Question

Which shows the best use of the associative and commutative properties to make simplifying 3-5+9-+2 easier?

A. [2+3/4+(-5)] + [(–2/4) + 9]
B. [3/4+(-2/4)] + [9+2+(-5)]
C. (3/4+9+(-5)] + [2+(-2/4)]
D. [3/4+(-5)] + [9+(-2/4) + 2]

Answer 1

The best use of the associative and commutative properties to simplify the expression 3-5+9-2 is shown in option B.

Step-by-step explanation:

The best use of the associative and commutative properties to simplify the expression 3-5+9-2 is shown in option B. [3/4+(-2/4)] + [9+2+(-5)].

Here's the step-by-step explanation:

1. Start by grouping the positive and negative terms: [3/4+(-2/4)] + [9+2+(-5)].
2. Apply the commutative property to rearrange the terms: [(-2/4)+3/4] + [(-5)+2+9].
3. Simplify the addition within each group: [1/4] + [6].
4. Apply the associative property to combine the groups: 1/4 + 6.
5. Simplify the addition: 1/4 + 6 = 25/4.