Order of Operations Worksheets | Order of Operations Worksheets ... - Free Printable
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Step-by-step solution for: Order of Operations Worksheets | Order of Operations Worksheets ...
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Show Answer Key & Explanations
Step-by-step solution for: Order of Operations Worksheets | Order of Operations Worksheets ...
Here are the step-by-step solutions for each problem on the worksheet. I have followed the order of operations (PEMDAS): Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
1) $((14 + 3) + (20 \div 2)^2) + 5^2$
* Step 1: Solve inside the inner parentheses first. $(14 + 3) = 17$ and $(20 \div 2) = 10$.
* Equation becomes: $(17 + 10^2) + 5^2$
* Step 2: Solve the exponents. $10^2 = 100$ and $5^2 = 25$.
* Equation becomes: $(17 + 100) + 25$
* Step 3: Solve the remaining parentheses. $17 + 100 = 117$.
* Equation becomes: $117 + 25$
* Step 4: Add the final numbers. $117 + 25 = 142$.
2) $(12 \div 3)^2 + ((10 - 4) \times 6^2)$
* Step 1: Solve inside the parentheses. $(12 \div 3) = 4$ and $(10 - 4) = 6$.
* Equation becomes: $4^2 + (6 \times 6^2)$
* Step 2: Solve the exponents. $4^2 = 16$ and $6^2 = 36$.
* Equation becomes: $16 + (6 \times 36)$
* Step 3: Multiply inside the parentheses. $6 \times 36 = 216$.
* Equation becomes: $16 + 216$
* Step 4: Add the final numbers. $16 + 216 = 232$.
3) $(6^2 + (18 \div 9 + 5^2)) - 3^2$
* Step 1: Solve the innermost parentheses first. Inside $(18 \div 9 + 5^2)$, do division and exponent first.
* $18 \div 9 = 2$ and $5^2 = 25$.
* So, $(2 + 25) = 27$.
* Equation becomes: $(6^2 + 27) - 3^2$
* Step 2: Solve the remaining exponents. $6^2 = 36$ and $3^2 = 9$.
* Equation becomes: $(36 + 27) - 9$
* Step 3: Solve the parentheses. $36 + 27 = 63$.
* Equation becomes: $63 - 9$
* Step 4: Subtract. $63 - 9 = 54$.
4) $(6^2 + (8 \div 4 + 3^2)) - 4^2$
* Step 1: Solve the innermost parentheses first. Inside $(8 \div 4 + 3^2)$, do division and exponent first.
* $8 \div 4 = 2$ and $3^2 = 9$.
* So, $(2 + 9) = 11$.
* Equation becomes: $(6^2 + 11) - 4^2$
* Step 2: Solve the remaining exponents. $6^2 = 36$ and $4^2 = 16$.
* Equation becomes: $(36 + 11) - 16$
* Step 3: Solve the parentheses. $36 + 11 = 47$.
* Equation becomes: $47 - 16$
* Step 4: Subtract. $47 - 16 = 31$.
5) $((18 - 3) - (20 \div 2)^2) \times 7^2$
* Step 1: Solve inside the parentheses. $(18 - 3) = 15$ and $(20 \div 2) = 10$.
* Equation becomes: $(15 - 10^2) \times 7^2$
* Step 2: Solve the exponents. $10^2 = 100$ and $7^2 = 49$.
* Equation becomes: $(15 - 100) \times 49$
* Step 3: Solve the parentheses. $15 - 100 = -85$.
* Equation becomes: $-85 \times 49$
* Step 4: Multiply. $-85 \times 49 = -4165$.
6) $((9 - 4)^2 + 4) + 13 + 5^2$
* Step 1: Solve inside the parentheses. $(9 - 4) = 5$.
* Equation becomes: $(5^2 + 4) + 13 + 5^2$
* Step 2: Solve the exponents. $5^2 = 25$. Note there are two $5^2$s.
* Equation becomes: $(25 + 4) + 13 + 25$
* Step 3: Solve the parentheses. $25 + 4 = 29$.
* Equation becomes: $29 + 13 + 25$
* Step 4: Add from left to right. $29 + 13 = 42$, then $42 + 25 = 67$.
7) $((10 - 3)^2 + 7) - 4 + 6^2$
* Step 1: Solve inside the parentheses. $(10 - 3) = 7$.
