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Measuring Area Using Distributive Property

Key Concepts

  • Define Distributive property.
  • How to apply distributive property
  • Use of distributive property
  • Distributive property over addition
  • Distributive property over addition
  • How to find Area using distributive property

Introduction :

1.1 Distribute means: 

“Distribute” means to divide something or give a share or part of something or spread over the area. 
A multiplication fact can be broken apart into the sum of two other multiplication facts 

Multiplicaction

1.2 Distribute Definition: 

The distributive property involves the operations of 

 “multiplication and addition or multiplication and subtraction.” 

Multiplicaction and addition

How to apply? 

Jack wanted to plant some flowers in his garden 

 First he finds the total area of the garden? 

Let’s Find the area of the garden (Rectangle) ? 

Area of a rectangle = Length x width 

                                     = 7 feet x 5 feet 

                                     = 35 square feet 

Jack thinks of planting two types of flower plants in the garden so he divides the garden into two parts 

  • In one part he plants Rose. 
  • In another part he plants Lavender. 

Jack divides length of the garden as shown below: 

Diagram

Description automatically generated

Jack finds the area of the Rose garden and lavender garden 

Area of Rose garden =  5 feet x 4 feet = 20 square feet 

Area of Lavender garden = 5 feet x 3 feet = 15 feet 

Jack realizes 

Total area of the garden = Area of Rose Garden + Area of Lavender Garden 

5 x 7              =  (5 x 4)   +(5 x 3) 

35 sq.ft           = 20 feet +15 feet = 35 sq feet 

Total area of Garden 

5 x 7 

5  x (4 + 3) 

Area of Rose + Lavender = (5 x 4)   +   (5 x 3) 

Distributive property over addition 

When applying the distributive property over addition…. 

The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together give the same result as multiplying the first number by the sum. 

Example: 

Solution: 

David grows lettuce in 10 square feet and cucumbers in 15 square feet in his garden area as shown below. Find the total area of the garden. 

Total area of the garden = 5 (3 + 2) 

              = 5 x 3 + 5 x 2 

                  = 15   +   10  

                    = 25 Square ft  

How to apply? 

Harry house wants to build a swimming pool beside his house of length 5meters and width 10 meters. The total area of house and swimming pool together is 80 meters? Find the area of his house  

Total area = 5 x 16 = 80 square meter 

Area of the House = Total Area – Area of swimming pool 

                                   = 80 – 5 x 10 

                                   = (5 x 16) – (5 x 10) 

                                   = 5 x (16-10) 

          = 5 x 6 

Area of the house is 30 square mt 

Concept: Distributive property over subtraction 

When applying the distributive property over subtraction. 

The distributive property of multiplication states that when a number is multiplied by the difference of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then subtracting the two products together for the same result as multiplying the first number by the difference. 

Example: 

Assessment 

  • Select all the ways to break apart the area of the large rectangle into sum of the areas of two  smaller rectangles. Then give the area of the larger rectangle.   
  •  Select all the correct options and discuss  
  •  5 x 7 = 5 x (2 + 5) = (5 x 2) + (5 x 5) 
  •  5 x 7 = 5 x (3 + 4) = (5 x 3) + (5 x 4) 
  •  5 x 7 = 5 x (1 + 6) = (5 x 1) + (5 x 6) 

Total area = __________ square units 

  • Mary sold 3 shells last week and 4 shells this week. If each shell cost $5, how much money did Mary make in two weeks.
    (solve using distributive property)   
  • Amit attaches two play mats one is 6 feet by 3 feet and another is 6feet by 2 feet. What is the total area of the mat he made finally by attaching both the mats? 
    (solve using distributive property) 

Exercise:

Use the distributive property to find the area of the filed rectangles.

1.

2.

3.

4.

5.

Concept Map:

What we have learnt:

  • The Area of a surface or a plane figure is the number of square units needed to cover the surface of the figure
  • Area of the Rectangle / square  =  Length * Width
  • Area is measured using Standard units
  • The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum
  •  5 x (4 +6) = (5 x 4) + (5 x 6)
  •  5 x (10- 6) = (5 x 10) – (5 x 6)

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