154 Review Questions and Answers
Question 5-4
Suppose a mathematician says, “The operations of addition, subtraction, and multiplication
are closed over the set of integers, but the operation of division is not.” What does he/she
mean by this?Answer 5-4
He/She means that we always get an integer if we add, subtract, or multiply one integer by
another. But he/she also warns us that we don’t always get an integer if we divide one integer
by another.Question 5-5
Which of the following “rules” is actually false? How can its wording be changed to make it
right?(a) When we multiply a positive integer by 2 or more, the result stays positive and the
absolute value increases.
(b) When we divide a positive integer by 2 or more, the result stays positive and the absolute
value decreases.
(c) When we multiply a negative integer by −2 or less, the result stays negative and the
absolute value increases.
(d) When we divide a negative integer by −2 or less, the result becomes positive and the
absolute value decreases.Answer 5-5
All of the above “rules” are true except (c). Remember that if we multiply a negative by a
negative, we get a positive! The correct way to state this rule would be, “When we multiply a
negative integer by −2 or less, the result becomes positive and the absolute value increases.”Question 5-6
Sometimes we’ll come across an expression that doesn’t contain parentheses, brackets, or
braces. This can be confusing if we don’t know the order in which the operations should be
done. Suppose we see this:6 × 8 − 14/2 + 3What number does this represent?Answer 5-6
Remember the rules for precedence of operations when we see expressions without parenthe-
ses. The steps go in this order:- Do all the multiplications.
- Do all the divisions.
- Convert all the subtractions to negative additions.
- Do all the additions.