Here are the step-by-step solutions for each problem on the worksheet. I have followed the order of operations: Parentheses/Exponents first, then Multiplication/Division, and finally Addition/Subtraction.
1. $(2.4 + 3.5) \div 2$
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Step 1: Solve inside the parentheses: $2.4 + 3.5 = 5.9$
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Step 2: Divide by 2: $5.9 \div 2 = 2.95$
2. $5^2 \times 10 - 12^2$
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Step 1: Solve the exponents: $5^2 = 25$ and $12^2 = 144$
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Step 2: Multiply: $25 \times 10 = 250$
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Step 3: Subtract: $250 - 144 = 106$
3. $(9 + 1.1)^2 - (11^2 - 117)$
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Step 1: Solve the first set of parentheses: $9 + 1.1 = 10.1$. Then square it: $10.1^2 = 102.01$
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Step 2: Solve the second set of parentheses: First do the exponent $11^2 = 121$. Then subtract: $121 - 117 = 4$
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Step 3: Subtract the results: $102.01 - 4 = 98.01$
4. $10^2 \div (21 - 7)$
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Step 1: Solve the exponent: $10^2 = 100$
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Step 2: Solve inside the parentheses: $21 - 7 = 14$
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Step 3: Divide: $100 \div 14 \approx 7.14$ (rounded to two decimal places).
* *Note: As a fraction, this is $\frac{100}{14}$ which simplifies to $\frac{50}{7}$ or $7 \frac{1}{7}$.*
5. $(4.2 + 1.12) \times 3$
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Step 1: Solve inside the parentheses: $4.2 + 1.12 = 5.32$
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Step 2: Multiply by 3: $5.32 \times 3 = 15.96$
6. $(1^8 \times 10^2) - 7^2 + 2^2$
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Step 1: Solve all exponents:
* $1^8 = 1$
* $10^2 = 100$
* $7^2 = 49$
* $2^2 = 4$
*
Step 2: Rewrite the equation: $(1 \times 100) - 49 + 4$
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Step 3: Multiply inside parentheses: $100 - 49 + 4$
*
Step 4: Subtract and add from left to right:
* $100 - 49 = 51$
* $51 + 4 = 55$
7. $1\% \div 2\% \times 10^2$
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Step 1: Convert percentages to decimals: $1\% = 0.01$ and $2\% = 0.02$
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Step 2: Solve the exponent: $10^2 = 100$
*
Step 3: Rewrite the equation: $0.01 \div 0.02 \times 100$
*
Step 4: Divide first (left to right): $0.01 \div 0.02 = 0.5$
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Step 5: Multiply: $0.5 \times 100 = 50$
8. $4^2 - (125 - 25)$
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Step 1: Solve the exponent: $4^2 = 16$
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Step 2: Solve inside the parentheses: $125 - 25 = 100$
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Step 3: Subtract: $16 - 100 = -84$
9. $(6.88 \div 2) - [9.3 - (9.03)]$
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Step 1: Solve the first part (division): $6.88 \div 2 = 3.44$
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Step 2: Solve inside the brackets. The inner parentheses $(9.03)$ is just $9.03$. So, $9.3 - 9.03 = 0.27$
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Step 3: Subtract the results: $3.44 - 0.27 = 3.17$
10. $1\% \div 2\% + 6^3$
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Step 1: Convert percentages: $1\% = 0.01$ and $2\% = 0.02$
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Step 2: Solve the exponent: $6^3 = 6 \times 6 \times 6 = 216$
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Step 3: Rewrite the equation: $0.01 \div 0.02 + 216$
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Step 4: Divide first: $0.01 \div 0.02 = 0.5$
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Step 5: Add: $0.5 + 216 = 216.5$
Final Answer:
1. 2.95
2. 106
3. 98.01
4. 7.14 (or $7 \frac{1}{7}$)
5. 15.96
6. 55
7. 50
8. -84
9. 3.17
10. 216.5
Parent Tip: Review the logic above to help your child master the concept of operations with exponents worksheet.
