Q1.
Express the following fractions in lowest terms: a. 17⁄51 b. 64⁄144 c. 126⁄147 d. 525⁄112
Answer
Divide the numerator and the denominator by their highest common factor.
a. 51 = 17 × 3, so the HCF is 17
17/51 = (17 ÷ 17)/(51 ÷ 17) = 1/3
17/51 = (17 ÷ 17)/(51 ÷ 17) = 1/3
b. 64 = 16 × 4, 144 = 16 × 9, so the HCF is 16
64/144 = (64 ÷ 16)/(144 ÷ 16) = 4/9
In steps: 64/144 = 32/72 = 16/36 = 8/18 = 4/9
64/144 = (64 ÷ 16)/(144 ÷ 16) = 4/9
In steps: 64/144 = 32/72 = 16/36 = 8/18 = 4/9
c. 126 = 21 × 6, 147 = 21 × 7, so the HCF is 21
126/147 = (126 ÷ 21)/(147 ÷ 21) = 6/7
126/147 = (126 ÷ 21)/(147 ÷ 21) = 6/7
d. 525 = 7 × 75, 112 = 7 × 16, so the HCF is 7
525/112 = (525 ÷ 7)/(112 ÷ 7) = 75/16 (= 4 11/16)
525/112 = (525 ÷ 7)/(112 ÷ 7) = 75/16 (= 4 11/16)
How to be sure it is lowest: check that the two final numbers share no factor except 1 — 4 and 9, 6 and 7, 75 and 16 have none.