Page 52 - Mathematics of Business and Finance

32 Chapter 1 | Review of Basic Arithmetic

Solution (i) 3 × 4 = 3 × 4 2 Dividing by common factors between the numerators and
2 11 2 11 denominators,
1
3 2 Multiplying the numerators together and denominators together
= ×
1 11 to get the new fraction,
6
=
11

3 4 6
Therefore, the result of × is .
2 11 11

1
(ii) 3 × 2 4 5 Converting the mixed numbers to improper fractions,
8
(3 × 8) + 1 (2 × 5) + 4
= ×
8 5
25 14 5 25 14 7 Dividing by common factors between the numerators and
= × = ×
8 5 8 5 denominators,
4 1

5 7 Multiplying the numerators together and denominators
= ×
4 1 together to get the new fraction,
35 Converting the improper fraction to a mixed number,
=
4

= 8 3 4

3
4
1
Therefore, the result of 3 × 2 is 8 .
4
5
8
Dividing Fractions
When dividing fractions,
When a fraction is
inverted, the resulting Step 1: Convert any mixed numbers to improper fractions.
fraction is called the
reciprocal of the Step 2: Simplify the fractions, if possible.
original fraction.
Step 3: Multiply the first fraction by the reciprocal of the second fraction.

1
Note: Dividing by 2 is the same as multiplying by the reciprocal of 2, which is .
2

Example 1.3(f) Dividing Fractions
Divide:
15 9 3 4
(i) by (ii) 3 by 1
16 20 20 5

Solution (i) 15 9 15 9 20
9
16 ÷ 20 Multiplying 16 by the reciprocal of 20 , which is ,
15 20 5 15 20 5 Dividing by common factors between the numerators and
= × = ×
16 9 16 9 denominators,
4 3