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Order of Operations with Signed Numbers
Order of Operations with Signed Numbers
Apply PEMDAS exactly as before, but be careful with signs!
Example 1
Evaluate: $-4 + 3 \times (-2)$
- Multiply: $3 \times (-2) = -6$
- Add: $-4 + (-6) = -10$
Example 2
Evaluate: $(-3)^2 - 4(-2)(5)$
- Exponent: $(-3)^2 = 9$
- Multiply: $4(-2)(5) = -40$
- Subtract: $9 - (-40) = 9 + 40 = 49$
Example 3
Evaluate: $\dfrac{-8 + 2}{-3}$
Numerator: $-8 + 2 = -6$. Then $\dfrac{-6}{-3} = 2$.
Example 4
Evaluate: $-2x^2 + 3x - 5$ when $x = -4$
- $x^2 = (-4)^2 = 16$
- $-2(16) = -32$
- $3(-4) = -12$
- $-32 + (-12) - 5 = -49$
Example 5
Evaluate: $|{-5 + 2}| \times (-3) + 1$
- Inside absolute value: $-5 + 2 = -3$
- $|{-3}| = 3$
- $3 \times (-3) = -9$
- $-9 + 1 = -8$
Real-World Applications
Example 6
Temperature was $-8°F$ at 6 AM and rose $15°$ by noon. Noon temperature?
$-8 + 15 = 7°F$
Example 7
Account balance: $\$250$. Withdraw $\$180$, deposit $\$75$. New balance?
$250 + (-180) + 75 = \$145$
Practice Problems
1. $-5 + 2 \times (-3)$
2. $(-4)^2 - (-3)^2$
3. $\dfrac{-15 + 3}{-4}$
4. $3 - 2(-5 + 1)^2$
5. $(-1)^3 + (-1)^4 + (-1)^5$
6. $|{-8}| - |{-3}| \times 2$
7. $(-6)(2) - (-3)(4)$
8. Evaluate $x^2 - 2x + 1$ at $x = -3$
9. $\dfrac{(-4)^2 - 6}{-2 + 7}$
10. $-3|{-4 + 1}| + 7$
11. Temp is $5°C$, drops $12°$ overnight. New temp?
12. A submarine at $-200$ ft rises $75$ ft, then dives $120$ ft. Depth?
13. $(-2)^4 - 2^4$
14. $5(-3)^2 - 4(-2)^3$
15. $\dfrac{(-6)^2 - 36}{(-6) + 6}$
Show Answer Key
1. $-11$
2. $16 - 9 = 7$
3. $3$
4. $3 - 2(16) = -29$
5. $-1 + 1 + (-1) = -1$
6. $8 - 6 = 2$
7. $-12 + 12 = 0$
8. $9 + 6 + 1 = 16$
9. $\dfrac{10}{5} = 2$
10. $-9 + 7 = -2$
11. $-7°C$
12. $-200 + 75 - 120 = -245$ ft
13. $16 - 16 = 0$
14. $45 + 32 = 77$
15. Undefined ($0$ in denominator)