Let's solve each of these problems step by step using the
BODMAS rule:
>
BODMAS stands for:
> -
Brackets
> -
Orders (i.e., powers and square roots, etc.)
> -
Division
> -
Multiplication
> -
Addition
> -
Subtraction
We follow this order to evaluate mathematical expressions correctly.
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1. $ 8 + 3 \times 2 $
- Multiplication first: $ 3 \times 2 = 6 $
- Then addition: $ 8 + 6 = 14 $
✔ Answer: 14
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2. $ 10 - 6 \div 2 $
- Division first: $ 6 \div 2 = 3 $
- Then subtraction: $ 10 - 3 = 7 $
✔ Answer: 7
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3. $ (6 + 2) \div 4 $
- Brackets first: $ 6 + 2 = 8 $
- Then division: $ 8 \div 4 = 2 $
✔ Answer: 2
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4. $ (8 + 1) \times (2 + 3) $
- Brackets first:
- $ 8 + 1 = 9 $
- $ 2 + 3 = 5 $
- Then multiplication: $ 9 \times 5 = 45 $
✔ Answer: 45
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5. $ 15 - 3^2 + 4 $
- Orders (powers): $ 3^2 = 9 $
- Now expression becomes: $ 15 - 9 + 4 $
- Left to right: $ 15 - 9 = 6 $, then $ 6 + 4 = 10 $
✔ Answer: 10
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6. $ 2 + 3 \times (3 + 2) $
- Brackets: $ 3 + 2 = 5 $
- Multiplication: $ 3 \times 5 = 15 $
- Addition: $ 2 + 15 = 17 $
✔ Answer: 17
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7. $ 8 + 4^2 \div 2 $
- Orders: $ 4^2 = 16 $
- Now: $ 8 + 16 \div 2 $
- Division: $ 16 \div 2 = 8 $
- Addition: $ 8 + 8 = 16 $
✔ Answer: 16
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8. $ 20 - 8 - 3 \times (9 - 7) $
- Brackets: $ 9 - 7 = 2 $
- Multiplication: $ 3 \times 2 = 6 $
- Now: $ 20 - 8 - 6 $
- Left to right: $ 20 - 8 = 12 $, then $ 12 - 6 = 6 $
✔ Answer: 6
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9. $ 2^2 + 6^2 - 4^2 $
- Orders:
- $ 2^2 = 4 $
- $ 6^2 = 36 $
- $ 4^2 = 16 $
- Expression: $ 4 + 36 - 16 $
- Left to right: $ 4 + 36 = 40 $, then $ 40 - 16 = 24 $
✔ Answer: 24
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10. $ (12 - 7) \times (3^2 - 2^2) $
- Brackets:
- $ 12 - 7 = 5 $
- $ 3^2 = 9 $, $ 2^2 = 4 $ → $ 9 - 4 = 5 $
- Multiplication: $ 5 \times 5 = 25 $
✔ Answer: 25
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✔ Final Answers:
1. $ 8 + 3 \times 2 = 14 $
2. $ 10 - 6 \div 2 = 7 $
3. $ (6 + 2) \div 4 = 2 $
4. $ (8 + 1) \times (2 + 3) = 45 $
5. $ 15 - 3^2 + 4 = 10 $
6. $ 2 + 3 \times (3 + 2) = 17 $
7. $ 8 + 4^2 \div 2 = 16 $
8. $ 20 - 8 - 3 \times (9 - 7) = 6 $
9. $ 2^2 + 6^2 - 4^2 = 24 $
10. $ (12 - 7) \times (3^2 - 2^2) = 25 $
Let me know if you'd like a printable version or explanation in simpler terms!
Parent Tip: Review the logic above to help your child master the concept of bod maths worksheet.
