Order of Operations Practice Worksheet | Math = Love - Free Printable
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Step-by-step solution for: Order of Operations Practice Worksheet | Math = Love
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Show Answer Key & Explanations
Step-by-step solution for: Order of Operations Practice Worksheet | Math = Love
Here are the step-by-step solutions for each problem in the table. I will solve them one by one, following the Order of Operations (PEMDAS/BODMAS):
1. Parentheses/Brackets `()` `[]` `{}` (start with the innermost)
2. Exponents (none in these problems)
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)
---
1. Solve inside the square brackets first.
* Left bracket: $(9 \div 3) = 3$. Then $3 \cdot 2 = 6$. So, $[6]$.
* Right bracket: $(2 \cdot 6) = 12$. Then $12 \div 3 = 4$. So, $[4]$.
2. Now the equation is: $3 + 6 + 4$.
3. Add from left to right: $3 + 6 = 9$, then $9 + 4 = 13$.
Answer: 13
---
1. Solve inside the parentheses first.
* First part: $(3 + 9) = 12$ and $(3 \cdot 2) = 6$.
* Second part: $(2 \cdot 6) = 12$.
2. Now solve inside the square brackets.
* Left bracket: $12 \div 6 = 2$. So, $[2]$.
* Right bracket: $12 \div 3 = 4$. So, $[4]$.
3. Now the equation is: $2 + 4$.
4. Add: $2 + 4 = 6$.
Answer: 6
---
1. Solve the simple parenthesis first: $(3 + 9) = 12$.
2. Look at the big square bracket: $[(3 \cdot 2 + 2 \cdot 6) \div 3]$.
* Inside the inner parenthesis of the bracket, do multiplication first: $3 \cdot 2 = 6$ and $2 \cdot 6 = 12$.
* Now add them: $6 + 12 = 18$.
* Now divide by 3: $18 \div 3 = 6$.
* So the square bracket equals $6$.
3. Now the equation is: $12 \div 6$.
4. Divide: $12 \div 6 = 2$.
Answer: 2
---
*Note: The image shows `(3 + 9 ÷ 3 · 2)`. Inside the parenthesis, we must do division and multiplication before addition.*
1. First parenthesis: $(3 + 9 \div 3 \cdot 2)$
* Division first: $9 \div 3 = 3$.
* Multiplication next: $3 \cdot 2 = 6$.
* Addition last: $3 + 6 = 9$.
* So, the first part is $9$.
2. Second parenthesis: $(2 \cdot 6 \div 3)$
* Multiplication first: $2 \cdot 6 = 12$.
* Division next: $12 \div 3 = 4$.
* So, the second part is $4$.
3. Now add the two results: $9 + 4 = 13$.
Answer: 13
---
1. Solve the separate parenthesis on the right first: $(6 \div 3) = 2$.
2. Now solve the big square bracket on the left: $[(3 + 9) \div 3 \cdot 2 + 2]$.
* Inner parenthesis: $(3 + 9) = 12$.
* Now we have: $12 \div 3 \cdot 2 + 2$.
* Division first (left to right): $12 \div 3 = 4$.
* Multiplication next: $4 \cdot 2 = 8$.
* Addition last: $8 + 2 = 10$.
* So the square bracket equals $10$.
3. Now multiply the results: $10 \cdot 2 = 20$.
Answer: 20
---
1. First square bracket: $[(3 + 9 \div 3) \cdot 2]$.
* Inside the inner parenthesis, do division first: $9 \div 3 = 3$.
* Then add: $3 + 3 = 6$.
* Then multiply by 2: $6 \cdot 2 = 12$.
* So the first part is $12$.
2. Second parenthesis: $(2 \cdot 6 \div 3)$.
* Multiply first: $2 \cdot 6 = 12$.
* Divide next: $12 \div 3 = 4$.
* So the second part is $4$.
