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Algebraic Properties Practice
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Algebraic Properties Practice
Practise recognising and using the commutative, associative and distributive properties. Show working where it helps.
Recognise the properties
Choose the property that best describes each equation.
1.Which property is represented by the equation 7 × m = m × 7?
- Commutative property
- Associative property
- Distributive property
- Identity property
2.Which property is used in 5(p + 2) = 5p + 10?
- Commutative property
- Associative property
- Distributive property
- Identity property
3.Which property is represented by the equation (r + s) + t = r + (s + t)?
- Commutative property
- Associative property
- Distributive property
- Identity property
4.Match each equation to the property it demonstrates.
- 9 + a = a + 9
- 4(q + 3) = 4q + 12
- (u + v) + w = u + (v + w)
- 6 × (2 × n) = (6 × 2) × n
- Distributive
- Associative
- Associative
- Commutative
Use the properties
Rewrite or simplify each expression. Give an equivalent expression as your answer.
5.Rewrite 8 + k with the terms in the opposite order.
6.Expand 6(x + 4) by multiplying 6 by each term inside the parentheses.
7.Simplify 4a + 7 + 2a + 5 by collecting like terms.
8.Anahera buys 4 notebooks at $n each and 4 pens at $p each. Write the total cost as a sum, then rewrite it as a product by factoring out the common factor.
9.Simplify completely: 3(2x + 5) + 4(x − 2). Show the expansion and how you collect like terms.
10.Explain why 2(x + 6) and 2x + 12 have the same value for every value of x. Name the property that connects them.
11.Which expression is equivalent to 5a + 5b?
- 5(a + b)
- 10ab
- 5a + b
- a + 5b
12.Simplify 2(4y − 3) + 3(y + 2).
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