Page 51 - Mathematics of Business and Finance

Chapter 1 | Review of Basic Arithmetic 31

Solution Alternative Method Solution 25 23 The LCM of 2 and 3 is 6 (i.e. LCD = 6). Determining the equivalent
continued continued = 2 – 3 fractions using the LCD of 6,
5
5
3 + 1 Separating the whole numbers and the fractions,
9
6
5 5 The LCM of 6 and 9 is 18 (i.e. LCD = 18). Determining the = 75 – 46 Subtracting the numerators and keeping the denominator,
= (3 + 1) + e + o 6 6
6 9 equivalent fractions using the LCD of 18,
15 10 29 Converting the improper fraction to a mixed number,
= (3 + 1) + e + o Adding the whole numbers and the fractions, =
18 18 6
25
= 4 + Converting the improper fraction to a mixed number, 5
18 = 4 6
7
= 4 + 1 18 Adding the whole numbers, Alternative Method
7
= 5 18 1 2 The LCM of 2 and 3 is 6 (i.e. LCD = 6). Determining the equivalent
12 – 7 3 mixed numbers using the LCD of 6,
2
5
7
5
Therefore, the result of adding 3 and 1 is 5 . = 12 – 7 4 4 3
3
18
9
6
6 6 The fraction is greater than . Therefore, we have to regroup the
6
6
3
Subtracting Fractions mixed number 12 .
6
6
3
3
The process for subtracting fractions is the same as that for adding of fractions. Regrouping 12 = 11 + 1 + = 11 + + = 11 ,
9
3
6
6 { 6 6 6
{
Step 1: Determine the LCD. Subtracting the fractions and the whole numbers,
9
= 11 – 7 4 6
6
Step 2: Convert each fraction to its equivalent fraction with the LCD as the common denominator.
(9 – 4)
Step 3: Subtract the numerators of the equivalent fractions, keeping the LCD as the denominator. = 4
(That is, the resulting fraction will have the common denominator, and its numerator will be 6
the difference of the numerators of the equivalent fractions.) = 4 5 6
Express the final answer reduced to its lowest terms and as a mixed number, where applicable.
5
1
2
Therefore, the result of subtracting 7 from 12 is 4 .
6
3
2
Example 1.3(d) Subtracting Fractions
2 7 2 1 Multiplying Fractions
(i) Subtract from (ii) Subtract 7 from 12
8 10 3 2 When multiplying two or more fractions:
Solution (i) 7 2 The LCM of 8 and 10 is 40 (i.e. LCD = 40). Determining the Step 1: Convert any mixed numbers to improper fractions.
10 – 8 equivalent fractions using the LCD of 40, Step 2: Simplify the fractions, if possible. This includes dividing by common factors between the
numerators and denominators.
28 10 Subtracting the numerators and keeping the common denominator,
= –
40 40 Step 3: Multiply the numerators to get the new numerator and multiply the denominators to get the
new denominator.
18 18 9 Reducing to lowest terms,
= = Express the final answer reduced to its lowest terms and as a mixed number, wherever applicable.
40 40
20
Note: When multiplying mixed numbers, it is incorrect to multiply the whole number part separately
9 from the fractional parts to arrive at the answer.
=
20
Example 1.3(e) Multiplying Fractions
2 7 9
Therefore, the result from subtracting from is .
8 10 20 Multiply:
3 4 1 4
1
(ii) 12 – 7 2 3 Converting the mixed numbers to improper fractions, (i) 2 × 11 (ii) 3 × 2 5
8
2
(12 × 2) +1 (7 × 3) + 2
= –
2 3