☰ Year plan · Mathematics

Operations on integers

Week 4 Β· Operations on integers: addition, subtraction, multiplication and division Β· 3 lessons
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 Β· a βˆ’ b means a + (βˆ’b)additive inverse Β· the number you add to get 0, such as βˆ’6 for 6change Β· the final value minus the starting valuesign Β· the + or βˆ’ in front of a number
Explanation

To subtract, add the opposite: a βˆ’ b = a + (βˆ’b). So 6 βˆ’ 10 = 6 + (βˆ’10) = βˆ’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 βˆ’ 0 = 5 the pattern continues: 5 βˆ’ (βˆ’1) = 6 and 5 βˆ’ (βˆ’2) = 7. Subtracting a negative number is the same as adding a positive number: βˆ’4 βˆ’ (βˆ’6) = βˆ’4 + 6 = 2. Be careful with the first sign too: βˆ’5 βˆ’ 3 = βˆ’5 + (βˆ’3) = βˆ’8, not βˆ’2. The change from a start value to a final value is final βˆ’ start.

SubtractionResult
5 βˆ’ 32
5 βˆ’ 23
5 βˆ’ 14
5 βˆ’ 05
5 βˆ’ (βˆ’1)6
5 βˆ’ (βˆ’2)7
Worked examples
Find 6 βˆ’ 10. Write it as 6 + (βˆ’10). Opposite signs: 10 βˆ’ 6 = 4, and 10 is negative, so the answer is βˆ’4.
βˆ’6βˆ’5βˆ’4βˆ’3βˆ’2βˆ’101234+6
Find βˆ’4 βˆ’ (βˆ’6). Subtracting βˆ’6 is adding 6: βˆ’4 + 6 = 2. The number line agrees: start at βˆ’4 and jump 6 to the right.
Find βˆ’5 βˆ’ 3. Write it as βˆ’5 + (βˆ’3). Same signs: 5 + 3 = 8, so βˆ’8. The temperature at night was βˆ’4 Β°C and at noon 9 Β°C. The change is 9 βˆ’ (βˆ’4) = 9 + 4 = 13 Β°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 βˆ’ morning. Which city changed most?

Practice
1
Find 8 βˆ’ 12.
2
Find βˆ’3 βˆ’ (βˆ’7).
3
Find βˆ’6 βˆ’ 5.
4
The temperature rises from βˆ’7 Β°C to 5 Β°C. What is the change?
5
Omar says βˆ’5 βˆ’ 3 = βˆ’2. What is wrong?