Order of Operations Worksheets - Math Monks - Free Printable
Educational worksheet: Order of Operations Worksheets - Math Monks. Download and print for classroom or home learning activities.
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Step-by-step solution for: Order of Operations Worksheets - Math Monks
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Show Answer Key & Explanations
Step-by-step solution for: Order of Operations Worksheets - Math Monks
Here are the step-by-step solutions for each problem using PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
1) $(12 \div 2) \times 5^2 - 8$
* Parentheses: Solve inside $(12 \div 2)$ first. $12 \div 2 = 6$.
* Equation becomes: $6 \times 5^2 - 8$
* Exponents: Solve $5^2$. $5 \times 5 = 25$.
* Equation becomes: $6 \times 25 - 8$
* Multiplication: Multiply $6 \times 25$. $6 \times 25 = 150$.
* Equation becomes: $150 - 8$
* Subtraction: Subtract $8$ from $150$. $150 - 8 = 142$.
2) $(4^3 \div 2) \times 6 - 3$
* Parentheses: Inside the parentheses, do the exponent first ($4^3$), then the division.
* $4^3 = 4 \times 4 \times 4 = 64$.
* $64 \div 2 = 32$.
* Equation becomes: $32 \times 6 - 3$
* Multiplication: Multiply $32 \times 6$. $32 \times 6 = 192$.
* Equation becomes: $192 - 3$
* Subtraction: Subtract $3$ from $192$. $192 - 3 = 189$.
3) $9 \times [(-3) + 4 - (-2)^2]$
* Brackets/Parentheses: Start with the innermost part. First, handle the exponent $(-2)^2$.
* $(-2) \times (-2) = 4$.
* The bracket becomes: $[(-3) + 4 - 4]$.
* Inside Brackets: Add and subtract from left to right.
* $-3 + 4 = 1$.
* $1 - 4 = -3$.
* Equation becomes: $9 \times (-3)$
* Multiplication: Multiply $9 \times -3$. Result is $-27$.
4) $(14^2 \times 15) - (2^2 + 20)$
* Parentheses (Left Side): Calculate the exponent first.
* $14^2 = 196$.
* $196 \times 15 = 2940$.
* Parentheses (Right Side): Calculate the exponent first.
* $2^2 = 4$.
* $4 + 20 = 24$.
* Subtraction: Subtract the right side result from the left side result.
* $2940 - 24 = 2916$.
5) $4^2 + (8 - 2)^2 \div 4$
* Parentheses: Solve $(8 - 2)$. Result is $6$.
* Equation becomes: $4^2 + 6^2 \div 4$
* Exponents: Solve $4^2$ and $6^2$.
* $4^2 = 16$.
* $6^2 = 36$.
* Equation becomes: $16 + 36 \div 4$
* Division: Divide $36 \div 4$. Result is $9$.
* Equation becomes: $16 + 9$
* Addition: Add $16 + 9$. Result is $25$.
6) $(15^2 - 9) \times 2 - 15$
* Parentheses: Handle the exponent first.
* $15^2 = 225$.
* $225 - 9 = 216$.
* Equation becomes: $216 \times 2 - 15$
* Multiplication: Multiply $216 \times 2$. Result is $432$.
* Equation becomes: $432 - 15$
* Subtraction: Subtract $15$ from $432$. Result is $417$.
7) $(6^2 + 4) \div (18 - 14)$
* Parentheses (Left): Handle the exponent first.
* $6^2 = 36$.
* $36 + 4 = 40$.
* Parentheses (Right): Subtract.
* $18 - 14 = 4$.
* Division: Divide the left result by the right result.
* $40 \div 4 = 10$.
8) $(6^2 + 18 - 8) \div 2$
* Parentheses: Handle the exponent first.
* $6^2 = 36$.
* Now solve addition and subtraction inside: $36 + 18 - 8$.
* $36 + 18 = 54$.
* $54 - 8 = 46$.
* Equation becomes: $46 \div 2$
* Division: Divide $46$ by $2$. Result is $23$.
