2
Subtracting integers by adding the opposite
Mathematics Prep 1 Term 1, Unit 1, Lesson 4
GoalSubtract integers by changing the subtraction into adding the opposite.
New words
subtraction · a − b means a + (−b)additive inverse · the number you add to get 0, such as −6 for 6change · the final value minus the starting valuesign · the + or − in front of a number
Explanation
To subtract, add the opposite: a − b = a + (−b). So 6 − 10 = 6 + (−10) = −4. Why? Look at the pattern in the table: when the number we subtract goes down by 1, the answer goes up by 1. After 5 − 0 = 5 the pattern continues: 5 − (−1) = 6 and 5 − (−2) = 7. Subtracting a negative number is the same as adding a positive number: −4 − (−6) = −4 + 6 = 2. Be careful with the first sign too: −5 − 3 = −5 + (−3) = −8, not −2. The change from a start value to a final value is final − start.
| Subtraction | Result |
|---|---|
| 5 − 3 | 2 |
| 5 − 2 | 3 |
| 5 − 1 | 4 |
| 5 − 0 | 5 |
| 5 − (−1) | 6 |
| 5 − (−2) | 7 |
Worked examples
Find 6 − 10. Write it as 6 + (−10). Opposite signs: 10 − 6 = 4, and 10 is negative, so the answer is −4.
Find −4 − (−6). Subtracting −6 is adding 6: −4 + 6 = 2. The number line agrees: start at −4 and jump 6 to the right.
Find −5 − 3. Write it as −5 + (−3). Same signs: 5 + 3 = 8, so −8. The temperature at night was −4 °C and at noon 9 °C. The change is 9 − (−4) = 9 + 4 = 13 °C.
Class activity
Temperature tour. With a grown-up, write the morning and noon temperature of three cities (they may be below 0 in winter somewhere in the world). For each city find the change: noon − morning. Which city changed most?
Practice
1
Find 8 − 12.
8 + (−12) = −4.
2
Find −3 − (−7).
−3 + 7 = 4.
3
Find −6 − 5.
−6 + (−5) = −11.
4
The temperature rises from −7 °C to 5 °C. What is the change?
5 − (−7) = 5 + 7 = 12 °C.
5
Omar says −5 − 3 = −2. What is wrong?
−5 − 3 = −5 + (−3) = −8. Subtracting 3 moves further left, away from 0.