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?
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The Distributive Property Quick Check
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Question
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=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=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=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)
A correct way to rewrite 78 using the Distributive Property of Multiplication over Addition is: 78 = 10 x 7 + 10 x 8.
To rewrite 78 using the Distributive Property of Multiplication over Addition, we need to express it as a sum of two numbers that we can multiply separately and then add the products together.
The Distributive Property states that for any numbers a, b, and c, a * (b + c) = (a * b) + (a * c).
To apply this property to 78, we need to find two numbers that we can multiply by a common factor and then add the products.
One way to rewrite 78 using the Distributive Property is:
78 = 10 * 7 + 10 * 8
In this case, we have broken down 78 into two numbers (7 and 8) that we can multiply by 10 individually, and then add the products together.
Hence, 78 can be rewritten using the Distributive Property as 10 * 7 + 10 * 8.
To rewrite the number 78 using the Distributive Property of Multiplication over Addition, you need to split 78 into two numbers that can be multiplied by a common factor. The Distributive Property states that for any numbers a, b, and c, the expression a × (b + c) is equal to (a × b) + (a × c).
In this case, you need to find two numbers that add up to 78 and can be multiplied by a common factor. Let's look at some possibilities to find the correct answer:
1. 78 = 39 + 39: If you split 78 into two numbers of 39, you can rewrite it as 78 = 2 × 39. However, this doesn't demonstrate the Distributive Property because there is no addition involved.
2. 78 = 38 + 40: If you split 78 into two numbers of 38 and 40, you can rewrite it as 78 = 2 × (38 + 40). This follows the Distributive Property because 2 can be factored out and then multiplied by the sum of 38 and 40.
Therefore, the correct answer to rewrite 78 using the Distributive Property of Multiplication over Addition is 78 = 2 × (38 + 40).