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=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=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
To rewrite 78 using the Distributive Property of Multiplication over Addition, we can use the equation 78=22+56=(2×11)+(2×28)=2(11×28). Therefore, the correct way to rewrite 78 using the Distributive Property is 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.
To rewrite the number 78 using the Distributive Property of Multiplication over Addition, you need to break down 78 into two numbers that can be multiplied and added together.
Let's look at each option:
1. 78=11+67=(1×11)+(1×67)=1(11×67)
This option breaks down 78 into the sum of 11 and 67, then uses the Distributive Property to multiply 1 with both numbers. The correct answer is 78 = 1(11×67).
2. 78=18+60=(6×3)+(6×10)=6(3+10)
This option breaks down 78 into the sum of 18 and 60, then uses the Distributive Property to multiply 6 with both numbers. However, the expression inside the parentheses should be added, not multiplied. So, this answer is incorrect.
3. 78=24+54=(6×4)+(6×9)=6(4×9)
This option breaks down 78 into the sum of 24 and 54, then uses the Distributive Property to multiply 6 with both numbers. However, the multiplication of 4 and 9 should not be further simplified. So, this answer is incorrect.
4. 78=22+56=(2×11)+(2×28)=2(11×28)
This option breaks down 78 into the sum of 22 and 56, then uses the Distributive Property to multiply 2 with both numbers. The correct answer is 78 = 2(11×28).
Therefore, the correct way to rewrite 78 using the Distributive Property of Multiplication over Addition is 78 = 1(11×67) or 78 = 2(11×28).