Question

Which shows the best use of the associative and commutative properties to

make simplifying į – 15+8 - ] + 3 easier?
A. [3+ } +(-15)] + [(-3) + 8]
B. [+(-1)] + [8+3+(-15)
C. [ + (-15)] + [8+(-) +3]
D. } +8+(-15)] + [3+(-3)]

Answer 1

The equation utilizes the associative property by grouping numbers to simplify the expression, and the commutative property to rearrange terms. Option D effectively pairs numbers that cancel each other out, thereby simplifying the calculation.

Step-by-step explanation:

The student is asking which option best demonstrates the use of the associative and commutative properties for simplifying the expression ½ − 15 + 8 − ⅓ + 3. The commutative property states that A+B=B+A, meaning that the order in which two numbers are added does not change the sum. This property applies to the addition of ordinary numbers; for example, adding 2 + 3 gives the same result as adding 3 + 2.

The associative property refers to grouping and indicates that when adding or multiplying several numbers, the way in which the numbers are grouped does not affect the sum or product. In mathematical terms, (A + B) + C = A + (B + C).

Option D. [ ½ + 8 + (-15) ] + [ 3 + (-3) ] uses the associative property by grouping the numbers to simplify the expression. It also implicitly uses the commutative property as the terms are rearranged in the groups to pair up easily manageable numbers. This results in a simplified calculation where positive and negative numbers cancel out directly.