Page 46 - Mathematics of Business and Finance

26 Chapter 1 | Review of Basic Arithmetic

2
For example, to determine two equivalent fractions of :
5
2 2 × 2
= Multiplying both the numerator and denominator by 2,
5 5 × 2
4
=
10
2 2 × 3
= Multiplying both the numerator and
5 5 × 3
denominator by 3,

6
=
15
4 6 2
Therefore, and are equivalent fractions of .
10 15 5
18
Consider another example to determine two equivalent fractions of :
24
18 18 ÷ 2
= Dividing both the numerator and denominator by 2,
24 24 ÷ 2
9
=
12
18 18 ÷ 6
= Dividing both the numerator and denominator by 6,
24 24 ÷ 6
3
=
4
9 3 18
Therefore, and are equivalent fractions of .
12 4 24
Reducing or Simplifying a Fraction

Dividing both the numerator and denominator of a fraction by the same number, which results in an
equivalent fraction, is called reducing or simplifying the fraction.
16
For example, we can simplify as shown:
20
16 16 ÷ 2
= Dividing both the numerator and denominator by 2,
20 20 ÷ 2
8
=
10
8 ÷ 2
= Further dividing both the numerator and denominator by 2,
10 ÷ 2
4
=
5
16 16 ÷ 4
OR, = Dividing both the numerator and denominator by 4,
20 20 ÷ 4
4
=
5
8 4 16
Therefore, and are reduced fractions of .
10 5 20