Algebra Know-It-ALL

152 Review Questions and Answers

The associative law says that we can group a sum of three integers in a certain order by twos

either way, and the result will always be the same. If a, b, and c are integers, then

(a+b)+c=a+ (b+c)

In combination, the commutative and associative laws allow us to arrange and group a sum of

integers in any possible way, and the result will always be the same.

Question 4-7

Does the commutative law for addition apply to sums of more than two integers? Does the

associative law apply for sums of more than three integers?

Answer 4-7

Both of these laws will work for sums having as many addends as we want, as long as the

number of addends is finite.

Question 4-8

Does the commutative law work for subtraction?

Answer 4-8

We cannot apply the commutative law to subtraction problems and expect valid results. Let’s

look at these two subtractions:

5 − 10 =− 5

but

10 − 5 = 5

Question 4-9

Does the associative law work for subtraction done twice?

Answer 4-9

We can’t apply the associative law to subtraction done twice and expect valid results. Here’s an

example showing its failure:

(5− 10) − 15 =− 5 − 15 =− 20

but

5 − (10 − 15) = 5 − (−5)

= 5 + 5

= 10