4B Adding Negative Quantities

Sally invested in a stock. When looking at the stock’s price per share over the last few weeks, she noticed that the stock price had decreased $4.50, then increased $1.25 and lastly decreased again $5. How much has the stock price fallen overall? These are the types of problems we will be looking at in this section. When the stock decreases, that corresponds to a negative value. When the stock increases, that corresponds to a positive value.

How do we add these quantities? Let’s review.

To add two numbers with the same sign, (both negative or both positive) we add their absolute values and keep the common sign. For example, what is $-10+-7$ ? Since both the numbers are negative, we simply add 10 + 7 = 17 and then keep the negative sign. So $-10+-7=-17$.

To add two numbers with opposite signs (one negative and one positive) we subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value. If the absolute values are equal, the sum is zero. For example, what is $-13++8$ ? Since the signs are opposite, we subtract 13 – 8 = 5 and keep the sign of the larger. 13 is larger than 8 and the sign on the 13 is negative, so our answer will be $-13++8=-5$.

Money is a great example of negative numbers. Suppose you owe the bank $240 for your car payment. Notice this would correspond to $(-240)$. If you were only able to pay them $180 $(+180)$, would you still owe the bank money? If so how much? Since we still owe the bank $60, $(-60)$this would show that $-240++180=-60$.

Add the following numbers with your instructor.

The same rules of addition apply to fractions and decimals. When we add two fractions or decimals with the same sign, we add their absolute values and keep the common sign. When they have opposite signs, we subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value. If the absolute values are equal, the sum is zero.

Add the following numbers with your instructor.

Practice Problems Section 4B

Add the following:

1. $$-7+-12$$

   Check answer

   ^-19

2. $$+9+-15$$

   Check answer

   ^-6

3. $$-14+-8$$

   Check answer

   ^-22

4. $$-9++7$$

   Check answer

   ^-2

5. $$-12+-3$$

   Check answer

   ^-15

6. $$-17++17$$

   Check answer

   0

7. $$-12+-16$$

   Check answer

   ^-28

8. $$+8+-33$$

   Check answer

   ^-25

9. $$-13+-43$$

   Check answer

   ^-56

10. $$-19++4$$

    Check answer

    ^-15

11. $$-26+-14$$

    Check answer

    ^-40

12. $$+57+-24$$

    Check answer

    33

13. $$-35+-27$$

    Check answer

    ^-62

14. $$+28+-53$$

    Check answer

    ^-25

15. $$-23+-48$$

    Check answer

    ^-71

16. $$-109++109$$

    Check answer

    0

17. $$-76+-59$$

    Check answer

    ^-135

18. $$-538+-249$$

    Check answer

    ^-787

Remember the same rules of addition apply to fractions and decimals. Add the following.

19. $$-2.6+-5.71$$

    Check answer

    ^-8.31

20. $$+7.78+-9.52$$

    Check answer

    ^-1.74

21. $$-0.68+-0.349$$

    Check answer

    ^-1.029

22. $$+3.5+-12.89$$

    Check answer

    ^-9.39

23. $$-7.31+-9$$

    Check answer

    ^-16.31

24. $$-0.0047++0.185$$

    Check answer

    0.1803

25. $$(-\frac{1}{3})+(-\frac{3}{4})$$

    Check answer

    ^- $1⁤\frac{1}{12}$

26. $$\frac{6}{7}+(-\frac{1}{5})$$

    Check answer

    $$\frac{23}{35}$$

27. $$(-\frac{5}{8})+(-\frac{7}{12})$$

    Check answer

    ^- $1⁤\frac{5}{24}$

28. $$(-1⁤\frac{1}{3})+(+4⁤\frac{3}{4})$$

    Check answer

    $$3⁤\frac{5}{12}$$

29. $$(-8⁤\frac{1}{4})+(-3⁤\frac{5}{7})$$

    Check answer

    ^- $11⁤\frac{27}{28}$

30. $$(+1⁤\frac{3}{8})+(-2⁤\frac{5}{6})$$

    Check answer

    ^- $1⁤\frac{11}{24}$

There are many applications of negative numbers. Try these.

31. Jim gambles on fantasy football. On week 1, Jim lost $23. On week 2, he lost $14. On week 3, he made $8. On week 4, he lost $33. What was his net gain or loss?

    Check answer

    $62 loss

32. The temperature on Monday was $+3\text{°}F$. On Tuesday the temperature dropped 7 degrees and on Wednesday it dropped 5 more degrees. What was the temperature on Wednesday?

    Check answer

    -9$\text{°F}$

33. Jesse was scuba diving at a depth of 65 feet below sea level. He then dived an additional 19 feet down. He then swam up 23 feet. What was his new depth?

    Check answer

    61 ft below sea level

34. In Reno, NV, the temperature at 5:00 AM was $-8\text{°}F$. Over the next 7 hours, the temperature had risen $29\text{°}F$. What was the new temperature at noon?

    Check answer

    21$\text{°F}$

35. A roadside fruit stand has a credit balance of $-543$ dollars. In the summer, they make a profit of $6,150. What is their new balance?

    Check answer

    $5,607

36. A basketball player’s “plus/minus” is a number that is calculated by adding all of the positive points her team scores with all of the negative points her team gives up while she is in the game. While the starting point guard was in the game, her team scored 62 points and gave up 71 points. Calculate her plus/minus value.

    Check answer

    -9

37. Paloma is balancing her checkbook for the month of May. At the beginning of the month, she had a balance of $89.05 in her checking account. She wrote a check for $450, took out $40 from the ATM, and deposited a paycheck worth $915.25. What is Paloma’s new account balance?

    Check answer

    $514.30

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