# Arithmetic properties: Associative property

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##### Intros
###### Lessons
1. Introduction to the associative property of addition and multiplication:
2. Showing that $(a + b) + c = a + (b + c)$
3. Why is it called the "associative" property?
4. Addition shortcuts using the associative property
5. Showing that (a × b) × c = a × (b × c)
6. Multiplication shortcuts using the associative property
7. The general formulas for the associative property
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##### Examples
###### Lessons
1. Associative Property Equations
Use the associative property (for addition and multiplication) to fill in the blanks.
1. (7 + 2) + 8 = 7 + (2 + __)
2. $\large \frac{1}{4} \, \times \, (\frac{1}{6} \, \times \, \frac{1}{5}) = (\frac{1}{4} \, \times \,$ ______ $\large ) \, \times \, \frac{1}{5}$
3. ($x$ + 3 + 8) + __ = (3 + 9 + x) + 8
2. Changing the grouping to add lists of numbers
Decide how to group the addends as a shortcut for addition. Double check your answer by adding without groups.
1. 0.1 + 0.6 + 0.9 + 0.4 =
2. $\large \frac{2}{10} + \frac{3}{10} + \frac{1}{10} + \frac{4}{10} + \frac{9}{10} + \frac{7}{10} + \frac{6}{10} + \frac{8}{10} =$
3. $\large \frac{2}{3} + \frac{5}{9} + \frac{1}{3} + \frac{4}{9} + \frac{6}{7} =$
3. Changing the grouping to multiply lists of numbers
Decide how to group the factors as a shortcut for multiplication. Double check your answer by multiplying without groups.
1. 20 × 15 × 5
2. 0.8 × 0.9 × 0.5
3. 6 × 20 × 5 × 2
4. Associative property of addition word problem
Ryan added these numbers together and his answer is correct. Show another way of adding numbers (with grouping) using the associative property!

1. Associative property of multiplication word problem
Explain which choice is NOT an equal statement to: (6 × 8) × 5
1. 6 × 40
2. 48 × 5
3. 6 × (8 × 5)
4. 14 × 5
1. Associative property and volume
The formula for the volume of a rectangular prism is given by:

Volume = length × width × height

Use the associative property of multiplication to show 2 ways to solve for this prism.
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