☰ Year plan · Mathematics

Operations on integers

Week 4 Β· Operations on integers: addition, subtraction, multiplication and division Β· 3 lessons
1

Adding integers: the number line and absolute values

Mathematics Prep 1 Term 1, Unit 1, Lesson 4
GoalAdd integers using the number line and the rule of absolute values.
New words
integers Z Β· … βˆ’2, βˆ’1, 0, 1, 2 …: negative numbers, zero and positive numbersabsolute value Β· a number’s distance from 0, written |βˆ’4| = 4opposite Β· the number with the same absolute value and the other signzero pair Β· a +1 and a βˆ’1 together make 0
Explanation

The integers Z are the negative numbers, zero and the positive numbers, placed in order on the number line. To add, start at the first number and move right for a positive number or left for a negative number. You can also use +1 and βˆ’1 counters: a +1 and a βˆ’1 cancel, making a zero pair. The faster rule uses absolute values. Same signs: add the absolute values and keep the sign, so βˆ’4 + (βˆ’5) = βˆ’9. Opposite signs: subtract the smaller absolute value from the larger, and keep the sign of the number with the larger absolute value, so 7 + (βˆ’10) = βˆ’3. A number plus its opposite is 0, and the order of adding does not change the sum.

βˆ’6βˆ’5βˆ’4βˆ’3βˆ’2βˆ’10123456+5
Worked examples
βˆ’6βˆ’5βˆ’4βˆ’3βˆ’2βˆ’10123456+5
Number line: βˆ’3 + 5. Start at βˆ’3 and move 5 steps to the right. You land on 2, so βˆ’3 + 5 = 2. The picture shows the jump.
Same signs: βˆ’4 + (βˆ’5). The absolute values are 4 and 5. Add them: 4 + 5 = 9. Keep the minus sign. So βˆ’4 + (βˆ’5) = βˆ’9. Opposite signs: 7 + (βˆ’10). The absolute values are 7 and 10. Subtract: 10 βˆ’ 7 = 3. 10 is bigger and it is negative, so the answer is βˆ’3.
βˆ’5βˆ’4βˆ’3βˆ’2βˆ’1012345678βˆ’9
Calculate cleverly: βˆ’13 + 7 + 13. Change the order and group the opposites: (βˆ’13 + 13) + 7 = 0 + 7 = 7. A temperature of 6 Β°C falls by 9 degrees: 6 + (βˆ’9) = βˆ’3 Β°C.
Class activity

Counter game. With a grown-up, use dark buttons for +1 and light buttons for βˆ’1. Pick 5 dark and 8 light. Pair them off into zero pairs. What is left? Write the addition: 5 + (βˆ’8). Try three more.

Practice
1
Find βˆ’7 + 3.
2
Find βˆ’6 + (βˆ’4).
3
Calculate cleverly: βˆ’25 + 18 + 25.
4
Ahmed’s bank balance is βˆ’80 LE (he owes 80 LE). He pays in 200 LE. What is his balance now?
5
Hana says βˆ’5 + 2 = 3. What is wrong?