Multiplication of Fractions

Multiplication of Fractions

Think about the situation 1 (Multiplication of a fraction by a whole number)

Sunitha wanted to give 1/4 kg of sweets to each of her 3 friends. So she went to a sweet stall and she asked the salesman to give three 1/4 kg packets of sweets, how much sweet did she buy?

Solution

Weight of three 1/4 kg packets of sweets = 1/4 + 1/4 + 1/4 = [1 + 1 + 1] / 4 = 3/4 kg

We can illustrate this in the following diagram. In each of these the shaded part is 1/4 of a circle. Can you find the shaded parts in 3 circles together?

To know the fraction of shaded part in all the three circles, we add the fractions which are represented in each of the circles. So 3 × 1/4 = 3/4 .

The adjacent circle represents 3/4 parts of the circle.

Think about the situation 2 (Multiplication of a fraction using the operator ‘of’)

Kannan has 30 beads and Kanmani has one sixth of it. How many beads does Kanmani have?

Solution

The number of beads that Kanmani has = 1/6 of 30 beads

                                                                = 1/6 × 30 = 30/6

                                                                 = 5 beads

Think about the situation 3 (Multiplication of a fraction by another fraction)

Sunitha bought three 1/4  kg sweet packets for her three friends from a sweet stall. But 6 of her friends had come to her home. So she decided to divide each1/4 kg sweet packets into halves. If she has done in that way, what would be the weight of the sweet packet  that each one of her friend will receive?

Solution

The weight of the sweet packets that each one of her friends will receive = half of 1 / 4 kg

= 1 / 2 of 1 / 4 kg

= 1/2 × 1/4

The product 1/2 and 1/4 means 1/2 of 1/4. This can be illustrated as follows. We shade  1 part out of 4 parts which represents 1/4. Now divide this horizontally into 2 equal parts  and shade one part of it.

Here, the double shaded part represents the product 1/8 and it is got by finding the product of the numerators and the product of denominators as follows:

1/2 × 1/4  = [1 × 1] / [2 × 4] = 1 / 8

Example 16

Maruthu, a milk man has 4 bottles of milk each containing 1 1/2 litres. How  much milk does he have in all?

 Solution

Since Maruthu has 4 bottles of milk and each containing 1 1/2 litres, he has 4  times of 1 1/2 litres of milk.

1 ½ × 4 = ( 1 + ½ ) × 4 = 4 + 4/2

= 4 + 2 = 6 litres.

Example 17

A man wants to fill 3 3/4  kg of rice equally in 3 bags. How much rice does each bag contain?

Solution

Think

2 ¼  × 3 is not equal to 6 ¼ . Why?

Example 18

 In a juice shop, if a man prepared 1 1/2 litres of juice from 1  kg of oranges, then how many litres of juice can be prepared from 12 3/4  kg of oranges?

 Solution  

 The quantity of juice prepared from 1kg of oranges = 1 ½  litres

The quantity of juice prepared from 12 3/4   kg of oranges = 12 3/4  × 1 1/2

                                                                                             = 51/4 × 3/2 = 153/8

                                                                                            = 19 1/8 litres

Try these

i) Simplify: 35 × 3/7

35 × 3/7 = 15

ii) Find the value of 1/5 of 15.

15 × 1/5 = 3

iii) Find the value of 1/3 of 3/4

3/4 × 1/3 = 1/4

iii) Multiply 7 ¾ by 5 ½

31/4 × 11/2 = 341/8

= 42 5/8 

Activity

Take a paper. Fold it into 4 parts vertically of equal width. Shade one part of it with red. Then, fold it into 3 parts horizontally of equal width. Shade two parts of it with blue. Now, you count the number of shaded grids which have both the colours.

(Hint: The total number of grids is the product of 2/3 and 1/4 )