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 (from left to right), and finally Addition and Subtraction (from left to right).
1. $(5 + 7) \times 10 \div 2$
* First, solve inside the parentheses: $5 + 7 = 12$.
* The equation becomes: $12 \times 10 \div 2$.
* Next, do multiplication and division from left to right. Multiply: $12 \times 10 = 120$.
* Finally, divide: $120 \div 2 = 60$.
2. $(9 - 7) + (4 \div 2)$
* Solve the first set of parentheses: $9 - 7 = 2$.
* Solve the second set of parentheses: $4 \div 2 = 2$.
* Add the results together: $2 + 2 = 4$.
3. $2^2 + 6 \times (4 + 6)$
* First, solve inside the parentheses: $4 + 6 = 10$.
* The equation becomes: $2^2 + 6 \times 10$.
* Next, handle the exponent: $2^2$ means $2 \times 2$, which equals $4$.
* Now multiply: $6 \times 10 = 60$.
* Finally, add: $4 + 60 = 64$.
4. $9 + 6 \times 10 - 6 - 4$
* There are no parentheses or exponents, so start with multiplication: $6 \times 10 = 60$.
* The equation becomes: $9 + 60 - 6 - 4$.
* Solve addition and subtraction from left to right.
* Add: $9 + 60 = 69$.
* Subtract: $69 - 6 = 63$.
* Subtract again: $63 - 4 = 59$.
5. $10 - 8 + 6^2$
* First, handle the exponent: $6^2$ means $6 \times 6$, which equals $36$.
* The equation becomes: $10 - 8 + 36$.
* Solve addition and subtraction from left to right.
* Subtract: $10 - 8 = 2$.
* Add: $2 + 36 = 38$.
6. $(3 + 9) \div 6 + 2 \times 8$
* First, solve inside the parentheses: $3 + 9 = 12$.
* The equation becomes: $12 \div 6 + 2 \times 8$.
* Next, do multiplication and division from left to right.
* Divide: $12 \div 6 = 2$.
* Multiply: $2 \times 8 = 16$.
* Finally, add the results: $2 + 16 = 18$.
7. $4 \times (11 - 8) - 3$
* First, solve inside the parentheses: $11 - 8 = 3$.
* The equation becomes: $4 \times 3 - 3$.
* Next, multiply: $4 \times 3 = 12$.
* Finally, subtract: $12 - 3 = 9$.
Final Answer:
1. 60
2. 4
3. 64
4. 59
5. 38
6. 18
7. 9
Parent Tip: Review the logic above to help your child master the concept of order of operations worksheet grade 6.
