Let's solve each expression step by step using
PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
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1. $ 4 \times 2 - [5^2 \div (8 + 2 - 5)] $
Step-by-step:
- First, simplify inside the parentheses:
$ 8 + 2 - 5 = 10 - 5 = 5 $
- Now:
$ 5^2 = 25 $
- So:
$ 25 \div 5 = 5 $
- Now the expression becomes:
$ 4 \times 2 - 5 = 8 - 5 = 3 $
✔ Answer: 3
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2. $ 2^3 + [(90 \div 3^2 \times 5) \times 6] $
Step-by-step:
- $ 2^3 = 8 $
- Inside brackets:
$ 3^2 = 9 $
- $ 90 \div 9 = 10 $
- $ 10 \times 5 = 50 $
- $ 50 \times 6 = 300 $
- Now:
$ 8 + 300 = 308 $
✔ Answer: 308
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3. $ 1 + [(7 \times 2^2) - 11] + 3^3 $
Step-by-step:
- $ 2^2 = 4 $
- $ 7 \times 4 = 28 $
- $ 28 - 11 = 17 $
- $ 3^3 = 27 $
- Now:
$ 1 + 17 + 27 = 45 $
✔ Answer: 45
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4. $ [(10 + 4^2) - 10] + 9 \times 56 \div 7 $
Step-by-step:
- $ 4^2 = 16 $
- $ 10 + 16 = 26 $
- $ 26 - 10 = 16 $
- Now:
$ 9 \times 56 = 504 $
- $ 504 \div 7 = 72 $
- Now:
$ 16 + 72 = 88 $
✔ Answer: 88
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5. $ (7^3 - 2 \times 12) \times (15 - 11) \div 2 $
Step-by-step:
- $ 7^3 = 343 $
- $ 2 \times 12 = 24 $
- $ 343 - 24 = 319 $
- $ 15 - 11 = 4 $
- Now:
$ 319 \times 4 = 1276 $
- $ 1276 \div 2 = 638 $
✔ Answer: 638
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6. $ 10 + 3^3 - [4 + 9 \times (6^3 \div 36)] $
Step-by-step:
- $ 3^3 = 27 $
- $ 6^3 = 216 $
- $ 216 \div 36 = 6 $
- $ 9 \times 6 = 54 $
- $ 4 + 54 = 58 $
- Now:
$ 10 + 27 - 58 = 37 - 58 = -21 $
✔ Answer: -21
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7. $ [2^4 + (3^2 - 1) \times 7] + 56 $
Step-by-step:
- $ 2^4 = 16 $
- $ 3^2 = 9 $
- $ 9 - 1 = 8 $
- $ 8 \times 7 = 56 $
- $ 16 + 56 = 72 $
- $ 72 + 56 = 128 $
✔ Answer: 128
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8. $ [2^2 \times (6 - 9)] \div 3 + (-4)^2 $
Step-by-step:
- $ 2^2 = 4 $
- $ 6 - 9 = -3 $
- $ 4 \times (-3) = -12 $
- $ -12 \div 3 = -4 $
- $ (-4)^2 = 16 $
- $ -4 + 16 = 12 $
✔ Answer: 12
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✔ Final Answers:
1.
3
2.
308
3.
45
4.
88
5.
638
6.
-21
7.
128
8.
12
Let me know if you'd like a printed version or explanation in simpler terms!
Parent Tip: Review the logic above to help your child master the concept of order of operations worksheet with answers.
