Middle Years

# 5.01 Integers and the number line

Worksheet
Number lines
1

State the integer where the point is plotted on the following number lines:

a
b
c
d
e
f
g
h
i
j
2

State the number that is 6 units to the right of the plotted point:

3

State the number that is 7 units to the left of the plotted point:

4

State the number that is 6 units to the left of the plotted point:

5

State the number that is 7 units to the right of the plotted point:

6

State the number that is 9 units to the left of the plotted point:

7

State the number that is 7 units to the right of the plotted point:

Integers
8

Describe how to tell if two integers on a number line are opposites.

9

For each of the following number lines:

i

State the number that has been plotted.

ii

State the opposite of the number that has been plotted.

a
b
c
d
10

Consider the integer 8.

a

State its opposite.

b

True or False: "The opposite of a number is always greater than the number itself."

11

State the number that is the opposite of 0.

12

The opposite of a number is - 16. State the original number.

Comparison and order of integers
13

State the greatest number plotted on the following number lines:

a
b
14

State the smallest number plotted on the following number lines:

a
b
15

State the greatest number in each set:

a

13, - 14, 2

b

- 7, - 17, - 12

c

8, - 8, 7

d

35, - 36, -40

16

State the smallest number in each set:

a

- 14, - 4, -21

b

- 7, - 24, 10

c

1, - 1, 5

d

34, - 36, -2

17

Arrange the following numbers in ascending order: 10, - 25, 16, - 11, 27

18

Arrange the following numbers in descending order: 3, - 13, 11, - 9, 15

19

For each pair of temperatures, state the higher temperature:

a

- 19 \degree \text{C} or 4 \degree \text{C}

b

-3\degree \text{C} or - 17\degree \text{C}

20

For each pair of temperatures, state the lower temperature:

a

- 15\degree \text{ C} or - 3\degree \text{ C}

b

- 10\degree \text{ C} or 1\degree \text{ C}

21

Write an inequality that compares the two integers plotted on the following number lines:

a
b
22

For each of the following inequalities:

i

Write the inequality in words.

ii

State if the inequality is true or false.

a

- 7 \lt - 2

b

7 \gt - 5

c

0 \gt - 1

d

23 \lt -47

23

Identify the inequality sign, \lt or \gt, that should appear between each pair of numbers to make each statement true:

a

7 \, ⬚ \, - 4

b

- 9 \, ⬚ \, 9

c

0 \, ⬚ \, - 8

d

- 2 \, ⬚ \, - 5

e

39 \, ⬚ \, - 72

f

-12 \, ⬚ \, -14

g

-45 \, ⬚ \, 22

h

-1 \, ⬚ \, - 30

Applications
24

Consider the following statement: "Arriving 14 minutes late."

a

State the opposite of "Arriving 14 minutes late".

b

Suppose "Arriving 14 minutes late" is represented by the number 14. State the integer that should represent its opposite.

25

Consider the following statement: "Cycling 8\text{ km} due south."

a

State the opposite of "Cycling 8\text{ km} due south".

b

Suppose "Cycling 8 \text{ km} due south" is represented by the number 8. State the integer that should represent its opposite.

26

A gain of \$400 can be represented by the integer 400. a State whether the following would represent the opposite of this situation: i Gaining another \$400.

ii

Losing \$400. iii Losing \$800.

b

27

State the integer that represents the opposite of the following:

a

The statement "Descending 2 floors" is represented by the number - 2.

b

The statement "A weight gain of 11 \text{ kg}" is represented by the number 11.

c

A temperature of 10 degrees below freezing is represented by the integer - 10.

28

A temperature drop of 14 \degree \text{C} can be represented by the integer - 14.

a

State an integer that represents the opposite of a temperature drop of 14 \degree \text{C}.

b

State an integer that represents the opposite of the opposite of a temperature drop of 14\degree \text{C}.

29

A mountain peak is measured to have a height of 5100 \text{ m} above sea level. An ocean trench is found that is the same distance below sea level.

a

If the height above sea level of the mountain peak is represented by the number 5100, state the integer that represents the location of the trench.

b

In this scenario, state what the integer 0 represents.

30

For each of the following scenarios, write down an inequality that compares the two quantities:

a

Yuri has \$8 in savings. Kenneth has \$13 saved.

b

Christa's account balance is - \$10. Ray's account balance is - \$17.

c

Elizabeth and Roxanne both buy some tickets in the raffle at the local fete. After counting up their winnings, Elizabeth has made \$86, but Roxanne has lost \$146.

d

Paul has read 27 books this year. His sister Eileen has read 17 books.

e

Quiana has made \$78.79 this week in her part time job, and has spent \$35.33 on food in that time.

f

The melting point of krypton is - 157 \degree \text{C}. The melting point of radon is - 71 \degree \text{C}.