* Equation becomes: $(7^2 + 7) - 4 + 6^2$
* Step 2: Solve the exponents. $7^2 = 49$ and $6^2 = 36$.
* Equation becomes: $(49 + 7) - 4 + 36$
* Step 3: Solve the parentheses. $49 + 7 = 56$.
* Equation becomes: $56 - 4 + 36$
* Step 4: Add and subtract from left to right. $56 - 4 = 52$, then $52 + 36 = 88$.
8) $10 + (10 + (10 - 5)^2) + 6$
* Step 1: Solve the innermost parentheses. $(10 - 5) = 5$.
* Equation becomes: $10 + (10 + 5^2) + 6$
* Step 2: Solve the exponent. $5^2 = 25$.
* Equation becomes: $10 + (10 + 25) + 6$
* Step 3: Solve the remaining parentheses. $10 + 25 = 35$.
* Equation becomes: $10 + 35 + 6$
* Step 4: Add from left to right. $10 + 35 = 45$, then $45 + 6 = 51$.
9) $7 + (5 + (9 - 6)^2) - 9$
* Step 1: Solve the innermost parentheses. $(9 - 6) = 3$.
* Equation becomes: $7 + (5 + 3^2) - 9$
* Step 2: Solve the exponent. $3^2 = 9$.
* Equation becomes: $7 + (5 + 9) - 9$
* Step 3: Solve the remaining parentheses. $5 + 9 = 14$.
* Equation becomes: $7 + 14 - 9$
* Step 4: Add and subtract from left to right. $7 + 14 = 21$, then $21 - 9 = 12$.
10) $(20 \div 4)^2 + ((16 - 3) \times 5^2)$
* Step 1: Solve inside the parentheses. $(20 \div 4) = 5$ and $(16 - 3) = 13$.
* Equation becomes: $5^2 + (13 \times 5^2)$
* Step 2: Solve the exponents. $5^2 = 25$.
* Equation becomes: $25 + (13 \times 25)$
* Step 3: Multiply inside the parentheses. $13 \times 25 = 325$.
* Equation becomes: $25 + 325$
* Step 4: Add the final numbers. $25 + 325 = 350$.
Final Answer:
1) 142
2) 232
3) 54
4) 31
5) -4165
6) 67
7) 88
8) 51
9) 12
10) 350
1) $((14 + 3) + (20 \div 2)^2) + 5^2$
* Step 1: Solve inside the inner parentheses first. $(14 + 3) = 17$ and $(20 \div 2) = 10$.
* Equation becomes: $(17 + 10^2) + 5^2$
* Step 2: Solve the exponents. $10^2 = 100$ and $5^2 = 25$.
* Equation becomes: $(17 + 100) + 25$
* Step 3: Solve the remaining parentheses. $17 + 100 = 117$.
* Equation becomes: $117 + 25$
* Step 4: Add the final numbers. $117 + 25 = 142$.
2) $(12 \div 3)^2 + ((10 - 4) \times 6^2)$
* Step 1: Solve inside the parentheses. $(12 \div 3) = 4$ and $(10 - 4) = 6$.
* Equation becomes: $4^2 + (6 \times 6^2)$
* Step 2: Solve the exponents. $4^2 = 16$ and $6^2 = 36$.
* Equation becomes: $16 + (6 \times 36)$
* Step 3: Multiply inside the parentheses. $6 \times 36 = 216$.
* Equation becomes: $16 + 216$
* Step 4: Add the final numbers. $16 + 216 = 232$.
3) $(6^2 + (18 \div 9 + 5^2)) - 3^2$
* Step 1: Solve the innermost parentheses first. Inside $(18 \div 9 + 5^2)$, do division and exponent first.
* $18 \div 9 = 2$ and $5^2 = 25$.
* So, $(2 + 25) = 27$.
* Equation becomes: $(6^2 + 27) - 3^2$
* Step 2: Solve the remaining exponents. $6^2 = 36$ and $3^2 = 9$.
* Equation becomes: $(36 + 27) - 9$
* Step 3: Solve the parentheses. $36 + 27 = 63$.
* Equation becomes: $63 - 9$
* Step 4: Subtract. $63 - 9 = 54$.
4) $(6^2 + (8 \div 4 + 3^2)) - 4^2$
* Step 1: Solve the innermost parentheses first. Inside $(8 \div 4 + 3^2)$, do division and exponent first.
