Chapter 4 Review

A good understanding of negative numbers is vital for many applications. Finance, business, temperature and altitude are a few examples that frequently use negative numbers. Here are a few key things to remember.

When adding two negative numbers, add their absolute values and keep the negative sign.
When adding a negative and positive number, subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value. If their absolute values are equal, the sum is zero.
When subtracting, we can rewrite any subtraction as adding the opposite. Then we can use the addition rules to finish the problem.
When multiplying or dividing two negative numbers, the answer will always be positive.
When multiplying or dividing a negative number and a positive number, the answer will always be negative.
Don’t confuse the addition and multiplication rules. (Two negatives does not always make a positive!)

Review Problems Chapter 4

Describe the following as a negative or positive quantity.

The depth of a scuba diver is 53 feet below sea level.

Check answer

negative
The temperature is 16 degrees below zero.

Check answer

negative
An airplane is flying at 2500 feet above sea level.

Check answer

positive
Pat won $250 while gambling at a Casino.

Check answer

positive
The number of people in a small town has decreased by 87.

Check answer

negative

Find the following absolute values:

$vertical bar minus 11 vertical bar$

Check answer

11
$vertical bar plus 24 vertical bar$

Check answer

24
$vertical bar minus 19 vertical bar$

Check answer

19

Add the following:

$- 38 + - 17$

Check answer

^-55
$+ 8.2 + - 13.7$

Check answer

^-5.5
$- 7 \frac{1}{6} + - 1 \frac{5}{6}$

Check answer

^-9
$- 124 + + 527$

Check answer

403
$- 0.0014 + - 2.579$

Check answer

^-2.5804
$\frac{1}{12} + (- \frac{5}{6})$

Check answer

$- \frac{3}{4}$

Subtract the following:

$- 21 - + 9$

Check answer

^-30
$+ 17 - - 6$

Check answer

23
$- 3 - - 3$

Check answer

0
$+ 21 - + 30$

Check answer

^-9
$+ 8.4 - + 25.7$

Check answer

^-17.3
$- \frac{5}{8} - (\frac{3}{4})$

Check answer

-1 $\frac{3}{8}$

Multiply the following:

$- 9 \times + 12$

Check answer

^-108
$- 12 \times - 3$

Check answer

36
$- 2.6 \times + 1.8$

Check answer

^-4.68
$(- 16) (+ 1)$

Check answer

^-16
$(+ 0.09) (- 1.1)$

Check answer

^-0.099
$open parenthesis minus 21 close parenthesis open parenthesis 0 close parenthesis$

Check answer

0

Divide the following:

$0 \div (- 8)$

Check answer

0
$- 0.48 \div + 0.9$

Check answer

^-0. $5 with 3 repeating$ or - $\frac{8}{15}$
$(\frac{1}{2}) \div (- \frac{5}{7})$

Check answer

$- \frac{7}{10}$
$- 2.39 \div - 1$

Check answer

2.39
$\frac{- 15}{0}$

Check answer

undefined
$\frac{- 2.73}{- 3}$

Check answer

0.91

Simplify the following:

$minus 13 squared$

Check answer

^-169
$open parenthesis minus 4 close parenthesis squared$

Check answer

16
$- 5^{2} - {(- 3)}^{2}$

Check answer

^-34
$- 2 (- 18) \div (- 1 \times + 9) + (- 8)$

Check answer

-12

Answer the following application questions:

On Monday, John made $234 in the stock market. On Tuesday, he lost $417 and on Wednesday he lost an additional $175. What was his net gain or loss over the three-day period?

Check answer

$358 loss
Use the temperature formula $F = 1.8 \times C + 32$ to convert $minus 6 ° C$ into Fahrenheit.

Check answer

21.2 $°F$
Use the temperature formula $C = \frac{(F - 32)}{1.8}$ to convert $28.4 ° F$ into Celsius.

Check answer

^-2 $°C$
We used Statistics to find the following Cost formula for a company. $C = 1.05 {(x - 33)}^{2} + 1240$ (x represents the number of hours their employees work per week and C represents the company’s cost in dollars.) Find the company’s cost if the employees work 40 hours in a week. Find the company’s cost if the employees work 35 hours in a week.

Check answer

40 hours --- $1,291.45; 35 hours --- $1,244.2

Adapted from Preparing for Algebra and Statistics, Third Edition, by Matt Teachout. License: CC BY 4.0. Copyright and sources.