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Draw arrows on a number line to represent these situations:
The temperature was -5 degrees. Then the temperature rose 5 degrees.
A climber was 30 feet above sea level. Then she descended 30 feet.
What’s the opposite?
A mountaineer is climbing on a cliff. She is 400 feet above the ground. If she climbs up, this will be a positive change. If she climbs down, this will be a negative change.
Complete the table.
| starting elevation (feet) |
change (feet) |
final elevation (feet) |
|
|---|---|---|---|
| A | +400 | 300 up | |
| B | +400 | 150 down | |
| C | +400 | 400 down | |
| D | +400 | +50 |
Write an addition equation and draw a number line diagram for B. Include the starting elevation, change, and final elevation in your diagram.
A spelunker is down in a cave next to the cliff. If she climbs down deeper into the cave, this will be a negative change. If she climbs up, whether inside the cave or out of the cave and up the cliff, this will be a positive change.
Complete the table.
| starting elevation (feet) |
change (feet) |
final elevation (feet) |
|
|---|---|---|---|
| A | -200 | 150 down | |
| B | -200 | 100 up | |
| C | -200 | 200 up | |
| D | -200 | 250 up | |
| E | -200 | -500 |
Write an addition equation and draw a number line diagram for C and D. Include the starting elevation, change, and final elevation in your diagram.
What does the expression tell us about the spelunker? What does the value of the expression tell us?
The opposite of a number is the same distance from 0 but on the other side of 0.
A number line with the numbers negative 10 through 10 indicated. An arrow starts at 0, points to the left, and ends at negative 9. There is a solid dot indicated at negative 9. A second arrow starts at 0, points to the right, and ends at 9. There is a solid dot indicated at 9.
The opposite of -9 is 9. When we add opposites, we always get 0. The following diagram shows that .
A number line with the numbers negative 10 through 10 indicated. An arrow starts at 0, points to the right, and ends at 9. A second arrow starts at 9, points to the left, and ends at 0. there is a solid dot indicated at 0.
When we add two numbers with the same sign, the arrows that represent them point in the same direction. When we put the arrows tip to tail, we see the sum has the same sign as the original numbers.
A number line, an arrow starts at 0, points to the right, and ends at 4. A second arrow starts at 4, points to the right, and ends at 7. There is a solid dot indicated at 7.
A number line, an arrow starts at 0, points to the left, and ends at negative 5. A second arrow starts at negative 5, points to the left, and ends at negative 9. There is a solid dot indicated at negative 9.
To find the sum, we add the magnitudes and give it the correct sign. For example, .
On the other hand, when we add two numbers with different signs, we subtract their magnitudes (because the arrows point in the opposite direction) and give it the sign of the number with the larger magnitude. For example, .
A number line with the numbers negative 10 through 10 indicated. An arrow starts at 0, points to the left, and ends at negative five. A second arrow starts at negative five, points to the right, and ends at 7. There is a solid dot indicated at 7.
Two numbers are opposites if they are the same distance from 0 on the number line, but on different sides. One is negative, and the other is positive.