Using Distributive Property

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Distributive Property

Presentation transcript:

Using Distributive Property Prime Time Investigations 4.2 & 4.3

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.

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

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

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.

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.

DISTRIBUTIVE PROPERTY EXPANDED FORM Directions: Write in expanded form. Find the solution. Use the previous slide as an example. 1) 6 7+2 2) 4 9−4 3) 3 2+5

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

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

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

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)