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Properties in Expressions
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Properties in Expressions
Use the properties of operations to identify, rewrite, and simplify expressions. Show your reasoning where asked.
Identify the Property
1.Which property changes the order of the addends in 9 + k = k + 9?
- Commutative Property
- Associative Property
- Distributive Property
2.Which property is used to rewrite 6 + (p + 2) as (6 + p) + 2?
- Commutative Property
- Associative Property
- Distributive Property
3.Select every expression equivalent to 4(a + 3).
- 4a + 12
- 4a + 3
- 4 · a + 4 · 3
- a + 3 + 4
Rewrite and Simplify
4.Simplify 7 + r + 8 by combining the number terms.
5.Rewrite (m + 5) + 7 as a simplified expression. Show how regrouping helps.
6.Use the distributive property to expand and simplify 6(3 + x).
7.At a fruit orchard, Aaliyah buys 4 baskets of pears at $3 each and 4 bags of apples at $2 each. Write an expression for the cost, use the distributive property to simplify it, and find the total.
Apply and Explain
8.At the orchard, Isabella picks 5 peaches, b berries, and 8 plums. Gabriela picks 8 plums, 5 peaches, and b berries. Write one expression for each person's fruit count and explain why the expressions are equivalent.
9.A fruit stand packs 3 crates, each with 2 pounds of apples and 5 pounds of pears. Write the total weight in two equivalent ways, using the distributive property, and state the total weight.
10.Choose the Commutative, Associative, or Distributive Property. Explain how it can help simplify an expression and give a correct example.
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