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Calculating the Total Area of Adjacent Gardens Using the Distributive Property

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This guide demonstrates how to calculate the total area of two adjacent gardens using different methods, including the distributive property and basic area multiplication. We explore a scenario with vegetable and flower gardens having dimensions of 8 ft x 12 ft and 8 ft x 16 ft, respectively. By finding the area of each garden separately and also through a combined expression, we arrive at a total area of 224 square feet. Additionally, we provide examples of simplifying expressions using the distributive property to enhance understanding of algebraic concepts.

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Calculating the Total Area of Adjacent Gardens Using the Distributive Property

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  1. The Distributive Property Section 2.7

  2. Find the area 8 ft 8 ft 12 ft 16 ft 1. Find the area of each garden and then add the areas together. Area = 8(12) + 8(16) Area = 96 + 128 Area = 224 square feet 2. Find the total length then multiply it times the common width Area = 8 ( 12 + 16) Area = 8 (28) Area = 224 square feet You are planting a vegetable garden and a flower garden. The diagram shows the dimensions of the two adjacent gardens. How can you find the total area of the two gardens?(Show more than one method)

  3. Distributive Property Example 1 Use the distributive property -4(a + 13) = 5(2 – x + 3y) = a(b+c) = ab + ac 9(2+6) = 9(2) + 9(6) a(b-c) = ab – ac 8(7-1) = 8(7) – 8(1)

  4. Example 2: Simplify the expressions(distribute and combine like terms) 2(9+ y) + 3 y -7 ( 3x-1) + y - 2

  5. Your turn: Use the distributive property to simplify and combine like terms 1. -3(8+ w)= 2. 6(2y – 15)=

  6. Your turn: Use the distributive property to simplify and combine like terms 4. 6( t – 7 ) – t + 12 5. 6 – 4(2w – 5) Be careful on this one!

  7. 6. Write two expressions for the total area of the two rectangles 10 ft 10 ft 12 ft 22 ft

  8. 7. Write two expressions for the total area of the two rectangles 5ft 5ft xft 14ft

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