Here are the step-by-step solutions for each problem using the order of operations (PEMDAS): Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
1) $2 \times (7 + 33 - 21) - 4$
* First, solve inside the parentheses: $7 + 33 = 40$, then $40 - 21 = 19$.
* The equation becomes: $2 \times 19 - 4$.
* Multiply: $2 \times 19 = 38$.
* Subtract: $38 - 4 = 34$.
2) $2 \times 7 + 33 - (21 - 4)$
* First, solve inside the parentheses: $21 - 4 = 17$.
* The equation becomes: $2 \times 7 + 33 - 17$.
* Multiply: $2 \times 7 = 14$.
* Add and subtract from left to right: $14 + 33 = 47$, then $47 - 17 = 30$.
3) $2 + 18 \div 3 \times (21 - 16)$
* First, solve inside the parentheses: $21 - 16 = 5$.
* The equation becomes: $2 + 18 \div 3 \times 5$.
* Do multiplication and division from left to right: $18 \div 3 = 6$, then $6 \times 5 = 30$.
* Add: $2 + 30 = 32$.
4) $2 \times 7 + 33 - 21 - 4$
* There are no parentheses or exponents. Start with multiplication: $2 \times 7 = 14$.
* The equation becomes: $14 + 33 - 21 - 4$.
* Add and subtract from left to right:
* $14 + 33 = 47$
* $47 - 21 = 26$
* $26 - 4 = 22$
5) $9 \times 5 - (15 + 14 \times 2)$
* Inside the parentheses, do multiplication first: $14 \times 2 = 28$.
* Then add inside the parentheses: $15 + 28 = 43$.
* The equation becomes: $9 \times 5 - 43$.
* Multiply: $9 \times 5 = 45$.
* Subtract: $45 - 43 = 2$.
6) $(29 - 8) \times 9 - 12 - 38$
* First, solve inside the parentheses: $29 - 8 = 21$.
* The equation becomes: $21 \times 9 - 12 - 38$.
* Multiply: $21 \times 9 = 189$.
* Subtract from left to right:
* $189 - 12 = 177$
* $177 - 38 = 139$
7) $3 \times 17 - (6 + 14 - 13)$
* First, solve inside the parentheses from left to right: $6 + 14 = 20$, then $20 - 13 = 7$.
* The equation becomes: $3 \times 17 - 7$.
* Multiply: $3 \times 17 = 51$.
* Subtract: $51 - 7 = 44$.
8) $10 \times (19 + 20 - 13) + 13$
* First, solve inside the parentheses from left to right: $19 + 20 = 39$, then $39 - 13 = 26$.
* The equation becomes: $10 \times 26 + 13$.
* Multiply: $10 \times 26 = 260$.
* Add: $260 + 13 = 273$.
9) $13 \times 3 - (21 + 12) + 25$
* First, solve inside the parentheses: $21 + 12 = 33$.
* The equation becomes: $13 \times 3 - 33 + 25$.
* Multiply: $13 \times 3 = 39$.
* Add and subtract from left to right:
* $39 - 33 = 6$
* $6 + 25 = 31$
10) $9 \times 4 \times 4 - (33 + 22)$
* First, solve inside the parentheses: $33 + 22 = 55$.
* The equation becomes: $9 \times 4 \times 4 - 55$.
* Multiply from left to right: $9 \times 4 = 36$, then $36 \times 4 = 144$.
* Subtract: $144 - 55 = 89$.
Final Answer:
1) 34
2) 30
3) 32
4) 22
5) 2
6) 139
7) 44
8) 273
9) 31
10) 89
Parent Tip: Review the logic above to help your child master the concept of 6th grade order of operations with exponents worksheet.
