Page 29 - Maths Skills - 7

Fractions and Decimals 27

3 34× 12 5
× 4 = = = 1
7 7 7 7
● When multiplying a mixed fraction by a whole number, we first convert the mixed fraction into an improper
fraction and then multiply.
5 26 Fact-o-meter
4
For example, 3 × = × 4
7 7 Product of numerators
26 4× 104 6 Product of fractions = Product of denominators
= = = 14
7 7 7
(ii) Multiplying a Fraction by Another Fraction
To multiply a fraction by another fraction, we multiply the corresponding numerators and denominators.

7 13 713× 91 19
For example, let us multiply × = = = 2
9 4 94× 36 36
1 11 13 11 13 11 143× 3
Now multiply, 3 × = × = = = 7 .
4 5 4 5 45× 20 20

FRACTION AS AN OPERATOR ‘OF’
If I tell you to give me the one-fourth of your pizza, you may easily do it by dividing the pizza into four equal
parts and give me one part. Now, let us change the situation. You have one rupee note and I ask you to give me
one-fourth of a rupee. What will you do? Are you going to tear the note into four equal parts and give me one
part? Certainly not! Here, you need to change the one-rupee into paise before you divide it into four equal parts.
So, 1 rupee = 100 paise

1
1
1 of 1 rupee = of 100 paise = × 100 = 25 paise
4 4 4
There are two ways of finding a fraction of a quantity.

Divide the quantity by the denominator of the fraction and multiply the result by the numerator
Method 1:
of the fraction.
Method 2: Change ‘of’ to ‘×’ and multiply.

PROPERTIES OF MULTIPLICATION OF FRACTIONS

1. Multiplicative property of zero: Any fraction multiplied by 0 gives the product 0.
0
0
For example; (i) 1 × 0 = = 0 (ii) 15 ×= 15 0× = 0 = 0
3 3 5 5 5
2. Multiplicative property of 1: Any fraction multiplied by 1 gives the fraction itself.

For example; 8 ×= 81× = 8
1
19 19 19
3. Commutative law: Multiplication of two fractions is commutative, i.e., two or more fractions can be
multiplied in any order, their product remains the same.

1 2 12× 2 2 1 21× 2
For example; × = = and ×= =
5 7 57× 35 7 5 75× 35
So, the product remains the same irrespective of the order.