Integers. a) Circle the positive integers from the following set: 18, −10, 25, 7, 30, 12, −5, 14, −2. b)…

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Integers. a) Circle the positive integers from the following set: 18, −10, 25, 7, 30, 12, −5, 14, −2. b) Circle the negative integers from the following set: 19, −4, 0, 11, −7, −15, −3, 9, 6. 2. Peter

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Here are the solutions to the problems.

1. Integers

a) Circle the positive integers from the following set:
$\{18, -10, 25, 7, 30, 12, -5, 14, -2\}$
The positive integers are numbers greater than zero.
The numbers to be circled are: $\boxed{18, 25, 7, 30, 12, 14}$ .

b) Circle the negative integers from the following set:
$\{19, -4, 0, 11, -7, -15, -3, 9, 6\}$
The negative integers are numbers less than zero.
The numbers to be circled are: $\boxed{-4, -7, -15, -3}$ .

2. Petero used a ladder to climb an avocado tree. He made 8 steps up the ladder and 4 steps down the ladder. Use a number line to represent:

a) The number of steps he made up the ladder.
Moving up is represented by a positive integer.
The number of steps up is $\boxed{+8}$ .
On a number line, this is a movement of 8 units to the right from 0.

b) The number of steps he made down the ladder.
Moving down is represented by a negative integer.
The number of steps down is $\boxed{-4}$ .
On a number line, this is a movement of 4 units to the left from 0.

3. A grade 8 learner was carrying out a science experiment on heat change. The original temperature reading was $9^\circ C$ . The temperature fell by $9^\circ C$ . Using a number line, show the new reading of the new temperature.

Identify the initial temperature and the change.
Original temperature $= 9^\circ C$ .
Temperature fell by $9^\circ C$ , which means a decrease of $9^\circ C$ .
Calculate the new temperature.
New temperature $= 9^\circ C - 9^\circ C = 0^\circ C$ .

Represent on a number line.

Start at 9 on the number line and move 9 units to the left. This movement ends at 0.
The new temperature reading is $\boxed{0^\circ C}$ .

4. Represent the following numbers on a number line:

a) 9
Draw a straight line and mark a point as 0. Mark equal intervals to the right for positive numbers and to the left for negative numbers. Place a dot or mark at the position corresponding to $\boxed{9}$ on the number line.

5. Fill in the following blank spaces:

a) $-8 + \boxed{\phantom{X}} = -15$
Let the blank be $x$ .

-8 + x = -15

x = -15 - (-8)

x = -15 + 8

x = -7

The blank is $\boxed{-7}$ .

b) $\boxed{\phantom{X}} - (-4) = 8$
Let the blank be $y$ .

y - (-4) = 8

y + 4 = 8

y = 8 - 4

y = 4

The blank is $\boxed{4}$ .

c) $10 - \boxed{\phantom{X}} = -7$
Let the blank be $z$ .

10 - z = -7

-z = -7 - 10

-z = -17

z = 17

The blank is $\boxed{17}$ .

6. Complete the table below by identifying equivalent integers in the respective blank spaces in the table.

Description	Positive integer	Negative integer
100 m below sea level	$\boxed{100}$	$\boxed{-100}$
20 cm to the right of 0 on a number line	$\boxed{20}$	$\boxed{-20}$
Eight steps below a ladder	$\boxed{8}$	$\boxed{-8}$
6 floors up	$\boxed{6}$	$\boxed{-6}$

Integers. a) Circle the positive integers from the following set: 18, -10, 25, 7, 30, 12, -5, 14, -2. b) Circle the negative integers from the following set: 19, -4, 0, 11, -7, -15, -3, 9, 6. 2. Peter

Step-by-step solution

Identify the initial temperature and the change.

Calculate the new temperature.

Represent on a number line.

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