Question

Which correctly shows how to use the GCF and the distributive property to find an expression equivalent to 45 + 72?

3 (15 + 24)
9 (5 + 8)
(5) (9) + (2) (36)
(3) (15) + (8) (9)

Answer 1

To find an expression equivalent to \( 45 + 72 \) using the GCF (Greatest Common Factor) and the distributive property, we first need to identify the GCF of the two numbers.

1. The GCF of \( 45 \) and \( 72 \) is \( 9 \).

Now we can express \( 45 \) and \( 72 \) in terms of \( 9 \):
- \( 45 = 9 \times 5 \)
- \( 72 = 9 \times 8 \)

Thus, we can write:
\[
45 + 72 = 9 \times 5 + 9 \times 8
\]

Now, factoring out the \( 9 \) gives us:
\[
45 + 72 = 9(5 + 8)
\]

Now let's evaluate the options given:
1. \( 3 (15 + 24) \) does not equal \( 45 + 72 \).
2. \( 9 (5 + 8) \) is correct as shown above.
3. \( (5) (9) + (2) (36) \) does not represent \( 45 + 72 \).
4. \( (3) (15) + (8) (9) \) simplifies to \( 45 + 72 \) but does not utilize the GCF.

The correct choice using GCF and the distributive property is:

**9 (5 + 8)**