Question

question
enter the missing values in the area model to find 3(7z - 2)
answer
attempt 1 out of 2

Explanation:

Step1: Multiply 3 and 7z

To find the area of the top rectangle, we multiply the length \(3\) and the width \(7z\). Using the distributive property of multiplication, \(3\times7z = 21z\).

Step2: Multiply 3 and -2 (to get -6)

We know that the bottom rectangle has an area of \(-6\), and since the height of the big rectangle is \(3\), we can find the width by dividing \(-6\) by \(3\), but actually, in the area model for \(3(7z - 2)\), we distribute \(3\) to both terms inside the parentheses. We already have the second term as \(-6\) (since \(3\times(- 2)=-6\)), and we need to find the width corresponding to \(-6\) with height \(3\), but actually, the missing value next to \(-6\) is the result of \(-6\div3=-2\), and the missing value in the top rectangle is \(3\times7z = 21z\).

Answer:

The missing value in the top rectangle is \(21z\) and the missing value next to \(-6\) is \(-2\). So the top box should be filled with \(21z\) and the right box (next to \(-6\)) should be filled with \(-2\).