5.02 Adding and subtracting integers
Use the plotted point on the number line to add the following integers:
5 + 9
- 3 + 8
- 6 + 3
- 7 + 7
3 + 9 + 7
- 8 + 6 + 9
- 7 + 7 + 4
- 10 + 5 + 12
Evaluate:
14 + 7
- 7 + 15
- 15 + 6
- 15 + 15
- 9 + 0
- 39 + 97
- 26 + 15
- 45 + 45
- 13 + 8 + 2
- 24 + 10 + 54
- 21 + 0 + 21
- 88 + 28 + 92
Use the plotted point on the number line to subtract the following integers:
8 - 5
7 - 9
3 - 3
- 9 - 9
- 2 + 7 - 4
10 - 7 - 2
14 - 18 + 1
- 1 - 15 - 3
Evaluate:
12 - 3
9 - 13
11 - 11
- 13 - 13
- 32 - 41
36 - 53
- 9 - 5 - 8
- 12 - 3 + 16
27 - 19 -10
0 - 11 + 36
- 7 - 8 - 15
14 - 49 + 35
Evaluate:
7 + \left( - 5 \right)
- 7 + \left( - 8 \right)
2 - \left( - 3 \right)
- 3 - \left( - 9 \right)
- 12 - \left( - 12 \right)
17 + \left( - 14 \right)
29 - \left( - 52 \right)
- 30 - \left( - 32 \right)
12 + 17 + \left( - 15 \right)
- 12 + 16 + \left( - 18 \right)
17 - 27 + \left( - 17 \right)
- 5 + \left( - 2 \right) + \left( - 7 \right)
- 9 - 2 - \left( - 8 \right)
- 5 - \left( - 2 \right) - \left( - 10 \right)
- 17 + 23 + \left( - 20 \right)
34 - 63 - \left( - 34 \right)
Valentina dives off a platform that is 8\text{ m} above the water. She descends 14\text{ m} before returning to the surface.
If Valentina's initial position on the diving platform is represented by the directed number 8, find the directed number that represents her lowest position throughout the dive.
Hence, state the greatest depth that Valentina reaches during the dive.
One evening in Moscow the temperature fell to - 3 \degree \text{C}. By midday the next day, the temperature was forecast to be 15 \degree \text{C}. Find the expected rise in temperature.
Liquid nitrogen can be used to make ice cream. The ice cream mixture starts at 26 \degree \text{ C}, then rapidly cools to - 185 \degree \text{ C} after liquid nitrogen is added to it. State the directed number that represents this change in temperature.
Three contestants are heading into the final round of a game show. Eileen has 39 points and Roxanne has - 3 points. If Oprah has 14 more points than Eileen, calculate how many points separate Roxanne and Oprah.
A submarine is 148 \text{ m} below sea level. It rises 34 \text{ m}, then dives 47 \text{ m}. Find the distance of the submarine below sea level.
Each bottle of orange juice is supposed to contain 250 \text{ mL}. Nine bottles are inspected by the quality assurance department. The results of the inspection are shown in the table:
| \text{Bottle} | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| \text{Amount below or above} \\ \text{the required volume (mL)} | +4 | -7 | -11 | +9 | +3 | 0 | -1 | -5 | +6 | +1 |
Find the actual volume of:
Bottle 1
Bottle 2
Bottle 6
Bottle 10
Calculate the total volume contained in the 10 bottles.
Each letter has been assigned to an integer. A word must be formed using these letters and each letter can only be used once. The table shows the assignment of the integers:
| Letter | A | E | I | C | T | N | R | S |
|---|---|---|---|---|---|---|---|---|
| Integer | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
The score of the word is the sum of the integers assigned to its letters. Find the score of the following words:
NET
EAR
RAIN
CARES