3. Add them together: $12 + 4 = 16$.
Answer: 16
---
1. Start with the innermost parenthesis: $(3 \cdot 2) = 6$.
2. Now look at the next layer: $(3 + 9 \div 6)$.
* Wait, looking closely at the image text: `[(3 + 9 ÷ (3 · 2)) + 2]`.
* Let's re-evaluate. Usually, these problems result in whole numbers. Let me re-read the image carefully.
* Image text: `[(3 + 9 ÷ (3 · 2)) + 2] · 6 ÷ 3`? No, let me look at the spacing. It looks like `[(3 + 9 ÷ (3 · 2)) + 2]`.
* If it is $9 \div (3 \cdot 2)$, that is $9 \div 6 = 1.5$. This creates decimals. Let me check if I misread the operator.
* Ah, looking at similar problems, sometimes the dot is hard to see. Is it possible it is `(3 + 9) ...`? No, the parenthesis closes after 9.
* Let's look really closely at crop 4. It says `[(3 + 9 ÷ (3 · 2)) + 2]`.
* Okay, let's calculate with decimals if needed, or check if I missed a symbol.
* Actually, let's look at the standard order. Maybe it is `[(3 + 9) ÷ (3 · 2)]`? No, the closing paren is after the 9.
* Let's assume the question allows decimals or fractions.
* Step 1: Inner parens $(3 \cdot 2) = 6$.
* Step 2: Division $9 \div 6 = 1.5$.
* Step 3: Addition $3 + 1.5 = 4.5$.
* Step 4: Outer bracket addition $4.5 + 2 = 6.5$.
* Step 5: Multiply by 6: $6.5 \cdot 6 = 39$.
* Step 6: Divide by 3: $39 \div 3 = 13$.
* This results in a clean integer! So the decimal path was correct.
Answer: 13
---
1. First parenthesis: $(9 \div 3) = 3$.
2. Second parenthesis: $(2 + 2 \cdot 6 \div 3)$.
* Inside this parenthesis, do multiplication/division first.
* $2 \cdot 6 = 12$.
* $12 \div 3 = 4$.
* Now add: $2 + 4 = 6$.
* So the second parenthesis is $6$.
3. Now the equation is: $3 + 3 \cdot 6$.
4. Do multiplication before addition: $3 \cdot 6 = 18$.
5. Add: $3 + 18 = 21$.
Answer: 21
---
1. Innermost parentheses:
* $(9 \div 3) = 3$.
* $(2 + 2) = 4$.
* $(6 \div 3) = 2$.
2. Square brackets: $[3 \cdot 4] = 12$.
3. Curly braces: $\{12 \cdot 2\} = 24$.
4. Final addition: $3 + 24 = 27$.
Answer: 27
---
1. First square bracket: $[(3 + 9) \div 3]$.
* $(3 + 9) = 12$.
* $12 \div 3 = 4$.
2. Second square bracket: $[(2 \cdot 6) \div 3]$.
* $(2 \cdot 6) = 12$.
* $12 \div 3 = 4$.
3. Now the equation is: $4 \cdot 2 + 4$.
4. Multiplication first: $4 \cdot 2 = 8$.
5. Addition last: $8 + 4 = 12$.
Answer: 12
──────────────────────────────────────
Final Answer:
Row 1 Left: 13
Row 1 Right: 6
Row 2 Left: 2
Row 2 Right: 13
Row 3 Left: 20
Row 3 Right: 16
Row 4 Left: 13
Row 4 Right: 21
Row 5 Left: 27
Row 5 Right: 12
1. Parentheses/Brackets `()` `[]` `{}` (start with the innermost)
2. Exponents (none in these problems)
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)
---
Row 1, Left: $3 + [(9 \div 3) \cdot 2] + [(2 \cdot 6) \div 3]$
1. Solve inside the square brackets first.
* Left bracket: $(9 \div 3) = 3$. Then $3 \cdot 2 = 6$. So, $[6]$.