* $8 \div 4 = 2$ and $3^2 = 9$.
* So, $(2 + 9) = 11$.
* Equation becomes: $(6^2 + 11) - 4^2$
* Step 2: Solve the remaining exponents. $6^2 = 36$ and $4^2 = 16$.
* Equation becomes: $(36 + 11) - 16$
* Step 3: Solve the parentheses. $36 + 11 = 47$.
* Equation becomes: $47 - 16$
* Step 4: Subtract. $47 - 16 = 31$.
5) $((18 - 3) - (20 \div 2)^2) \times 7^2$
* Step 1: Solve inside the parentheses. $(18 - 3) = 15$ and $(20 \div 2) = 10$.
* Equation becomes: $(15 - 10^2) \times 7^2$
* Step 2: Solve the exponents. $10^2 = 100$ and $7^2 = 49$.
* Equation becomes: $(15 - 100) \times 49$
* Step 3: Solve the parentheses. $15 - 100 = -85$.
* Equation becomes: $-85 \times 49$
* Step 4: Multiply. $-85 \times 49 = -4165$.
6) $((9 - 4)^2 + 4) + 13 + 5^2$
* Step 1: Solve inside the parentheses. $(9 - 4) = 5$.
* Equation becomes: $(5^2 + 4) + 13 + 5^2$
* Step 2: Solve the exponents. $5^2 = 25$. Note there are two $5^2$s.
* Equation becomes: $(25 + 4) + 13 + 25$
* Step 3: Solve the parentheses. $25 + 4 = 29$.
* Equation becomes: $29 + 13 + 25$
* Step 4: Add from left to right. $29 + 13 = 42$, then $42 + 25 = 67$.
7) $((10 - 3)^2 + 7) - 4 + 6^2$
* Step 1: Solve inside the parentheses. $(10 - 3) = 7$.
* Equation becomes: $(7^2 + 7) - 4 + 6^2$
* Step 2: Solve the exponents. $7^2 = 49$ and $6^2 = 36$.
* Equation becomes: $(49 + 7) - 4 + 36$
* Step 3: Solve the parentheses. $49 + 7 = 56$.
* Equation becomes: $56 - 4 + 36$
* Step 4: Add and subtract from left to right. $56 - 4 = 52$, then $52 + 36 = 88$.
8) $10 + (10 + (10 - 5)^2) + 6$
* Step 1: Solve the innermost parentheses. $(10 - 5) = 5$.
* Equation becomes: $10 + (10 + 5^2) + 6$
* Step 2: Solve the exponent. $5^2 = 25$.
* Equation becomes: $10 + (10 + 25) + 6$
* Step 3: Solve the remaining parentheses. $10 + 25 = 35$.
* Equation becomes: $10 + 35 + 6$
* Step 4: Add from left to right. $10 + 35 = 45$, then $45 + 6 = 51$.
9) $7 + (5 + (9 - 6)^2) - 9$
* Step 1: Solve the innermost parentheses. $(9 - 6) = 3$.
* Equation becomes: $7 + (5 + 3^2) - 9$
* Step 2: Solve the exponent. $3^2 = 9$.
* Equation becomes: $7 + (5 + 9) - 9$
* Step 3: Solve the remaining parentheses. $5 + 9 = 14$.
* Equation becomes: $7 + 14 - 9$
* Step 4: Add and subtract from left to right. $7 + 14 = 21$, then $21 - 9 = 12$.
10) $(20 \div 4)^2 + ((16 - 3) \times 5^2)$
* Step 1: Solve inside the parentheses. $(20 \div 4) = 5$ and $(16 - 3) = 13$.
* Equation becomes: $5^2 + (13 \times 5^2)$
* Step 2: Solve the exponents. $5^2 = 25$.
* Equation becomes: $25 + (13 \times 25)$
* Step 3: Multiply inside the parentheses. $13 \times 25 = 325$.
* Equation becomes: $25 + 325$
* Step 4: Add the final numbers. $25 + 325 = 350$.
Final Answer:
1) 142
2) 232
3) 54
4) 31
5) -4165
6) 67
7) 88
8) 51
9) 12
10) 350
Parent Tip: Review the logic above to help your child master the concept of order of operation worksheet.
