# Arithmetic properties: Distributive property

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##### Intros

###### Lessons

- Introduction to the distributive property:
- Showing that a × (b + c) = (a × b) + (a × c)
- Common mistakes to avoid when using the distributive property
- Using area blocks to demonstrate the distributive property
- Why is it called the "distributive" property?
- The general formula for the distributive property
- Using the distributive property for other types of real numbers (decimals, fractions, integers)

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##### Examples

###### Lessons

**Distributive Property Equations**

Use the distributive property to fill in the blanks.- 6 × (3 + 5 + 4) = 6 × ___ + 6 × ___ + 6 × ___

$\qquad \qquad \qquad \qquad$ = _______+ _______+ ______

$\qquad \qquad \qquad \qquad$ = _______

$\qquad \qquad \qquad \qquad$ 6 × (___) = _______

$\qquad \qquad \qquad \qquad$ _______ = _______

- 12 × (10. 5 + 1.2) = 12 × ___ + 12 × ___

$\qquad \qquad \qquad \qquad$ = _______ + _______

$\qquad \qquad \qquad \qquad$ = _______

$\qquad \qquad \qquad \qquad$ 12 × (___) = _______

$\qquad \qquad \qquad \qquad$ _______ = _______

- 3 × ($\frac{3}{5} + \frac{4}{5}$) = 3 × ___ + 3 × ___

$\qquad \qquad \qquad \qquad$ = _______ + _______

$\qquad \qquad \qquad \qquad$ = _______

$\qquad \qquad \qquad \qquad$ 3 × (___) = _______

$\qquad \qquad \qquad \qquad$ _______ = _______

- 8 × (6 + __) = 8 × ___ + 8 × ___

$\qquad \qquad \qquad \qquad$ = _______ + _______

$\qquad \qquad \qquad \qquad$ = 104

$\qquad \qquad \qquad \qquad$ 8 × (___) = 104

$\qquad \qquad \qquad \qquad$ _______ = 104

- 6 × (3 + 5 + 4) = 6 × ___ + 6 × ___ + 6 × ___
**Distributive property as a shortcut**

Use the distributive property to split up one of the factors. This can be a shortcut so that you can use your times tables knowledge. Solve and check the answer using long (normal) multiplication**Distributive property using area blocks**

Use an area block to show each distributive property, then solve.**Rewriting a sum as a distributive property**

Rewrite each sum as a distributive property expression. Recall that the general formula for the distributive property is: a × (b + c) = a × b + a × c- Hint: find the greatest common factor of each number first.
**Distributive property word problem 1**

Eight people go to a restaurant for a buffet dinner. The cost per person for the meal is $11.50 and there is a separate drink cost of $2.10. How much did they pay all together?**Distributive property word problem 2**

In a movie theatre, there are 3 sections you can sit in (left, middle, right). Each row has 6 seats in the left section, 14 in the middle section, and 8 in the right section.- If there are 10 rows, how many seats are there in each section? And how many total seats are there in the theatre?

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