* Right bracket: $(2 \cdot 6) = 12$. Then $12 \div 3 = 4$. So, $[4]$.
2. Now the equation is: $3 + 6 + 4$.
3. Add from left to right: $3 + 6 = 9$, then $9 + 4 = 13$.
Answer: 13
---
Row 1, Right: $[(3 + 9) \div (3 \cdot 2)] + [(2 \cdot 6) \div 3]$
1. Solve inside the parentheses first.
* First part: $(3 + 9) = 12$ and $(3 \cdot 2) = 6$.
* Second part: $(2 \cdot 6) = 12$.
2. Now solve inside the square brackets.
* Left bracket: $12 \div 6 = 2$. So, $[2]$.
* Right bracket: $12 \div 3 = 4$. So, $[4]$.
3. Now the equation is: $2 + 4$.
4. Add: $2 + 4 = 6$.
Answer: 6
---
Row 2, Left: $(3 + 9) \div [(3 \cdot 2 + 2 \cdot 6) \div 3]$
1. Solve the simple parenthesis first: $(3 + 9) = 12$.
2. Look at the big square bracket: $[(3 \cdot 2 + 2 \cdot 6) \div 3]$.
* Inside the inner parenthesis of the bracket, do multiplication first: $3 \cdot 2 = 6$ and $2 \cdot 6 = 12$.
* Now add them: $6 + 12 = 18$.
* Now divide by 3: $18 \div 3 = 6$.
* So the square bracket equals $6$.
3. Now the equation is: $12 \div 6$.
4. Divide: $12 \div 6 = 2$.
Answer: 2
---
Row 2, Right: $(3 + 9 \div 3 \cdot 2) + (2 \cdot 6 \div 3)$
*Note: The image shows `(3 + 9 ÷ 3 · 2)`. Inside the parenthesis, we must do division and multiplication before addition.*
1. First parenthesis: $(3 + 9 \div 3 \cdot 2)$
* Division first: $9 \div 3 = 3$.
* Multiplication next: $3 \cdot 2 = 6$.
* Addition last: $3 + 6 = 9$.
* So, the first part is $9$.
2. Second parenthesis: $(2 \cdot 6 \div 3)$
* Multiplication first: $2 \cdot 6 = 12$.
* Division next: $12 \div 3 = 4$.
* So, the second part is $4$.
3. Now add the two results: $9 + 4 = 13$.
Answer: 13
---
Row 3, Left: $[(3 + 9) \div 3 \cdot 2 + 2] \cdot (6 \div 3)$
1. Solve the separate parenthesis on the right first: $(6 \div 3) = 2$.
2. Now solve the big square bracket on the left: $[(3 + 9) \div 3 \cdot 2 + 2]$.
* Inner parenthesis: $(3 + 9) = 12$.
* Now we have: $12 \div 3 \cdot 2 + 2$.
* Division first (left to right): $12 \div 3 = 4$.
* Multiplication next: $4 \cdot 2 = 8$.
* Addition last: $8 + 2 = 10$.
* So the square bracket equals $10$.
3. Now multiply the results: $10 \cdot 2 = 20$.
Answer: 20
---
Row 3, Right: $[(3 + 9 \div 3) \cdot 2] + (2 \cdot 6 \div 3)$
1. First square bracket: $[(3 + 9 \div 3) \cdot 2]$.
* Inside the inner parenthesis, do division first: $9 \div 3 = 3$.
* Then add: $3 + 3 = 6$.
* Then multiply by 2: $6 \cdot 2 = 12$.
* So the first part is $12$.
2. Second parenthesis: $(2 \cdot 6 \div 3)$.
* Multiply first: $2 \cdot 6 = 12$.
* Divide next: $12 \div 3 = 4$.
* So the second part is $4$.
