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Algebraic Properties Application
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Algebraic Properties Application
Choose the best answer where options are given. Some questions may have more than one correct answer. Show working for calculation questions.
Identify the Properties
1.Which property is used to rewrite 4(y + 7) as 4y + 28?
- Commutative property
- Associative property
- Distributive property
2.Which property is illustrated by the equation n + 12 = 12 + n?
- Commutative property of addition
- Associative property of addition
- Distributive property
3.Select every equation that demonstrates the associative property.
- (5 + y) + 2 = 5 + (y + 2)
- 6(y + 1) = 6y + 6
- (4 × y) × 3 = 4 × (y × 3)
- y × 9 = 9 × y
Algebra on a Camping Trip
4.Mele packs 4 snack bags for a camping trip. Each bag has (a + 3) pieces of food. Write an expanded expression for the total number of pieces, then find the total when a = 5.
5.At camp, Nikau records the cost of two supplies as ($18 + p) and (p + $18). Why do the supplies have the same combined cost whichever expression is written first? Name the property.
6.Keira and Mele count firewood in two ways: (7 + t) + 5 pieces and 7 + (t + 5) pieces. Explain why these expressions always give the same total.
Apply and Explain
7.Solve 3(x + 2) + 5 = 20. Show your steps and name one algebraic property used.
8.Complete the expansion: 6(2x + 5) = + .
9.A camping group buys 3 bundles of tent pegs. Each bundle contains (m + 4) pegs. Write an expanded expression for the total, then calculate it when m = 6.
10.In one sentence, explain how knowing algebraic properties can help when simplifying or solving an equation.
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