Multiplication and Division
NZ Level 3
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Use the distributive property
Lesson

The area model of multiplication

We know how to solve problems such as $7\times6$7×6, but what happens if we need to solve $237\times6$237×6? The area model of multiplication is a great way to see how the distributive property of multiplication works, so let's start off with this in Video 1.

 

Using the distributive model

Now we can use the same approach, but we don't have to draw the rectangles each time. We can break our problem into smaller problems, which is what we are doing when we use the distributive property of multiplication. After you watched Video 2, you should be okay with your $347$347 times tables!

 

Worked Examples

Question 1

We want to find $2\times45$2×45.

  1. Use the area model to complete the following:

              $40$40           $5$5  
    $2$2                        
                       
    $2\times45$2×45 $=$= $2\times\left(40+5\right)$2×(40+5)
      $=$= $2\times\editable{}+2\times5$2×+2×5
      $=$= $\editable{}+\editable{}$+
      $=$= $\editable{}$

Question 2

We want to find $6\times795$6×795.

  1. Use the area model to complete the following:

              $700$700             $90$90       $5$5  
    $6$6                                  
                             
    $6\times795$6×795 $=$= $6\times\left(700+90+5\right)$6×(700+90+5)
      $=$= $6\times\editable{}+6\times\editable{}+6\times\editable{}$6×+6×+6×
      $=$= $\editable{}+\editable{}+\editable{}$++
      $=$= $\editable{}$

Question 3

Let's use the distributive property to find $8\times153$8×153.

  1. Using the fact that $153=100+50+3$153=100+50+3, how can we rewrite the number sentence in the form $8\times\editable{}+8\times\editable{}+8\times\editable{}$8×+8×+8×?

  2. Fill in the blanks to solve the following:

    $8\times153$8×153 $=$= $8\times100+8\times50+8\times3$8×100+8×50+8×3
      $=$= $\editable{}+\editable{}+\editable{}$++
      $=$= $\editable{}$

Outcomes

NA3-1

Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.

NA3-7

Generalise the properties of addition and subtraction with whole numbers

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