Page 76 - ICSE Math 5

• Equivalent fractions: Fractions which have
the same value or represent the same part
of a whole are called equivalent fractions.
4
1 2 3
For example, , , and are equivalent
2 4 6 8 1 2 1 2 3 4
fractions. They can be written as = = 2 4 6 8
2 4
4
3 = .
6 8
• Proper fractions: Fractions in which the Top Tip
numerator is less than the denominator • The value of a proper fraction is
are called proper fractions. always less than 1.
For example, 11 5 , 6 18 and 3 are • The value an improper fraction is
,
,
18 19 11 19 14 always greater than or equal to 1.
proper fractions.
• Improper fractions: Fractions in which the numerator is greater than or equal to the
denominator are called improper fractions.

For example, 13 3 21 17 and 11 are improper fractions.
, ,
,
5 2 19 10 11
• Mixed fractions: Fractions which are a combination of a whole number and a proper fraction
are called mixed fractions or mixed numbers.

4 7 4 8
For example, 3 , 2 , 1 and 7 are mixed fractions.
17 15 19 11
Reciprocal of a Fraction

The reciprocal of a fraction is obtained by turning the given fraction upside down or by
interchanging the numerator and the denominator of the fraction. For example, the reciprocal
7 15 1 3
of is and the reciprocal of is .
15 7 3 1
Finding Equivalent Fractions

We can find the equivalent fractions of a given fraction in two different ways.

1. By multiplying both the numerator and the denominator of the fraction by the same
number (other than 0).
1
For example, let’s find three equivalent fractions of by multiplying.
3
3 1
1 = 1 × 2 = ; = 1 × 3 = ; = 1 × 4 = 4
2 1
3 3 × 2 6 3 3 × 3 9 3 3 × 4 12
2 3 4 1
So, , and are the equivalent fractions of .
6 9 12 3
1 2 3 4
This can also be written as = = = .
3 6 9 12
2. By dividing both the numerator and the denominator of the fraction by the same number
(other than 0).

66