Question

Use any order, any grouping to write equivalent expressions.

a) 3(2x)
b) 47(5)
c) 4 - 2z
d) 3(2x) + 4y(5)

Answer 1

The student's question on writing equivalent expressions is addressed by demonstrating the use of different properties of operations like associative, commutative, and distributive to rearrange or regroup the terms in the given expressions.

Step-by-step explanation:

The student is asking how to write equivalent mathematical expressions by using any order or grouping for the given expressions. Let's address each one individually:

• 3(2x): This expression can be written as 6x, which is the same as (3 × 2)x, demonstrating the associative property of multiplication.

• 47(5): The expression is equivalent to 235. It can also be written as (47 × 5), following the commutative property of multiplication.

• 4 - 2z: To write this expression with different grouping, one could think of it as (4) + (-2z), highlighting the additive inverse.

• 3(2x) + 4y(5): Using the distributive property, this can be expressed as 6x + 20y, which is a result of distributing multiplication over addition.
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These examples illustrate properties such as the associative property, commutative property, and distributive property that help show the equivalence in different groupings or orders of operations.