Negative numbers · Grade 7
In Grade 7 you learn: counting back through zero; negative numbers in temperatures; the difference across zero; adding and subtracting negative numbers.
Negative numbers are numbers below zero. We meet them in cold temperatures, bank overdrafts, floors below ground and depths below sea level. A number line is the best way to picture them: further left means smaller, so −8 is less than −2.
Key facts
- On a number line, numbers get smaller to the left: −7 < −3 < 0 < 2.
- Adding a positive moves right; subtracting a positive moves left.
- Subtracting a negative is the same as adding: 5 − (−3) = 5 + 3 = 8.
- Adding a negative is the same as subtracting: 6 + (−4) = 6 − 4 = 2.
- Multiplying or dividing: same signs give positive, different signs give negative.
- The difference between two temperatures is how far apart they are on the number line.
Worked examples
Example 1
It is −4 °C at dawn. By midday it is 7 °C warmer. What is the temperature at midday?
Answer: 3 °C
Example 2
−6 − (−9)
Answer: 3
Example 3
(−8) × 3 and (−24) ÷ (−6)
Answer: −24 and 4
Example 4
A diver is at −18 m. A seagull is 7 m above sea level. How far apart are they?
Answer: 25 m