Question

question which expression is equivalent to 36 + 12? answer 3(12 + 9) 3(33 + 4) 3(12 + 4) 3(12 + 3)

Explanation:

Step1: Factor out the GCF of 36 and 12

The greatest common factor (GCF) of 36 and 12 is 12? Wait, no. Wait, 36 and 12: GCF of 36 and 12 is 12? Wait, 36 ÷ 12 = 3, 12 ÷ 12 = 1. Wait, no, wait. Wait, 36 and 12: let's find GCF. Factors of 36: 1,2,3,4,6,9,12,18,36. Factors of 12:1,2,3,4,6,12. So GCF is 12? Wait, no, wait the expression is 36 + 12. Wait, 36 is 3×12, 12 is 1×12? Wait, no, wait 36 + 12 = 12×3 + 12×1 = 12(3 + 1)? Wait, no, the options have 3 as the factor. Wait, let's check the options. The options are 3(12 + 9), 3(33 + 4), 3(12 + 4), 3(12 + 3). Wait, let's compute 36 + 12 = 48. Now let's compute each option:

First option: 3(12 + 9) = 3×21 = 63 ≠ 48.

Second option: 3(33 + 4) = 3×37 = 111 ≠ 48.

Third option: 3(12 + 4) = 3×16 = 48. Wait, 12×3 = 36, 4×3 = 12. So 3×12 + 3×4 = 36 + 12. Ah! So 3(12 + 4) = 3×12 + 3×4 = 36 + 12. So that's the equivalent expression.

Fourth option: 3(12 + 3) = 3×15 = 45 ≠ 48.

So the correct one is 3(12 + 4).

Step2: Verify by distributive property

Using distributive property \( a(b + c) = ab + ac \). For \( 3(12 + 4) \), distribute 3: \( 3×12 + 3×4 = 36 + 12 \), which matches the original expression \( 36 + 12 \).

Answer:

3(12 + 4) (the option corresponding to this expression)