Algebra Know-It-ALL

156 Review Questions and Answers

Question 5-9

Does the commutative law for multiplication apply to products of more than two integers?

Does the associative law apply for products of more than three integers?

Answer 5-9

Both of these laws will work for products having as many factors as we want, provided the

number of factors is finite.

Question 5-10

What are the left-hand and right-hand distributive laws of multiplication over addition and

subtraction? How do they work?

Answer 5-10

The distributive laws tell us how to work out products when one of the factors is a sum or

difference. Imagine three integers a, b, andc. The left-hand distributive law of multiplication

over addition says that

a(b+c)=ab+ac

The right-hand distributive law of multiplication over addition says that

(a+b)c=ac+bc

The left-hand distributive law of multiplication over subtraction says that

a(b−c)=ab−ac

The right-hand distributive law of multiplication over subtraction says that

(a−b)c=ac−bc

Chapter 6

Question 6-1

How can we express the following quotients in terms of an integer along with a proper

fraction?

(a) 5/2 (b) −7/3 (c) 19/2

(d)−25/7 (e) 31/9 (f ) 100/(−11)

Answer 6-1

The problems can be worked out as follows.

(a) The quotient is 2 with a remainder of 1 (out of 2). This is 2-1/2.

(b) The quotient is −2 with a remainder of −1 (out of 3). This is −2-1/3.