Order of Operations with Negative and Positive Integers (Six Steps ... - Free Printable

Let's solve each expression step by step using the correct order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

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1. $(-5)^2 - 4 \times (6 + ((-7) + 8)) \times 3$

#### Step-by-step:
- First, simplify inside parentheses:
- $(-7) + 8 = 1$
- So: $6 + 1 = 7$
- Now: $(-5)^2 = 25$ (since squaring a negative gives positive)
- Expression becomes:
$$
25 - 4 \times 7 \times 3
$$
- Perform multiplication from left to right:
- $4 \times 7 = 28$
- $28 \times 3 = 84$
- Final:
$$
25 - 84 = -59
$$

✔ Answer: $-59$

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2. $((-9) + 7)^2 \times (-5) + ((4 - (-6)) \times 2)$

#### Step-by-step:
- Simplify inside parentheses:
- $(-9) + 7 = -2$
- $4 - (-6) = 4 + 6 = 10$
- Now:
$$
(-2)^2 \times (-5) + (10 \times 2)
$$
- Exponent: $(-2)^2 = 4$
- Multiply:
- $4 \times (-5) = -20$
- $10 \times 2 = 20$
- Add:
$$
-20 + 20 = 0
$$

✔ Answer: $0$

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3. $(2^2 \times (6 - 9)) \div 3 + (-4)^2$

#### Step-by-step:
- Exponent: $2^2 = 4$
- Inside parentheses: $6 - 9 = -3$
- Multiply: $4 \times (-3) = -12$
- Divide: $-12 \div 3 = -4$
- Exponent: $(-4)^2 = 16$
- Add: $-4 + 16 = 12$

✔ Answer: $12$

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4. $((-7) + 7) \div (-9)^2 \times (8 - (-3)^2)$

#### Step-by-step:
- $(-7) + 7 = 0$
- $(-9)^2 = 81$
- $(-3)^2 = 9$, so $8 - 9 = -1$
- Expression becomes:
$$
0 \div 81 \times (-1)
$$
- $0 \div 81 = 0$
- $0 \times (-1) = 0$

✔ Answer: $0$

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5. $((-7) + 9 - 7)^2 \times (5 + (-5))^2$

#### Step-by-step:
- Simplify inside parentheses:
- $(-7) + 9 = 2$, then $2 - 7 = -5$
- $5 + (-5) = 0$
- Now:
$$
(-5)^2 \times (0)^2
$$
- $(-5)^2 = 25$, $0^2 = 0$
- $25 \times 0 = 0$

✔ Answer: $0$

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6. $((-3) \times (10 + (-7)))^2 \div 3 - (-9)^2$

#### Step-by-step:
- $10 + (-7) = 3$
- $(-3) \times 3 = -9$
- $(-9)^2 = 81$
- Now: $81 \div 3 = 27$
- $(-9)^2 = 81$ (again)
- So: $27 - 81 = -54$

✔ Answer: $-54$

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✔ Final Answers:

1. $-59$
2. $0$
3. $12$
4. $0$
5. $0$
6. $-54$

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