๐ŸŒก๏ธ Negative Numbers: Below Zero & Beyond โ„๏ธ

Negative numbers are numbers less than zero. They have a minus sign (โˆ’) in front of them. We use them every day โ€” to describe cold temperatures, floors below ground, money owed, and depths below sea level!

๐ŸŒก๏ธ Temperature
โˆ’5ยฐC is 5 degrees below freezing
The lower the number, the colder it is!
๐Ÿ“ Number Line
... โˆ’4   โˆ’3   โˆ’2   โˆ’1   0   1   2   3   4 ...
Numbers get BIGGER as you go right
๐Ÿ’ฐ Debt
Owing ยฃ5 = โˆ’ยฃ5 in your account
Negative = you owe, Positive = you have

The Number Line

โ†
โˆ’6
โˆ’5
โˆ’4
โˆ’3
โˆ’2
โˆ’1
0
1
2
3
4
5
6
โ†’

โ† Smaller (more negative)     Larger (more positive) โ†’

The Golden Rules:

๐Ÿ“ Worked Examples

Study these carefully before trying the practice questions!

Example 1: Ordering Negative Numbers

Question: Write these numbers in order from smallest to largest: 3, โˆ’5, โˆ’1, 0, โˆ’8, 2

Think: on the number line, smaller = further left
Most negative first โ†’ โˆ’8, โˆ’5, โˆ’1, 0, 2, 3

Answer: โˆ’8, โˆ’5, โˆ’1, 0, 2, 3

Example 2: Temperature Difference

Question: The temperature in Moscow is โˆ’7ยฐC. In London it is 4ยฐC. What is the difference in temperature?

Step 1: Start at โˆ’7, count up to 4 on the number line
Step 2: From โˆ’7 to 0 = 7 steps. From 0 to 4 = 4 steps.
Step 3: Total = 7 + 4 = 11

Answer: The difference is 11ยฐC

Shortcut: 4 โˆ’ (โˆ’7) = 4 + 7 = 11

Example 3: Adding with Negative Numbers

Question: Calculate โˆ’4 + 9

Start at โˆ’4 on the number line
Move 9 places to the RIGHT (adding moves right)
โˆ’4 โ†’ โˆ’3 โ†’ โˆ’2 โ†’ โˆ’1 โ†’ 0 โ†’ 1 โ†’ 2 โ†’ 3 โ†’ 4 โ†’ 5

Answer: โˆ’4 + 9 = 5

Example 4: Subtracting into Negatives

Question: Calculate 3 โˆ’ 8

Start at 3 on the number line
Move 8 places to the LEFT (subtracting moves left)
3 โ†’ 2 โ†’ 1 โ†’ 0 โ†’ โˆ’1 โ†’ โˆ’2 โ†’ โˆ’3 โ†’ โˆ’4 โ†’ โˆ’5

Answer: 3 โˆ’ 8 = โˆ’5

๐Ÿ”ฌ Temperature Visualizer

Drag the sliders to set two temperatures and see the difference!

20ยฐ10ยฐ0ยฐโˆ’10ยฐโˆ’20ยฐ
โˆ’3ยฐC
City A
8ยฐC
City B
Difference = 11ยฐC

๐Ÿงฉ Drag 1: Smallest to Largest

Drag the numbers into the boxes in order from smallest โ†’ largest.

โˆ’4
2
โˆ’7
0
โˆ’1
๏ผœ
๏ผœ
๏ผœ
๏ผœ

๐Ÿงฉ Drag 2: Fill the Number Line

Drag the missing numbers to their correct positions on the number line.

โˆ’3
1
โˆ’5
3
โˆ’6
โ€”
โ€”
โˆ’4
โ€”
โ€”
0
โ€”
โ€”
2
โ€”

๐Ÿงฉ Drag 3: Temperature Difference

The temperature is โˆ’6ยฐC at night and 5ยฐC during the day.
Complete the steps to find the difference.

6
11
5
1
From โˆ’6 to 0 =
steps.   From 0 to 5 = 5 steps.
Total difference =
6
+ 5 =
ยฐC

๐Ÿงฉ Drag 4: Adding with Negatives

Drag the correct answer to each addition. Use the number line to help!

3
โˆ’2
7
โˆ’6
โˆ’5 + 8 =
โˆ’8 + 6 =

๐Ÿงฉ Drag 5: Subtracting into Negatives

Drag the correct answer. Remember: subtracting moves LEFT on the number line!

โˆ’3
โˆ’5
5
3
2 โˆ’ 7 =
โˆ’1 โˆ’ 2 =

๐Ÿงฉ Drag 6: Which is Greater?

Drag > or < to make each statement correct.

>
<
>
<
โˆ’2
โˆ’8
โˆ’10
โˆ’3

๐Ÿ“ Practice Questions

Grab your pencil and use a number line to help!