Final Answer:
1) 142
2) 189
3) -27
4) 2916
5) 25
6) 417
7) 10
8) 23
1) $(12 \div 2) \times 5^2 - 8$
* Parentheses: Solve inside $(12 \div 2)$ first. $12 \div 2 = 6$.
* Equation becomes: $6 \times 5^2 - 8$
* Exponents: Solve $5^2$. $5 \times 5 = 25$.
* Equation becomes: $6 \times 25 - 8$
* Multiplication: Multiply $6 \times 25$. $6 \times 25 = 150$.
* Equation becomes: $150 - 8$
* Subtraction: Subtract $8$ from $150$. $150 - 8 = 142$.
2) $(4^3 \div 2) \times 6 - 3$
* Parentheses: Inside the parentheses, do the exponent first ($4^3$), then the division.
* $4^3 = 4 \times 4 \times 4 = 64$.
* $64 \div 2 = 32$.
* Equation becomes: $32 \times 6 - 3$
* Multiplication: Multiply $32 \times 6$. $32 \times 6 = 192$.
* Equation becomes: $192 - 3$
* Subtraction: Subtract $3$ from $192$. $192 - 3 = 189$.
3) $9 \times [(-3) + 4 - (-2)^2]$
* Brackets/Parentheses: Start with the innermost part. First, handle the exponent $(-2)^2$.
* $(-2) \times (-2) = 4$.
* The bracket becomes: $[(-3) + 4 - 4]$.
* Inside Brackets: Add and subtract from left to right.
* $-3 + 4 = 1$.
* $1 - 4 = -3$.
* Equation becomes: $9 \times (-3)$
* Multiplication: Multiply $9 \times -3$. Result is $-27$.
4) $(14^2 \times 15) - (2^2 + 20)$
* Parentheses (Left Side): Calculate the exponent first.
* $14^2 = 196$.
* $196 \times 15 = 2940$.
* Parentheses (Right Side): Calculate the exponent first.
* $2^2 = 4$.
* $4 + 20 = 24$.
* Subtraction: Subtract the right side result from the left side result.
* $2940 - 24 = 2916$.
5) $4^2 + (8 - 2)^2 \div 4$
* Parentheses: Solve $(8 - 2)$. Result is $6$.
* Equation becomes: $4^2 + 6^2 \div 4$
* Exponents: Solve $4^2$ and $6^2$.
* $4^2 = 16$.
* $6^2 = 36$.
* Equation becomes: $16 + 36 \div 4$
* Division: Divide $36 \div 4$. Result is $9$.
* Equation becomes: $16 + 9$
* Addition: Add $16 + 9$. Result is $25$.
6) $(15^2 - 9) \times 2 - 15$
* Parentheses: Handle the exponent first.
* $15^2 = 225$.
* $225 - 9 = 216$.
* Equation becomes: $216 \times 2 - 15$
* Multiplication: Multiply $216 \times 2$. Result is $432$.
* Equation becomes: $432 - 15$
* Subtraction: Subtract $15$ from $432$. Result is $417$.
7) $(6^2 + 4) \div (18 - 14)$
* Parentheses (Left): Handle the exponent first.
* $6^2 = 36$.
* $36 + 4 = 40$.
* Parentheses (Right): Subtract.
* $18 - 14 = 4$.
* Division: Divide the left result by the right result.
* $40 \div 4 = 10$.
8) $(6^2 + 18 - 8) \div 2$
* Parentheses: Handle the exponent first.
* $6^2 = 36$.
* Now solve addition and subtraction inside: $36 + 18 - 8$.
* $36 + 18 = 54$.
* $54 - 8 = 46$.
* Equation becomes: $46 \div 2$
* Division: Divide $46$ by $2$. Result is $23$.
Final Answer:
1) 142
2) 189
3) -27
4) 2916
5) 25
6) 417
7) 10
8) 23
Parent Tip: Review the logic above to help your child master the concept of 5th grade math worksheet order of operations.
