10.10 Distributive property using area
Are you ready?
Can you find the area of a rectangle?
Find the area of the rectangle shown.
 |
width = $3$3 cm |
| length = $9$9 cm |
$\text{Area }$Area $=$= $\text{length }\cdot\text{width }$length ·width cm2 $\text{Area }$Area $=$= $\editable{}\cdot\editable{}$· cm2 (Fill in the values for the length and width.) $\text{Area }$Area $=$= $\editable{}$ cm2 (Complete the multiplication to find the area.)
Learn
This video introduces the distributive property.
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question 1
We want to use the distributive property to rewrite $2\cdot19$2·19 as easier multiplications.
This diagram shows how $2$2 groups of $19$19 objects can be split up.
Use the diagram to fill in the blank to make the statement true.
$2\cdot19=2\cdot\left(10+\editable{}\right)$2·19=2·(10+)
Fill in the blanks to show how $2$2 groups of $\left(10+9\right)$(10+9) can be split up into smaller multiplications.
$2\cdot\left(10+9\right)=2\cdot10+2\cdot\editable{}$2·(10+9)=2·10+2·
Learn
This video shows us how to use the distributive property to solve problems.
Apply
question 2
We want to find $2\cdot42$2·42.
Use the area model to complete the following:
$40$40 $2$2 $2$2 $2\cdot42$2·42 $=$= $2\cdot\left(40+2\right)$2·(40+2) $=$= $2\cdot\editable{}+2\cdot2$2·+2·2 $=$= $\editable{}+\editable{}$+ $=$= $\editable{}$
We can represent the distributive property as splitting a rectangle into two parts, finding the area of each part and then adding them together.