34
Subtracting numbers
Textbook, pp. 159–163
GoalKnow the rule for subtracting integers: turning subtraction into addition.
New words
subtraction · ayirishminuend · kamayuvchisubtrahend · ayriluvchidifference · ayirma
Explanation
To subtract a number, add its opposite: a − b = a + (−b). For example 5 − 8 = 5 + (−8) = −3. Subtracting a negative number turns into adding: −3 − (−7) = −3 + 7 = 4, and 4 − (−6) = 4 + 6 = 10. On the number line a − b gives the distance and direction from b to a. With this rule subtraction can always be done: the integers are closed under subtraction.
Worked examples
−5 − (−9) = −5 + 9 = 4.
The highest temperature is +12 °C and the lowest −8 °C: the range is 12 − (−8) = 20 °C.
Class activity
“Height difference”: heights above sea level are written on a class chart (for example +500 m and −30 m). Groups calculate the height difference between two places by subtracting.
Practice
1
Compute 7 − 12.
-5
2
Compute −5 − (−9).
4
3
How many degrees warmer is +5 °C than −8 °C?
13
4
Why is 4 − (−6) = 10?
On the number line there are 10 units from −6 to 4, and subtracting means adding the opposite: 4 + 6.