Question

Which shows the best use of the associative and commutative properties to make simplifying 3 - 5 + 9 - 4 + 2 easier?

a) [2 + (-5)] + [(-4) + 9]
b) [9 + (-5)] + [2 + (-4)]
c) [9 + (-5)] + [9 + (-4) + 2]
d) [2 + (-4)] + [9 + 2 + (-5)]

Answer 1

Option b) [9 + (-5)] + [2 + (-4)] best demonstrates the use of the associative and commutative properties to simplify the expression by grouping and rearranging the numbers, making it easier to calculate.

Step-by-step explanation:

The question asks which option best demonstrates the use of the associative and commutative properties to simplify the expression 3 - 5 + 9 - 4 + 2. The associative property allows us to regroup numbers without changing the result, and the commutative property allows us to change the order of numbers in an addition.

Option b) [9 + (-5)] + [2 + (-4)] uses these properties effectively by first changing subtraction to the addition of the inverse and then grouping numbers to simplify the calculations:

• Original expression: 3 - 5 + 9 - 4 + 2
• Change subtraction to addition: 3 + (-5) + 9 + (-4) + 2
• Use commutative property to rearrange: 9 + (-5) + 2 + (-4) + 3
• Use associative property to group: [9 + (-5)] + [2 + (-4)] + 3
• Simplify within brackets: 4 + (-2) + 3
• Final simplification: 2 + 3 = 5

The associative and commutative properties made it easier to calculate by simplifying each bracket separately before adding them to the remaining number.