Basic Mathematics for College Students

172 Chapter 2 The Integers

c

1. a. b. c. d. 2. a. 63 b. 24 c. 510 d.82,000,000


2. a. 72 b. 54 c. 4. a. 72 b. 54 c. 5. a. b. 28 6. a. 81
   b. 64 c. 1 7. 16 8.84 ft below ground level (84 ft)

 480  480  10

 12  120 1,275 98,000

ANSWERS TO SELF CHECKS

We translate the words of the problem to numbers and symbols.

is equal to times

 25 (75)

SolveTo find the product, we use the rule for multiplying two integers that have

different signs. First, we find the absolute values: and.

Multiply the absolute values, 25 and 75, to get 1,875.

Since the integers have different signs, make the

final answer negative.

StateThe depth of the submersible was 1,875 feet below sea level ( feet)

when the 25th temperature measurement was taken.

CheckWe can use estimation or simply perform the actual multiplication again to

see if the result seems reasonable.

1,875

75

 25

375

1 500

1,875

25(75)1,875

0250  25 0  750  75



The depth of the

submersible when it

made the 25th

measurement

the amount it

was lowered

each time.

the number of

measurements

made

The depth of the

submersible when

it made the 25th

measurement

VOCABULARY

Fill in the blanks.

1. In the multiplication problem shown below, label
   each factorand the product.
    5  10  50


2. Two negative integers, as well as two positive integers,
   are said to have the same signs or signs.


3. A positive integer and a negative integer are said to
   have different signs or signs.


4. property of multiplication: The order in
   which integers are multiplied does not change their
   product.


5. property of multiplication: The way in
   which integers are grouped does not change their
   product.


6. In the expression , the is , and 5 is the
   .

(3)^5  3

CONCEPTS

Fill in the blanks.

7. Multiplication of integers is very much like
   multiplication of whole numbers. The only difference
   is that we must determine whether the answer is
   or.


8. When we multiply two nonzero integers, they either
   have signs or sign.


9. To multiply a positive integer and a negative integer,
   multiply their absolute values. Then make the final
   answer.


10. To multiply two integers that have the same sign,
    multiply their absolute values. The final answer is
    .


11. The product of two integers with signs
    is negative.


12. The product of two integers with signs is
    positive.


13. The product of any integer and 0 is.

SECTION 2.4 STUDY SET