(i) \frac{7}{8} - \frac{5}{9} + \frac{-11}{36} (ii) \frac{-9}{4} - \frac{8}{3} + \frac{1}{2} - 3
Answer (1)
Let's solve the given fractions step-by-step.
(i) 8 7 − 9 5 + 36 − 11
To solve this, we'll first find the least common denominator (LCD) for the fractions. The denominators are 8, 9, and 36. The least common multiple of these numbers is 72. Now let's rewrite each fraction with the denominator of 72:
Convert 8 7 : 8 7 = 72 7 × 9 = 72 63
Convert 9 5 : 9 5 = 72 5 × 8 = 72 40
Convert 36 − 11 : 36 − 11 = 72 − 11 × 2 = 72 − 22
Now, add or subtract the numerators:
72 63 − 72 40 + 72 − 22 = 72 63 − 40 − 22 = 72 1
Therefore, the result of part (i) is 72 1 .
(ii) 4 − 9 − 3 8 + 2 1 − 3
Again, we'll find the least common denominator for the fractions. The denominators are 4, 3, and 2. The least common multiple is 12. We will also express the integer as a fraction:
Convert 4 − 9 : 4 − 9 = 12 − 9 × 3 = 12 − 27
Convert 3 − 8 : 3 − 8 = 12 − 8 × 4 = 12 − 32
Convert 2 1 : 2 1 = 12 1 × 6 = 12 6
Convert − 3 to a fraction with 12 as the denominator: − 3 = 12 − 36
Now, add or subtract the numerators:
12 − 27 − 12 32 + 12 6 − 12 36 = 12 − 27 − 32 + 6 − 36 = 12 − 89
Therefore, the result of part (ii) is 12 − 89 .
