Question

Choose the set of equivalent fractions that correctly uses the LCD for these fractions: 2/9 and 5/12

None of these is correct.
24/108 and 45/108
8/36 and 15/36
16/70 and 30/70

Answer 1

Explanation:

the lowest common denominator (LCD) is the lowest common multiple (LCM) of the denominator numbers (the ones at the bottom of the fractions).

finding the LCM of 9 and 12 using the prime factor method :

9 = 3×3

12 = 2×2×3

the LCM is the combination of the longest chains per prime factor. which means we have 2×2 and 3×3 as longest chains for 2 and 3.

LCD = LCM = 2×2×3×3 = 36

2/9 turns into x/36 by multiplying by 4/4 :

2/9 × 4/4 = 8/36

5/12 turns into x/36 by multiplying by 3/3 :

5/12 × 3/3 = 15/36

so, the third answer option is correct.