Page 53 - Mathematics of Business and Finance

Chapter 1 | Review of Basic Arithmetic 33

5
Solution (i) 3 × 4 = 3 × 4 2 Dividing by common factors between the numerators and Solution = × 5 Multiplying the numerators and the denominators,
2 11 2 11 denominators, continued 4 3
1
25
3 2 Multiplying the numerators together and denominators together = Converting the improper fraction to a mixed number,
= × 12
1 11 to get the new fraction,
6 1
= = 2
11 12

1
3 4 6 Therefore, the result of 15 divided by 9 is 2 .
Therefore, the result of × is . 12
2 11 11 16 20
(ii) 3 3 ÷ 1 4 Converting the mixed numbers to improper fractions,
1
(ii) 3 × 2 4 5 Converting the mixed numbers to improper fractions, 20 5
8
63 9 63 9 5
(3 × 8) + 1 (2 × 5) + 4 = ÷ Multiplying by the reciprocal of , which is ,
9
= × 20 5 20 5
8 5
63 5 7 63 5 1 Dividing by common factors between the numerators and
25 14 5 25 14 7 Dividing by common factors between the numerators and = × = × denominators,
= × = × 20 9 20 9
8 5 8 5 denominators, 4 1
4 1
7 1
5 7 Multiplying the numerators together and denominators = × Multiplying the numerators and the denominators,
= × 4 1
4 1 together to get the new fraction,
7 Converting the improper fraction to a mixed number,
35 Converting the improper fraction to a mixed number, =
= 4
4
= 1 3 4
= 8 3 4

3 4 3
Therefore, the result of 3 divided by 1 is 1 .
4
1
3
Therefore, the result of 3 × 2 is 8 . 20 5 4
4
5
8
Dividing Fractions Converting a Complex Fraction into a Proper or Improper Fraction
When dividing fractions, A complex fraction can be converted to a proper or improper fraction by dividing the numerator by
When a fraction is the denominator and then simplifying the expression.
inverted, the resulting Step 1: Convert any mixed numbers to improper fractions.
fraction is called the For example,
reciprocal of the Step 2: Simplify the fractions, if possible.
original fraction.
7
Step 3: Multiply the first fraction by the reciprocal of the second fraction. d n 8
7
7
9
1
2
■ 2 = ÷ 5 = × = 7 ■ = 8 ÷ = 8 × = 16
1 5 2 2 5 10 9 2 9 9
Note: Dividing by 2 is the same as multiplying by the reciprocal of 2, which is . d n
2 2
Example 1.3(f) Dividing Fractions
1.3 Exercises Answers to the odd-numbered problems are available at the end of the textbook.
Divide:
15 9 3 4
(i) by (ii) 3 by 1 CONVERTING A MIXED NUMBER INTO AN IMPROPER FRACTION
16 20 20 5
1. Convert the following mixed numbers into improper fractions:
Solution (i) 15 9 15 9 20 2 6 4 3
9
16 ÷ 20 Multiplying 16 by the reciprocal of 20 , which is , a. 5 3 b. 5 7 c. 6 5 d. 4 4
15 20 5 15 20 5 Dividing by common factors between the numerators and 2. Convert the following mixed numbers into improper fractions:
= × = ×
16 9 16 9 denominators,
4 3 a. 1 3 8 b. 12 3 4 c. 7 3 5 d. 9 2 3