Page 48 - Mathematics of Business and Finance

28 Chapter 1 | Review of Basic Arithmetic

Solution (i) 9 or 11
25 25
Since the fractions have the same denominator, 25, we can compare the numerators to identify
the larger fraction.
11 9
11 > 9; therefore, > .
25 25

(ii) 5 3
12 or 8
We first determine the LCD of the fractions, which is the same as the LCM of the denominators.
The LCM of 12 and 8 is 24.
Next, convert each of the fractions to its equivalent fraction with 24 as the denominator.
5
Convert to an equivalent fraction with 24 as the denominator by multiplying both the
12
5 5 × 2 10
numerator and denominator by 2: = = .
12 12 × 2 24
3 3 3 × 3 9
Similarly, convert to an equivalent fraction with 24 as the denominator: = = .
8 8 8 × 3 24
Since the denominators are the same, we can now compare the numerators of the two fractions
to identify the larger fraction.
10 9 5 3
10 > 9, which implies that > ; therefore, > .
24 24 12 8
(iii) 19 11
60 or 36
We first determine the LCD of the fractions, which is the same as the LCM of the denominators.
The LCM of 60 and 36 is 180.
19
Convert to an equivalent fraction with 180 as the denominator by multiplying both the
60
19 19 × 3 57
numerator and denominator by 3: = = .
60 60 × 3 180
11 11 11 × 5 55
Similarly, convert to an equivalent fraction with 180 as the denominator: = = .
36 36 36 × 5 180

Since the denominators are the same, we can now compare the numerators of the two fractions
to identify the larger fraction.
57 55 19 11
57 > 55, which implies that > ; therefore, > .
180 180 60 36
(iv) 15 15
22 or 26
Since the fractions have the same numerator, 15, we can compare the denominators to identify
the larger fraction.
15 15
22 < 26; therefore, > .
22 26

Note: Another method of comparing fractions is to convert the fractions to decimal numbers and then
5 3 5
compare them. For example, to determine whether or is larger, we consider that = 0.625
8 5 8
3 5 3
and = 0.6. Since 0.625 > 0.6, we know > .
5 8 5