01Why this matters
Temperatures, debts and changes in height use a reference point. Signs tell you which side of that reference a quantity belongs to.
02See it
03Understand it
Positive numbers are above zero; negative numbers are below zero. Zero is neither positive nor negative.
On a number line, numbers increase to the right. Adding a positive number moves right; adding a negative number moves left. Subtracting a number means adding its opposite. This is why subtracting a negative moves right. A number’s distance from zero is its absolute value: −4 and 4 are equally far from zero.
04Guided example
The temperature is −3 °C and rises by 8 °C. What is the new temperature?
- Start at −3 on the number line. A rise means add a positive change.
- Move 3 steps right to reach zero, leaving 5 of the 8 steps.
- Move 5 more steps right: −3 + 8 = 5 °C.
05Try it
06Practise it
07Use it in the real world
If a balance is −$20 and you add $35, the new balance is $15. The same arithmetic describes movement across any chosen zero.
Go a little deeper
Two negative factors give a positive product. For example, −2 × −3 = 6. This rule keeps multiplication consistent with the distributive law.
08Quick check
09Summary
Positive numbers are above zero; negative numbers are below zero. Zero is neither positive nor negative. Move 5 more steps right: −3 + 8 = 5 °C.
Before moving on, explain the worked example in your own words. Use the hint on any question you want to revisit.
10Key idea
a − b = a + (−b)
a and b are signed numbers; use the same units when adding quantities.
a + (−b) = a − b
Find this in the formula library →