Page 50 - Mathematics of Business and Finance

30 Chapter 1 | Review of Basic Arithmetic

Solution Alternative Method
continued
5
5
3 + 1 Separating the whole numbers and the fractions,
6
9
5 5 The LCM of 6 and 9 is 18 (i.e. LCD = 18). Determining the
= (3 + 1) + e + o
6 9 equivalent fractions using the LCD of 18,
15 10
= (3 + 1) + e + o Adding the whole numbers and the fractions,
18 18
25
= 4 + Converting the improper fraction to a mixed number,
18
7
= 4 + 1 18 Adding the whole numbers,
7
= 5 18
5
7
5
Therefore, the result of adding 3 and 1 is 5 .
6
18
9
Subtracting Fractions
The process for subtracting fractions is the same as that for adding of fractions.
Step 1: Determine the LCD.

Step 2: Convert each fraction to its equivalent fraction with the LCD as the common denominator.
Step 3: Subtract the numerators of the equivalent fractions, keeping the LCD as the denominator.
(That is, the resulting fraction will have the common denominator, and its numerator will be
the difference of the numerators of the equivalent fractions.)

Express the final answer reduced to its lowest terms and as a mixed number, where applicable.

Example 1.3(d) Subtracting Fractions
2 7 2 1
(i) Subtract from (ii) Subtract 7 from 12
8 10 3 2

Solution (i) 7 2 The LCM of 8 and 10 is 40 (i.e. LCD = 40). Determining the
10 – 8 equivalent fractions using the LCD of 40,

28 10 Subtracting the numerators and keeping the common denominator,
= –
40 40
18 18 9 Reducing to lowest terms,
= =
40 40
20
9
=
20
2 7 9
Therefore, the result from subtracting from is .
8 10 20

1
(ii) 12 – 7 2 3 Converting the mixed numbers to improper fractions,
2
(12 × 2) +1 (7 × 3) + 2
= –
2 3