Question

we have two fractions, \\(\frac{2}{5}\\) and \\(\frac{3}{10}\\), and we want to rewrite them so that they have a common denominator (and whole number numerators). what numbers could we use for the denominator? choose 2 answers! a 5 b 10 c 15 d 20

Explanation:

Step1: Find LCM of denominators

Denominators are 5 and 10. Prime factors: \(5 = 5\), \(10 = 2\times5\). LCM is \(2\times5 = 10\). Multiples of 10 (like 10, 20, 30...) are common denominators.

Step2: Check each option

• Option A (5): \(\frac{3}{10}\) can't have denominator 5 (3÷2 not whole). Reject.
• Option B (10): \(\frac{2}{5}=\frac{4}{10}\), \(\frac{3}{10}\) stays. Valid.
• Option C (15): 5 and 10 don't both divide 15 (15÷5=3, 15÷10=1.5). Reject.
• Option D (20): 5 divides 20 (20÷5=4), 10 divides 20 (20÷10=2). \(\frac{2}{5}=\frac{8}{20}\), \(\frac{3}{10}=\frac{6}{20}\). Valid.

Answer:

B. 10, D. 20