1. Number

Worksheet

1

Use the plotted point on the number line to add the following integers:

a

5 + 9

b

- 3 + 8

c

- 6 + 3

d

- 7 + 7

e

3 + 9 + 7

f

- 8 + 6 + 9

g

- 7 + 7 + 4

h

- 10 + 5 + 12

2

Evaluate:

a

14 + 7

b

- 7 + 15

c

- 15 + 6

d

- 15 + 15

e

- 9 + 0

f

- 39 + 97

g

- 26 + 15

h

- 45 + 45

i

- 13 + 8 + 2

j

- 24 + 10 + 54

k

- 21 + 0 + 21

l

- 88 + 28 + 92

3

Use the plotted point on the number line to subtract the following integers:

a

8 - 5

b

7 - 9

c

3 - 3

d

- 9 - 9

e

- 2 + 7 - 4

f

10 - 7 - 2

g

14 - 18 + 1

h

- 1 - 15 - 3

4

Evaluate:

a

12 - 3

b

9 - 13

c

11 - 11

d

- 13 - 13

e

- 32 - 41

f

36 - 53

g

- 9 - 5 - 8

h

- 12 - 3 + 16

i

27 - 19 -10

j

0 - 11 + 36

k

- 7 - 8 - 15

l

14 - 49 + 35

5

Evaluate:

a

7 + \left( - 5 \right)

b

- 7 + \left( - 8 \right)

c

2 - \left( - 3 \right)

d

- 3 - \left( - 9 \right)

e

- 12 - \left( - 12 \right)

f

17 + \left( - 14 \right)

g

29 - \left( - 52 \right)

h

- 30 - \left( - 32 \right)

i

12 + 17 + \left( - 15 \right)

j

- 12 + 16 + \left( - 18 \right)

k

17 - 27 + \left( - 17 \right)

l

- 5 + \left( - 2 \right) + \left( - 7 \right)

m

- 9 - 2 - \left( - 8 \right)

n

- 5 - \left( - 2 \right) - \left( - 10 \right)

o

- 17 + 23 + \left( - 20 \right)

p

34 - 63 - \left( - 34 \right)

6

Valentina dives off a platform that is 8\text{ m} above the water. She descends 14\text{ m} before returning to the surface.

a

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.

b

Hence, state the greatest depth that Valentina reaches during the dive.

7

One evening in Pickering 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.

8

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.

9

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.

10

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.

11

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 |

a

Find the actual volume of:

i

Bottle 1

ii

Bottle 2

iii

Bottle 6

iv

Bottle 10

b

Calculate the total volume contained in the 10 bottles.

12

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:

a

NET

b

EAR

c

RAIN

d

CARES

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Apply an understanding of integers to describe location, direction, amount, and changes in any of these, in various contexts.