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?(1 point)
Responses
78=24+54=(6×4)+(6×9)=6(4×9)
78 equals 24 plus 54 equals left parenthesis 6 times 4 right parenthesis plus left parenthesis 6 times 9 right parenthesis equals 6 left parenthesis 4 times 9 right parenthesis
78=22+56=(2×11)+(2×28)=2(11×28)
78 equals 22 plus 56 equals left parenthesis 2 times 11 right parenthesis plus left parenthesis 2 times 28 right parenthesis equals 2 left parenthesis 11 times 28 right parenthesis
78=11+67=(1×11)+(1×67)=1(11×67)
78 equals 11 plus 67 equals left parenthesis 1 times 11 right parenthesis plus left parenthesis 1 times 67 right parenthesis equals 1 left parenthesis 11 times 67 right parenthesis
78=18+60=(6×3)+(6×10)=6(3+10)
78 equals 18 plus 60 equals left parenthesis 6 times 3 right parenthesis plus left parenthesis 6 times 10 right parenthesis equals 6 left parenthesis 3 plus 10 right parenthesis
78 equals 18 plus 60 equals (6 times 3) plus (6 times 10) equals 6 times (3 plus 10)
To rewrite the number 78 using the Distributive Property of Multiplication over Addition, we need to find two numbers that can be multiplied and added to give us 78.
Let's go through each option and see if it satisfies the condition:
Option 1: 78 = 24 + 54 = (6 × 4) + (6 × 9) = 6(4 × 9)
This option does not satisfy the condition because multiplying 4 and 9 separately and then multiplying the result by 6 does not give us 78.
Option 2: 78 = 22 + 56 = (2 × 11) + (2 × 28) = 2(11 × 28)
This option does not satisfy the condition because multiplying 11 and 28 separately and then multiplying the result by 2 does not give us 78.
Option 3: 78 = 11 + 67 = (1 × 11) + (1 × 67) = 1(11 × 67)
This option satisfies the condition because multiplying 11 and 67 separately and then multiplying the result by 1 does give us 78.
Option 4: 78 = 18 + 60 = (6 × 3) + (6 × 10) = 6(3 + 10)
This option does not satisfy the condition because adding 3 and 10 together and then multiplying the result by 6 does not give us 78.
Therefore, the correct way to rewrite 78 using the Distributive Property of Multiplication over Addition is:
78 = 11 + 67 = (1 × 11) + (1 × 67) = 1(11 × 67)