Addition and subtraction of positive and negative numbers
🎯 In this topic you will
- add and subtract positive and negative numbers.
🧠 Key Words
- integer
- negative number
- positive number
Show Definitions
- integer: A whole number that can be positive, negative, or zero, without any fractional or decimal part.
- negative number: A number less than zero, written with a minus sign, representing a value below zero on the number line.
- positive number: A number greater than zero, representing a value above zero on the number line.
Elevator Numbers Change
If you watch the floors as you go down in an elevator, the numbers change from positive to negative.
Underground Floor Levels
In this building, the car park is on level −2 which is the second floor underground.
Learning Goal of This Section
In this section you will learn to add and subtract positive and negative numbers.
❓ EXERCISES
Exercise $5.2$.
This number line shows positive and negative numbers.
You can use it to help you answer the questions in this exercise.
1. Here is part of a number line. Find the two missing numbers.
👀 Show answer
The first jump is an increase of $6$ from the left missing number to $-4$, so the left missing number is $-10$ because $-10 + 6 = -4$.
The second jump is another increase of $6$ from $-4$ to the right missing number, so the right missing number is $2$ because $-4 + 6 = 2$.
The missing numbers are $-10$ and $2$.
2.
a. What is $5$ less than $2$?
b. What is $4$ more than $-3$?
c. What is $400$ more than $-5$?
d. What is $30$ less than $1$?
👀 Show answer
a. $2 - 5 = -3$
b. $-3 + 4 = 1$
c. $-5 + 400 = 395$
d. $1 - 30 = -29$
3. Calculate.
a. $-4 + 2$
b. $2 - 6$
c. $-1 + 3$
Check your answers to questions $2$ and $3$ with your partner. Discuss any questions you did not agree on.
👀 Show answer
a. $-4 + 2 = -2$
b. $2 - 6 = -4$
c. $-1 + 3 = 2$
4. Copy and complete the table.
| Temperature now | Rise or fall in temperature | New temperature |
|---|---|---|
| $2^\circ\text{C}$ | A fall of $5$ degrees | |
| $-3^\circ\text{C}$ | A rise of $8$ degrees | |
| $1^\circ\text{C}$ | A fall of $5$ degrees | |
| $-4^\circ\text{C}$ | A rise of $2$ degrees | |
| $6^\circ\text{C}$ | A fall of $6$ degrees |
👀 Show answer
The completed new temperatures are:
$2^\circ\text{C}$ with a fall of $5$ degrees gives $-3^\circ\text{C}$.
$-3^\circ\text{C}$ with a rise of $8$ degrees gives $5^\circ\text{C}$.
$1^\circ\text{C}$ with a fall of $5$ degrees gives $-4^\circ\text{C}$.
$-4^\circ\text{C}$ with a rise of $2$ degrees gives $-2^\circ\text{C}$.
$6^\circ\text{C}$ with a fall of $6$ degrees gives $0^\circ\text{C}$.
5. The thermometers show the temperatures in London and Montreal on the same day.
a. How many degrees colder is it in Montreal than in London?
b. On a different day the temperature in London is $4^\circ\text{C}$. Montreal is $16^\circ$ colder than in London. What is the temperature in Montreal?
👀 Show answer
a. Read the temperatures from the thermometers and find the difference between them. The distance between the two values on the scale is $12^\circ$, so Montreal is $12^\circ$ colder than London.
b. If London is at $4^\circ\text{C}$ and Montreal is $16^\circ$ colder, then the temperature in Montreal is $4^\circ\text{C} - 16^\circ = -12^\circ\text{C}$.
6. Sort these calculations into groups according to their answer. Label each group.
$-4 + 4$
$-2 - 2$
$4 + 0$
$4 - 5$
$6 - 6$
$5 - 7$
$-3 - 1$
$-4 + 5$
👀 Show answer
Calculate each expression and group those with the same answer.
Answers:
$-4 + 4 = 0$
$-2 - 2 = -4$
$4 + 0 = 4$
$4 - 5 = -1$
$6 - 6 = 0$
$5 - 7 = -2$
$-3 - 1 = -4$
$-4 + 5 = 1$
So possible groups are:
Answer $0$: $-4 + 4$, $6 - 6$
Answer $-4$: $-2 - 2$, $-3 - 1$
Answer $4$: $4 + 0$
Answer $-1$: $4 - 5$
Answer $-2$: $5 - 7$
Answer $1$: $-4 + 5$
7. Calculate.
a. $0 - 78$
b. $45 - 150$
c. $-65 - 35$
d. $-13 + 79$
e. $-8 + 318$
f. $-20 + 370$
👀 Show answer
a. $0 - 78 = -78$
b. $45 - 150 = -105$
c. $-65 - 35 = -100$
d. $-13 + 79 = 66$
e. $-8 + 318 = 310$
f. $-20 + 370 = 350$