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=18+60=(6×3)+(6×10)=6(3+10)
78=11+67=(1×11)+(1×67)=1(11×67)
78=24+54=(6×4)+(6×9)=6(4×9)
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To rewrite the number 78 using the Distributive Property of Multiplication over Addition, we need to find two numbers that add up to 78 and multiply them together. Let's examine the answer choices:
1) 78 = 22 + 56 = (2×11) + (2×28) = 2(11×28)
The distribution property is not used correctly here because (2×11) + (2×28) should result in 70, not 78.
2) 78 = 18 + 60 = (6×3) + (6×10) = 6(3+10)
This is the correct application of the Distributive Property. (6×3) + (6×10) equals 18 + 60, which equals 78.
3) 78 = 11 + 67 = (1×11) + (1×67) = 1(11×67)
Here, the Distributive Property is not applied correctly because (1×11) + (1×67) should result in 78, not 78 being the sum of 11 and 67.
4) 78 = 24 + 54 = (6×4) + (6×9) = 6(4×9)
The distribution property is not used correctly here because (6×4) + (6×9) should result in 90, not 78.
Therefore, the correct way to rewrite 78 using the Distributive Property is:
78 = 18 + 60 = (6×3) + (6×10) = 6(3+10)