  1. Write these numbers in order, smallest first: 5, โˆ’3, โˆ’8, 0, 2, โˆ’1
  2. What number is 3 less than โˆ’2?
  3. What number is 5 more than โˆ’4?
  4. Calculate: โˆ’6 + 10
  5. Calculate: 4 โˆ’ 9
  6. Calculate: โˆ’3 + 3
  7. Calculate: โˆ’7 + 4
  8. Calculate: 1 โˆ’ 6
  9. The temperature is โˆ’4ยฐC. It rises by 7ยฐC. What is the new temperature?
  10. The temperature is 3ยฐC. It falls by 8ยฐC overnight. What is the new temperature?
  11. Find the difference between โˆ’5ยฐC and 6ยฐC.
  12. Find the difference between โˆ’3ยฐC and โˆ’10ยฐC.
  13. Which is greater: โˆ’9 or โˆ’4? Explain why.
  14. Write all integers between โˆ’4 and 2 (not including โˆ’4 and 2).
  15. A submarine is at โˆ’30 m (30 m below sea level). It rises 12 m. What is its new depth?
  16. Mark has ยฃ5 in his account. He spends ยฃ9. Write his new balance as a negative number.
  17. Put these in order from greatest to smallest: โˆ’100, โˆ’5, 0, โˆ’50, 3, โˆ’1
  18. Calculate: โˆ’2 + 8 โˆ’ 5
  19. The highest temperature in a week is 6ยฐC. The lowest is โˆ’9ยฐC. What is the range (difference)?
  20. Fill in the missing number: ___ + 7 = โˆ’1
  1. โˆ’8, โˆ’3, โˆ’1, 0, 2, 5
  2. โˆ’2 โˆ’ 3 = โˆ’5
  3. โˆ’4 + 5 = 1
  4. โˆ’6 + 10 = 4
  5. 4 โˆ’ 9 = โˆ’5
  6. โˆ’3 + 3 = 0
  7. โˆ’7 + 4 = โˆ’3
  8. 1 โˆ’ 6 = โˆ’5
  9. โˆ’4 + 7 = 3ยฐC
  10. 3 โˆ’ 8 = โˆ’5ยฐC
  11. 6 โˆ’ (โˆ’5) = 6 + 5 = 11ยฐC
  12. โˆ’3 โˆ’ (โˆ’10) = โˆ’3 + 10 = 7ยฐC
  13. โˆ’4 is greater โ€” it is further right on the number line (โˆ’4 > โˆ’9)
  14. โˆ’3, โˆ’2, โˆ’1, 0, 1
  15. โˆ’30 + 12 = โˆ’18 m
  16. 5 โˆ’ 9 = โˆ’ยฃ4
  17. 3, 0, โˆ’1, โˆ’5, โˆ’50, โˆ’100
  18. โˆ’2 + 8 = 6, then 6 โˆ’ 5 = 1
  19. 6 โˆ’ (โˆ’9) = 6 + 9 = 15ยฐC
  20. ___ = โˆ’1 โˆ’ 7 = โˆ’8

๐Ÿ”ฅ Challenge: Negative Numbers Word Problems

Show all your working!

  1. The temperature in five cities is: Oslo โˆ’12ยฐC, London 4ยฐC, Sydney 22ยฐC, Moscow โˆ’18ยฐC, Dubai 31ยฐC. Write the cities in order from coldest to warmest.
  2. A diver is at โˆ’45 m. She swims up 18 m, then down 7 m. What is her final depth?
  3. In a quiz game, Jake scores +8, โˆ’3, +5, โˆ’7, +2 over five rounds. What is his final total?
  4. The temperature on Monday is โˆ’6ยฐC. Each day it rises by 3ยฐC. What is the temperature on Friday?
  5. A lift is on floor โˆ’2 (2 floors underground). It goes up 5 floors, then down 3 floors. Which floor is it on now?
  6. The Dead Sea is about 430 m below sea level (โˆ’430 m). Mount Everest is 8,849 m above sea level (+8,849 m). What is the difference in height between them?
  7. Sarah owes her friend ยฃ12 (โˆ’12). She earns ยฃ20 and pays some back, but still owes ยฃ4. How much did she pay back?
  8. A number line shows: โˆ’10, ___, ___, โˆ’4, ___, 0, ___, 4. The gaps are all equal. What are the four missing numbers?
  9. The highest temperature ever recorded in the UK is 40ยฐC. The lowest is โˆ’27ยฐC. What is the difference between these extremes?
  10. Mr Josh records daily temperatures for a week: Mon โˆ’3ยฐC, Tue โˆ’1ยฐC, Wed 2ยฐC, Thu โˆ’4ยฐC, Fri 1ยฐC, Sat 3ยฐC, Sun โˆ’2ยฐC. What is the mean temperature for the week?
  1. Moscow (โˆ’18), Oslo (โˆ’12), London (4), Sydney (22), Dubai (31)
  2. โˆ’45 + 18 = โˆ’27, then โˆ’27 โˆ’ 7 = โˆ’34 m
  3. 8 โˆ’ 3 + 5 โˆ’ 7 + 2 = 5 points
  4. Mon: โˆ’6, Tue: โˆ’3, Wed: 0, Thu: 3, Fri: 6ยฐC
  5. โˆ’2 + 5 = 3, then 3 โˆ’ 3 = Floor 0 (ground floor)
  6. 8,849 โˆ’ (โˆ’430) = 8,849 + 430 = 9,279 m
  7. Started at โˆ’12, now at โˆ’4, so paid back โˆ’4 โˆ’ (โˆ’12) = ยฃ8
  8. Gaps are 2 each. Missing: โˆ’8, โˆ’6, โˆ’2, 2
  9. 40 โˆ’ (โˆ’27) = 40 + 27 = 67ยฐC
  10. Sum: โˆ’3 + (โˆ’1) + 2 + (โˆ’4) + 1 + 3 + (โˆ’2) = โˆ’4. Mean = โˆ’4 รท 7 โ‰ˆ โˆ’0.57ยฐC
Created by Mr Josh โœจ FractionRush