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4.04 The distributive law

Interactive practice questions

Use the given rectangle to demonstrate the distributive property geometrically.

a

Complete the table below by entering the areas of the two smaller rectangles:

  Rectangle $A$A Rectangle $B$B
Area $\editable{}$ $\editable{}$
b

Notice that we can combine the two rectangles $A$A and $B$B to form one large rectangle. Write an expression for the area of this large rectangle using your answers from part (a).

c

Notice that the total length of the bottom side is $m+n$m+n. Write an expression for the area of the total rectangle using this side length.

d

In part (b) and (c), we found expressions which both represent the area of the larger rectangle. We have now shown that: $\editable{}=\editable{}$=

Medium
3min

The larger rectangle has been divided into two smaller rectangles.

We will use it to show the Distributive Property geometrically.

Medium
1min

Expand the expression $5\left(s+7\right)$5(s+7).

Easy
< 1min

Expand the expression $9\left(5+w\right)$9(5+w).

Easy
< 1min
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Outcomes

MA4-9NA

operates with positive-integer and zero indices of numerical bases

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