Question

Which of the following expressions could you rewrite using the associative property?

1. (a + b) + c
2. a + (b + c)
3. (p * q) * r
4. p * (q * r)

Answer 1

The expressions (a + b) + c and p * (q * r) can be rewritten using the associative property, which states that the grouping of addition or multiplication does not affect the result. The expressions a + (b + c) and (p * q) * r are equivalent to the original expressions.

Step-by-step explanation:

The expression (a + b) + c can be rewritten using the associative property as a + (b + c). This property states that when adding or multiplying three or more numbers or variables, the grouping of the numbers or variables does not affect the result. For example, if a = 2, b = 3, and c = 4, then:

(2 + 3) + 4 = 5 + 4 = 9

2 + (3 + 4) = 2 + 7 = 9

Therefore, both expressions are equal.

The same applies to the expressions (p * q) * r and p * (q * r) using the associative property of multiplication. This property allows us to change the grouping of multiplication without changing the result. For example, if p = 2, q = 3, and r = 4, then:

(2 * 3) * 4 = 6 * 4 = 24

2 * (3 * 4) = 2 * 12 = 24

So, all the given expressions can be rewritten using the associative property.