33
Adding numbers with different signs
Textbook, pp. 152–158
GoalKnow and apply the rule for adding numbers with different signs.
New words
numbers with different signs · har xil ishorali sonlargreater modulus · katta moduldifference of the moduli · modullar ayirmasisum of opposite numbers · qarama-qarshi sonlar yig‘indisi
Explanation
To add two numbers with different signs, subtract the smaller modulus from the greater and put in front the sign of the number with the greater modulus. For example (−8) + 5: the moduli are 8 and 5, the difference is 3, the number with the greater modulus is −8 (negative), so the answer is −3. 9 + (−4) = 5 because the greater modulus, 9, is positive. The sum of opposite numbers is zero: (−7) + 7 = 0. We can also check the rule on the number line.
Worked examples
(−12) + 20: 20 − 12 = 8, the greater modulus 20 is positive, so the answer is 8.
15 + (−23): 23 − 15 = 8, the greater modulus 23 is negative, so the answer is −8.
Class activity
“Gains and losses”: two teams play for points: a win is positive and a loss is negative. After each round the teams update the total with the addition rule.
Practice
1
Compute (−12) + 20.
8
2
Compute 15 + (−23).
-8
3
Compute (−9) + 9.
0
4
Why is the answer to (−8) + 5 negative?
The modulus of −8 is bigger than 5: going 8 left and 5 right leaves us 3 units left of zero.