Training Signed Numbers Adding and Subtracting Signed Numbers
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Adding and Subtracting Signed Numbers

22 min Signed Numbers

Adding Signed Numbers

Adding and subtracting signed numbers extends the arithmetic you already know into the world of negatives. The rules are simple once you learn them: when adding two numbers with the same sign, add their absolute values and keep the sign; when the signs differ, subtract the smaller absolute value from the larger and keep the sign of the larger.

Subtraction of signed numbers becomes addition once you learn the key insight: subtracting a number is the same as adding its opposite. This single rule transforms every subtraction problem into an addition problem.

Same Sign

Rule

Add the absolute values and keep the common sign.

Example 1

$(-5) + (-3)$

$|{-5}| + |{-3}| = 8$. Common sign is negative. $(-5) + (-3) = -8$.

Different Signs

Rule

Subtract the smaller absolute value from the larger. Take the sign of the number with the larger absolute value.

Example 2

$(-7) + 4$

$7 - 4 = 3$. $|{-7}| > |4|$, so sign is negative. $(-7) + 4 = -3$.

Example 3

$6 + (-2)$

$6 - 2 = 4$. Positive wins. $6 + (-2) = 4$.

Subtracting Signed Numbers

Rule

Change subtraction to addition of the opposite: $\;a - b = a + (-b)$

Example 4

$3 - 8$

$3 + (-8) = -5$

Example 5

$-4 - (-6)$

$-4 + 6 = 2$

Example 6

$-2 + 5 - 3 - (-4)$

$= -2 + 5 + (-3) + 4 = 4$

Practice Problems

1. $(-8) + (-5)$
2. $(-12) + 7$
3. $9 + (-15)$
4. $5 - 12$
5. $-7 - (-3)$
6. $-6 + 6$
7. $-3 - 8 + 4$
8. $10 - (-10)$
9. $(-2) + (-3) + (-5)$
10. $-15 + 8 - (-3) + (-2)$
11. $0 - (-7)$
12. $-100 + 45 + 55$
13. $-1.5 + 3.2$
14. $-\dfrac{3}{4} - \dfrac{1}{2}$
15. $-8 - 7 + 20 - (-5)$
Show Answer Key

1. $-13$

2. $-5$

3. $-6$

4. $-7$

5. $-4$

6. $0$

7. $-7$

8. $20$

9. $-10$

10. $-6$

11. $7$

12. $0$

13. $1.7$

14. $-1\dfrac{1}{4}$

15. $10$

Integers and the Number Line Multiplying and Dividing Signed Numbers