Multiplication of a fraction by a whole number, Multiplication of a fraction using the operator ‘of’, Multiplication of a fraction by another fraction

**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 1*kg* 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 )

Tags : Fractions | Term 3 Chapter 1 | 6th Maths , 6th Maths : Term 3 Unit 1 : Fractions

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6th Maths : Term 3 Unit 1 : Fractions : Multiplication of Fractions | Fractions | Term 3 Chapter 1 | 6th Maths

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