Here are the step-by-step solutions for each problem on the worksheet. Remember to follow the order of operations: Parentheses first, then Exponents, then Multiplication and Division (left to right), and finally Addition and Subtraction (left to right).
1. $(14 + 7 + 9) \times 12$
* First, solve inside the parentheses: $14 + 7 = 21$, and $21 + 9 = 30$.
* Now multiply: $30 \times 12 = 360$.
2. $(7^2 \times 7) \times 7$
* First, handle the exponent inside the parentheses: $7^2 = 49$.
* Multiply inside the parentheses: $49 \times 7 = 343$.
* Finally, multiply by the last number: $343 \times 7 = 2401$.
3. $15 + 18 \times (7 + 3^2)$
* Inside the parentheses, do the exponent first: $3^2 = 9$.
* Finish the parentheses: $7 + 9 = 16$.
* Now multiply: $18 \times 16 = 288$.
* Finally, add: $15 + 288 = 303$.
4. $(7 \times 9) + 7 + 8$
* Solve the parentheses: $7 \times 9 = 63$.
* Add the remaining numbers: $63 + 7 = 70$, and $70 + 8 = 78$.
5. $45 \div 9 + (15 \times 2^2)$
* Inside the parentheses, do the exponent first: $2^2 = 4$.
* Finish the parentheses: $15 \times 4 = 60$.
* Do the division next: $45 \div 9 = 5$.
* Finally, add: $5 + 60 = 65$.
6. $68 \div (4^2 + 1)$
* Inside the parentheses, do the exponent first: $4^2 = 16$.
* Finish the parentheses: $16 + 1 = 17$.
* Finally, divide: $68 \div 17 = 4$.
7. $(30 \times 5 + 3) \div 3$
* Inside the parentheses, multiply first: $30 \times 5 = 150$.
* Finish the parentheses: $150 + 3 = 153$.
* Finally, divide: $153 \div 3 = 51$.
8. $60 + 10 \times (17 + 24)$
* Solve inside the parentheses: $17 + 24 = 41$.
* Multiply next: $10 \times 41 = 410$.
* Finally, add: $60 + 410 = 470$.
9. $3^3 + (3 + 8)$
* Calculate the exponent: $3^3 = 3 \times 3 \times 3 = 27$.
* Solve the parentheses: $3 + 8 = 11$.
* Finally, add: $27 + 11 = 38$.
10. $(4 + 3 + 3)$
* Simply add the numbers inside the parentheses: $4 + 3 = 7$, and $7 + 3 = 10$.
11. $6 + (6 + 6^2) \times 2$
* Inside the parentheses, do the exponent first: $6^2 = 36$.
* Finish the parentheses: $6 + 36 = 42$.
* Multiply next: $42 \times 2 = 84$.
* Finally, add: $6 + 84 = 90$.
12. $(6 + 3 \times 5) + 4^2$
* Inside the parentheses, multiply first: $3 \times 5 = 15$.
* Finish the parentheses: $6 + 15 = 21$.
* Calculate the exponent: $4^2 = 16$.
* Finally, add: $21 + 16 = 37$.
Final Answer:
1. 360
2. 2401
3. 303
4. 78
5. 65
6. 4
7. 51
8. 470
9. 38
10. 10
11. 90
12. 37
Parent Tip: Review the logic above to help your child master the concept of 6th grade order of operations with exponents worksheet.
