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Final review: adding and subtracting positive and negative numbers
Textbook, p. 229
GoalReview adding and subtracting positive and negative numbers.
New words
opposite number · qarama-qarshi sonabsolute value · modulsign · ishoracoordinate line · koordinata to‘g‘ri chizig‘i
Explanation
When adding numbers with the same sign, add the moduli and keep the common sign: (−4) + (−9) = −13. When adding numbers with different signs, subtract the smaller modulus from the larger and take the sign of the number with the larger modulus: (−8) + 13 = 5. Subtraction becomes addition: a − b = a + (−b), so subtracting a negative number increases the value: −5 − (−12) = −5 + 12 = 7. The sum of opposite numbers is zero. On the number line addition is a move to the right or left.
Worked examples
(−3) + (−9) − (−4) = −3 − 9 + 4 = −8.
The temperature rose from −7 °C to +5 °C: change 5 − (−7) = 12 °C.
Class activity
“Number-line trip”: on the floor number line a traveller follows card commands: “start at −4, +9, −12, +5”. The class predicts the number after each step and the final answer is checked by all.
Practice
1
Compute (−17) + 9.
-8
2
Compute 4 − (−11).
15
3
The temperature changed from −7 °C to +5 °C. Find the change.
12
4
Why does subtracting a negative number increase the value?
Subtracting means adding the opposite; the opposite of a negative is positive, so we add a positive number.