الأسبوع 4 · العمليات على الأعداد الصحيحة: الجمع والطرح والضرب والقسمة · 3 دروس
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 · … −2, −1, 0, 1, 2 …: negative numbers, zero and positive numbersabsolute value · a number’s distance from 0, written |−4| = 4opposite · the number with the same absolute value and the other signzero pair · a +1 and a −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 −1 counters: a +1 and a −1 cancel, making a zero pair. The faster rule uses absolute values. Same signs: add the absolute values and keep the sign, so −4 + (−5) = −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 + (−10) = −3. A number plus its opposite is 0, and the order of adding does not change the sum.
Worked examples
Number line: −3 + 5. Start at −3 and move 5 steps to the right. You land on 2, so −3 + 5 = 2. The picture shows the jump.
Same signs: −4 + (−5). The absolute values are 4 and 5. Add them: 4 + 5 = 9. Keep the minus sign. So −4 + (−5) = −9. Opposite signs: 7 + (−10). The absolute values are 7 and 10. Subtract: 10 − 7 = 3. 10 is bigger and it is negative, so the answer is −3.
Calculate cleverly: −13 + 7 + 13. Change the order and group the opposites: (−13 + 13) + 7 = 0 + 7 = 7. A temperature of 6 °C falls by 9 degrees: 6 + (−9) = −3 °C.
Class activity
Counter game. With a grown-up, use dark buttons for +1 and light buttons for −1. Pick 5 dark and 8 light. Pair them off into zero pairs. What is left? Write the addition: 5 + (−8). Try three more.
Practice
1
Find −7 + 3.
Opposite signs: 7 − 3 = 4, and 7 is negative, so −4.
2
Find −6 + (−4).
Same signs: 6 + 4 = 10, so −10.
3
Calculate cleverly: −25 + 18 + 25.
(−25 + 25) + 18 = 0 + 18 = 18.
4
Ahmed’s bank balance is −80 LE (he owes 80 LE). He pays in 200 LE. What is his balance now?
−80 + 200 = 120, so the balance is 120 LE.
5
Hana says −5 + 2 = 3. What is wrong?
The larger absolute value is 5 and it is negative, so the answer is negative: −5 + 2 = −3.
