Let’s make sense of negative amounts of money.
| activity | amount | |
|---|---|---|
| row 1 | do my chores | 30.00 |
| row 2 | babysit my cousin | 45.00 |
| row 3 | buy my lunch | -10.80 |
| row 4 | get my allowance | 15.00 |
| row 5 | buy a shirt | -18.69 |
| row 6 | pet my dog | 0.00 |
The manager of the concession stand keeps records of all of the supplies she buys and all of the items she sells. The table shows some of her records for Tuesday.
| row | item | quantity | value in dollars |
|---|---|---|---|
| 1 | doughnuts | -58 | 37.70 |
| 2 | straws | 3,000 | -10.35 |
| 3 | hot dogs | -39 | 48.75 |
| 4 | pizza | 13 | -116.87 |
| 5 | apples | -40 | 14.00 |
| 6 | french fries | -88 | 132.00 |
A vending machine in an office building sells bottled beverages. The machine keeps track of all changes in the number of bottles from sales and from machine refills and maintenance. This record shows the changes for every 5-minute period over one hour.
What might a positive number mean in this context? What about a negative number?
What would a “0” in the second column mean in this context?
Which numbers—positive or negative—result in fewer bottles in the machine?
| time | number of bottles |
|---|---|
| 8:00–8:04 | -1 |
| 8:05–8:09 | +12 |
| 8:10–8:14 | -4 |
| 8:15–8:19 | -1 |
| 8:20–8:24 | -5 |
| 8:25–8:29 | -12 |
| 8:30–8:34 | -2 |
| 8:35–8:39 | 0 |
| 8:40–8:40 | 0 |
| 8:45–8:49 | -6 |
| 8:50–8:54 | +24 |
| 8:55–8:59 | 0 |
| service |
Priya, Mai, and Lin went to a cafe on a weekend. Their shared bill came to \$25. Each student gave the server a \$10 bill. The server took this \$30 and brought back five \$1 bills in change. Each student took \$1 back, leaving the rest, \$2, as a tip for the server.
As she walked away from the cafe, Lin thought, “Wait—this doesn’t make sense. Since I put in \$10 and got \$1 back, I wound up paying \$9. So did Mai and Priya. Together, we paid \$27. Then we left a \$2 tip. That makes \$29 total. And yet we originally gave the waiter \$30. Where did the extra dollar go?”
Think about the situation and about Lin’s question. Do you agree that the numbers didn’t add up properly? Explain your reasoning.
Sometimes we represent changes in a quantity with positive and negative numbers. If the quantity increases, the change is positive. If it decreases, the change is negative.
It is especially common to represent money we receive with positive numbers and money we spend with negative numbers.
Whether a number is considered positive or negative depends on a person’s perspective. If Clare’s grandmother gives her \$20 for her birthday, Clare might see this as +20, because to her, the amount of money she has increased. But her grandmother might see it as -20, because to her, the amount of money she has decreased.
In general, when using positive and negative numbers to represent changes, we have to be very clear about what it means when the change is positive and what it means when the change is negative.
