Mei is playing a game with numbers. She decides to rewrite the number 78 using the Distributive Property. Which answer is a correct way to rewrite 78 using the Distributive Property of Multiplication over Addition? Responses 78=22+56=(2×11)+(2×28)=2(11×28) 78 is equal to 22 plus 56 is equal to open paren 2 times 11 close paren plus open paren 2 times 28 close paren is equal to 2 times open paren 11 times 28 close paren - no response given 78=11+67=(1×11)+(1×67)=1(11×67) 78 is equal to 11 plus 67 is equal to open paren 1 times 11 close paren plus open paren 1 times 67 close paren is equal to 1 times open paren 11 times 67 close paren - no response given 78=18+60=(6×3)+(6×10)=6(3+10) 78 is equal to 18 plus 60 is equal to open paren 6 times 3 close paren plus open paren 6 times 10 close paren is equal to 6 times open paren 3 plus 10 close paren - no response given 78=24+54=(6×4)+(6×9)=6(4×9)

Answer 1

To rewrite the number 78 using the Distributive Property, we need to find a way to express it as the sum of two numbers that can be expressed in a distributive format.

Let's evaluate the options one by one:

1. 78 = 22 + 56: \[ 78 = 22 + 56 = (2 \times 11) + (2 \times 28) \] This can then be factored as: \[ (2 \times 11) + (2 \times 28) = 2(11 + 28) \] This is incorrect as it does not factor correctly.

2. 78 = 11 + 67: \[ 78 = 11 + 67 = (1 \times 11) + (1 \times 67) \] This can be expressed as: \[ (1 \times 11) + (1 \times 67) = 1(11 + 67) \] Just like the first one, this does not factor correctly.

3. 78 = 18 + 60: \[ 78 = 18 + 60 = (6 \times 3) + (6 \times 10) \] This can be factored as: \[ (6 \times 3) + (6 \times 10) = 6(3 + 10) \] This option correctly uses the Distributive Property.

4. 78 = 24 + 54: \[ 78 = 24 + 54 = (6 \times 4) + (6 \times 9) \] This can be expressed as: \[ (6 \times 4) + (6 \times 9) = 6(4 + 9) \] This option also correctly uses the Distributive Property, but it does not yield the same expression as the initial number.

The correct way to rewrite 78 in the context of the Distributive Property is the third option:

78 = 18 + 60 = (6 × 3) + (6 × 10) = 6(3 + 10).