 1 biscuit is to be shared between 2 children equally, then each one of them will get 1/2 (1 ÷ 2) biscuits.

Similarly,

If 5 apples are distributed between 2 children equally, then each one will get 5 ÷ 2 or 5/2 apples.

For examples the divisions can be expressed as fractions.

(i) 8 ÷ 2 = 8/2;

(ii) 12 ÷ 4 = 12/4

(iii) 5 ÷ 3 = 5/3

(iv) 15 ÷ 5 = 15/5

(v) 11 ÷ 19 = 11/19

(vi) If Sufi has 3 cookies and she wants to give equal share to Rachel, what share both will get? We divide 3 by 2. It is written as fraction $\frac{3}{2}$.

1. For examples the fractions can be expressed as division.

(i) 9/7 = 9 ÷ 7

(ii) 3/11 = 3 ÷ 11

(iii) 90/63 = 90 ÷ 63

(iv) 1/5 = 1 ÷ 5

(v) 14/17 = 14 ÷ 17

2. Express each of the following fractions as division:

(i) $\frac{1}{7}$

(ii) $\frac{3}{8}$

(iii) $\frac{11}{15}$

Solution:

(i) $\frac{1}{7}$ = 1 ÷ 7

(ii) $\frac{3}{8}$ = 3 ÷ 8

(iii) $\frac{11}{15}$ = 11 ÷ 15

● Fraction