Question

1. which number is not a common denominator of the fractions being added?

\\(\frac{2}{9} + \frac{5}{12}\\)
\\(\boldsymbol{\text{a}}\\) 108
\\(\boldsymbol{\text{b}}\\) 72
\\(\boldsymbol{\text{c}}\\) 36
\\(\boldsymbol{\text{d}}\\) 24

Explanation:

Step1: Find LCM of 9 and 12

Prime factors of 9: $3\times3$, prime factors of 12: $2\times2\times3$. LCM is $2\times2\times3\times3 = 36$. Common denominators are multiples of 36.

Step2: Check each option

• Option A: 108 is $36\times3$, multiple of 36.
• Option B: 72 is $36\times2$, multiple of 36.
• Option C: 36 is LCM, multiple of itself.
• Option D: 24. Check if 24 is multiple of 36? No. 24 ÷ 36 is not integer. Also, 9 divides 24? 24 ÷ 9 = 2.666..., not integer. So 24 can't be common denominator.

Answer:

D. 24