3. Add them together: $12 + 4 = 16$.
Answer: 16
---
Row 4, Left: $[(3 + 9 \div (3 \cdot 2)) + 2] \cdot 6 \div 3$
1. Start with the innermost parenthesis: $(3 \cdot 2) = 6$.
2. Now look at the next layer: $(3 + 9 \div 6)$.
* Wait, looking closely at the image text: `[(3 + 9 ÷ (3 · 2)) + 2]`.
* Let's re-evaluate. Usually, these problems result in whole numbers. Let me re-read the image carefully.
* Image text: `[(3 + 9 ÷ (3 · 2)) + 2] · 6 ÷ 3`? No, let me look at the spacing. It looks like `[(3 + 9 ÷ (3 · 2)) + 2]`.
* If it is $9 \div (3 \cdot 2)$, that is $9 \div 6 = 1.5$. This creates decimals. Let me check if I misread the operator.
* Ah, looking at similar problems, sometimes the dot is hard to see. Is it possible it is `(3 + 9) ...`? No, the parenthesis closes after 9.
* Let's look really closely at crop 4. It says `[(3 + 9 ÷ (3 · 2)) + 2]`.
* Okay, let's calculate with decimals if needed, or check if I missed a symbol.
* Actually, let's look at the standard order. Maybe it is `[(3 + 9) ÷ (3 · 2)]`? No, the closing paren is after the 9.
* Let's assume the question allows decimals or fractions.
* Step 1: Inner parens $(3 \cdot 2) = 6$.
* Step 2: Division $9 \div 6 = 1.5$.
* Step 3: Addition $3 + 1.5 = 4.5$.
* Step 4: Outer bracket addition $4.5 + 2 = 6.5$.
* Step 5: Multiply by 6: $6.5 \cdot 6 = 39$.
* Step 6: Divide by 3: $39 \div 3 = 13$.
* This results in a clean integer! So the decimal path was correct.
Answer: 13
---
Row 4, Right: $3 + (9 \div 3) \cdot (2 + 2 \cdot 6 \div 3)$
1. First parenthesis: $(9 \div 3) = 3$.
2. Second parenthesis: $(2 + 2 \cdot 6 \div 3)$.
* Inside this parenthesis, do multiplication/division first.
* $2 \cdot 6 = 12$.
* $12 \div 3 = 4$.
* Now add: $2 + 4 = 6$.
* So the second parenthesis is $6$.
3. Now the equation is: $3 + 3 \cdot 6$.
4. Do multiplication before addition: $3 \cdot 6 = 18$.
5. Add: $3 + 18 = 21$.
Answer: 21
---
Row 5, Left: $3 + \{[(9 \div 3) \cdot (2 + 2)] \cdot (6 \div 3)\}$
1. Innermost parentheses:
* $(9 \div 3) = 3$.
* $(2 + 2) = 4$.
* $(6 \div 3) = 2$.
2. Square brackets: $[3 \cdot 4] = 12$.
3. Curly braces: $\{12 \cdot 2\} = 24$.
4. Final addition: $3 + 24 = 27$.
Answer: 27
---
Row 5, Right: $[(3 + 9) \div 3] \cdot 2 + [(2 \cdot 6) \div 3]$
1. First square bracket: $[(3 + 9) \div 3]$.
* $(3 + 9) = 12$.
* $12 \div 3 = 4$.
2. Second square bracket: $[(2 \cdot 6) \div 3]$.
* $(2 \cdot 6) = 12$.
* $12 \div 3 = 4$.
3. Now the equation is: $4 \cdot 2 + 4$.
4. Multiplication first: $4 \cdot 2 = 8$.
5. Addition last: $8 + 4 = 12$.
Answer: 12
──────────────────────────────────────
Final Answer:
Row 1 Left: 13
Row 1 Right: 6
Row 2 Left: 2
Row 2 Right: 13
Row 3 Left: 20
Row 3 Right: 16
Row 4 Left: 13
Row 4 Right: 21
Row 5 Left: 27
Row 5 Right: 12
Parent Tip: Review the logic above to help your child master the concept of order of operations practice worksheet.
