Select the correct answer.
Hattie rewrote the equation as shown:
[tex]
\begin{array}{l}
9 n+7-2 n=4(-n+5)-3 n \\
9 n+7-2 n=-4 n+20-3 n
\end{array}
[/tex]
Which property did she use to rewrite the equation?
A. addition property of equality
B. distributive property
C. multiplication property of equality
D. substitution property
Answer (1)
The distributive property is used to expand the expression 4 ( − n + 5 ) to − 4 n + 20 . Therefore, the correct answer is B. B
Explanation
Analyze the problem We are given the equation 9 n + 7 − 2 n = 4 ( − n + 5 ) − 3 n and Hattie rewrote it as 9 n + 7 − 2 n = − 4 n + 20 − 3 n . We need to identify which property she used to rewrite the equation.
Identify the change Comparing the two equations, we see that the left side of the equation remains unchanged. The right side of the equation changes from 4 ( − n + 5 ) − 3 n to − 4 n + 20 − 3 n . This change involves expanding the term 4 ( − n + 5 ) to − 4 n + 20 .
Apply the distributive property The expansion of 4 ( − n + 5 ) to − 4 n + 20 is an application of the distributive property, which states that a ( b + c ) = ab + a c . In this case, 4 ( − n + 5 ) = 4 ( − n ) + 4 ( 5 ) = − 4 n + 20 .
Conclusion Therefore, Hattie used the distributive property to rewrite the equation.
Examples
The distributive property is used in everyday life when you want to calculate the total cost of multiple items. For example, if you want to buy 4 apples that cost $0.75 each and 4 bananas that cost $0.50 each, you can calculate the total cost as $4(0.75 + 0.50) = 4(1.25) = $5. Alternatively, you can calculate the cost of the apples and bananas separately and then add them together: $4(0.75) + 4(0.50) = 3 + 2 = $5. Both methods give the same result due to the distributive property.
