Question

constructed response
question 7 and 8.)
a school is placing desks in the gymnasium for end - of - the - year testing. there are two sections of desks: the first section has 72 desks being used by sixth - grade students and the second section has 99 desks being used by fifth - grade students. each section of desks has 9 rows.
which numbers should go in the boxes below to complete the equation?
72 + 99 = 9 (_ + _)
explain what the numbers that you placed in the boxes mean in terms of the desks.

Explanation:

Step1: Apply the distributive property

The distributive property states that \(a\times(b + c)=a\times b+a\times c\). In the equation \(72 + 99=9(\_\_+\_\_)\), we need to find \(x\) and \(y\) such that \(72=9x\) and \(99 = 9y\).

Step2: Solve for \(x\)

If \(72=9x\), then \(x=\frac{72}{9}=8\).

Step3: Solve for \(y\)

If \(99=9y\), then \(y=\frac{99}{9}=11\).

In terms of desks, the number \(8\) represents the number of desks in each row for the sixth - grade section (since there are \(72\) desks in the sixth - grade section with \(9\) rows, \(72\div9 = 8\)). The number \(11\) represents the number of desks in each row for the fifth - grade section (since there are \(99\) desks in the fifth - grade section with \(9\) rows, \(99\div9=11\)).

Answer:

\(72 + 99=9(8 + 11)\)