1. Using Distributive Property
Prime Time
Investigations 4.2 & 4.3

2. About Distributive Property
The Distributive Property allows us to evaluate expressions in different ways. We can evaluate these expressions as sums or products. We can examine this property using areas of rectangles and squares; however, we can use this property to simplify many different types of expressions.

3. Distributive Property & Area
Let’s examine the 5𝑖𝑛. 𝑏𝑦 16𝑖𝑛. rectangle. Find the area.
5 in.
16 in.

4. Distributive Property & Area
We can cut this rectangle into sections to make it easier to find the area.
5 in.
5 ×10= 50𝑖𝑛 2
5 ×6= 30𝑖𝑛 2
10 in.
6 in.
Total area of rectangle = 𝟖𝟎𝒊𝒏 𝟐
Two ways to display the area:
Factored Form: 𝟓 𝟏𝟎+𝟔 =𝟖𝟎
Expanded From: 𝟓×𝟏𝟎)+(𝟓×𝟔 =𝟖𝟎

5. Distributive Property & Area
Directions: Find the area of each rectangle. Show how you cut the rectangles to make easier to solve 1) 2)
9 in.
7 in.
12 in.
18 in.

6. DISTRIBUTIVE PROPERTY
EXPANDED FORM
Evaluate the expression without rectangles: 𝟒(𝟗 + 𝟖)
STEP 1 - Using the distributive property, 4 is multiplied by 9: 𝟒(𝟗)
STEP 2 - Then, 4 is multiplied by 8: 𝟒(𝟖)
STEP 3 – Lastly, add the two products together
𝟒(𝟗) + 𝟒(𝟖) =
𝟑𝟔 𝟑𝟐 = 𝟔𝟖
We add because the 9 & 8 are added together in original expression.
When an expression is written as a sum or difference of two
products, we call this expanded form.

7. DISTRIBUTIVE PROPERTY
EXPANDED FORM
Directions: Write in expanded form. Find the solution. Use the previous slide as an example.
1) ) − )

8. DISTRIBUTIVE PROPERTY
EXPANDED FORM
We can replace some of these numbers with variables (𝑥, 𝑦, 𝑛, 𝑓) and still write expressions in expanded form.
For example: 𝟐 𝒚+𝟑 could be modeled with the following rectangle: 2 y 3

9. DISTRIBUTIVE PROPERTY
EXPANDED FORM
Based on the rectangle on the previous slide,
𝟐 𝒚 +𝟐 𝟑
We can simplify this even further by eliminating the parentheses for multiplication. Therefore, our simplified answer would be:
𝟐𝒚+𝟔

10. DISTRIBUTIVE PROPERTY
EXPANDED FORM
Directions: Write in expanded form. Refer to previous slide for assistance.
1) 𝟔(𝒙 + 𝟓) 2) 𝟑 𝟓+𝒚

11. DISTRIBUTIVE PROPERTY
EXPANDED FORM
Directions: Write in expanded form. Refer to previous slides for assistance.
1) 𝟑(𝟓 – 𝒚) 2) 𝟓(𝟕 + 𝒙) 3) 𝟐(𝒚 + 𝟑) 4) 𝟑(𝒙 – 𝟒)