Question

question
which expression is equivalent to 36 + 30?
answer
○ 6(30 + 5)
○ 6(6 + 24)
○ 3(12 + 10)
○ 2(18 + 30)

Explanation:

Step1: Factor out GCF of 36 and 30

First, find the greatest common factor (GCF) of 36 and 30. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. The GCF is 6.

Step2: Rewrite 36 + 30 using GCF

Factor out 6 from 36 and 30: \(36 + 30 = 6\times6 + 6\times5 = 6(6 + 5)\)? Wait, no, wait. Wait, 36 is 6×6? No, 36 is 6×6? Wait, 6×6 is 36, 6×5 is 30? No, 6×5 is 30? Wait, no, 36 + 30 = 66. Let's check each option:

• Option 1: \(6(30 + 5)=6\times35 = 210\), not 66.
• Option 2: \(6(6 + 24)=6\times30 = 180\), not 66.
• Option 3: \(3(12 + 10)=3\times22 = 66\). Wait, 36 + 30 = 66. 3×12=36, 3×10=30. So \(3(12 + 10)=36 + 30\). Wait, but also, let's check GCF again. Wait, GCF of 36 and 30: prime factors of 36: 2×2×3×3; prime factors of 30: 2×3×5. So GCF is 2×3=6. Wait, so 36 + 30 = 6×6 + 6×5 = 6(6 + 5)=6×11=66? Wait, no, 6×6 is 36, 6×5 is 30? No, 6×5 is 30? Wait, 6×5 is 30, yes. So 6×6 + 6×5 = 6(6 + 5)=6×11=66. But 3(12 + 10)=3×22=66. Also, 2(18 + 30)=2×48=96. Wait, maybe I made a mistake. Wait, 36 + 30 = 66. Let's calculate each option:

• \(6(30 + 5)=6×35=210\)
• \(6(6 + 24)=6×30=180\)
• \(3(12 + 10)=3×22=66\)
• \(2(18 + 30)=2×48=96\)

Ah, so the correct one is \(3(12 + 10)\)? Wait, but wait, GCF of 36 and 30 is 6, but 3 is also a common factor. Wait, maybe the question is about factoring, and we need to see which expression is equivalent. Let's expand each option:

• \(6(30 + 5)=180 + 30=210\)
• \(6(6 + 24)=36 + 144=180\)
• \(3(12 + 10)=36 + 30=66\)
• \(2(18 + 30)=36 + 60=96\)

And 36 + 30=66, so the equivalent expression is \(3(12 + 10)\)? Wait, but wait, another way: maybe I miscalculated the GCF. Wait, 36 and 30: GCF is 6, so 36 + 30 = 6×(6 + 5)=6×11=66. But 3×(12 + 10)=3×22=66. So both 6(6 + 5) and 3(12 + 10) would be equivalent? But in the options, 6(6 + 24) is 6×30=180, 6(30 + 5)=210, 3(12 + 10)=66, 2(18 + 30)=96. So the correct one is \(3(12 + 10)\)? Wait, but let's check again. 36 + 30 = 66. 3(12 + 10)=3×22=66. Yes. So the answer is \(3(12 + 10)\). Wait, but the options are:

• 6(30 + 5)
• 3(12 + 10)
• 6(6 + 24)
• 2(18 + 30)

So the correct option is the one with \(3(12 + 10)\). Wait, but maybe I made a mistake in the GCF. Let's see, 36 and 30: GCF is 6, but 3 is a common factor. So factoring out 3: 3(12 + 10), which is correct. So the equivalent expression is \(3(12 + 10)\).

Answer:

\(3(12 + 10)\) (the option with \(3(12 + 10)\))