Order of Operations Practice Worksheet | Math = Love - Free Printable

Let’s solve each problem one by one, following the order of operations:

> PEMDAS:
> Parentheses → Exponents → Multiplication & Division (left to right) → Addition & Subtraction (left to right)

We’ll go row by row, left to right.

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Problem 1: Left column, top row

`3 + [(9 ÷ 3) · 2] + [(2 · 6) ÷ 3]`

Step 1: Solve inside innermost parentheses first.

- `(9 ÷ 3)` = 3
- `(2 · 6)` = 12

Now plug back in:

`3 + [3 · 2] + [12 ÷ 3]`

Step 2: Do multiplication and division inside brackets.

- `3 · 2` = 6
- `12 ÷ 3` = 4

Now:

`3 + 6 + 4`

Step 3: Add left to right.

`3 + 6 = 9`, then `9 + 4 = 13`

✔ Answer: 13

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Problem 2: Right column, top row

`[(3 + 9) ÷ (3 · 2)] + [(2 · 6) ÷ 3]`

Step 1: Inner parentheses:

- `(3 + 9)` = 12
- `(3 · 2)` = 6
- `(2 · 6)` = 12

Plug in:

`[12 ÷ 6] + [12 ÷ 3]`

Step 2: Divide:

- `12 ÷ 6` = 2
- `12 ÷ 3` = 4

Add: `2 + 4 = 6`

✔ Answer: 6

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Problem 3: Left column, second row

`(3 + 9) ÷ [(3 · 2 + 2 · 6) ÷ 3]`

Step 1: Numerator: `(3 + 9)` = 12

Denominator: Inside big bracket: `(3 · 2 + 2 · 6) ÷ 3`

First, do multiplications inside:

- `3 · 2` = 6
- `2 · 6` = 12

So: `(6 + 12) ÷ 3` = `18 ÷ 3` = 6

Now whole expression: `12 ÷ 6 = 2`

✔ Answer: 2

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Problem 4: Right column, second row

`(3 + 9 ÷ 3 · 2) + (2 · 6 ÷ 3)`

Important: In `9 ÷ 3 · 2`, do left to right!

First part: `(3 + 9 ÷ 3 · 2)`

- `9 ÷ 3` = 3
- `3 · 2` = 6
- So: `3 + 6 = 9`

Second part: `(2 · 6 ÷ 3)`

- `2 · 6` = 12
- `12 ÷ 3` = 4

Total: `9 + 4 = 13`

✔ Answer: 13

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Problem 5: Left column, third row

`[(3 + 9) ÷ 3 · 2 + 2] · (6 ÷ 3)`

Step 1: `(3 + 9)` = 12

Then: `[12 ÷ 3 · 2 + 2] · (6 ÷ 3)`

Inside bracket: Left to right for ÷ and ·

- `12 ÷ 3` = 4
- `4 · 2` = 8
- `8 + 2` = 10

Other part: `(6 ÷ 3)` = 2

Multiply: `10 · 2 = 20`

✔ Answer: 20

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Problem 6: Right column, third row

`[(3 + 9 ÷ 3) · 2] + (2 · 6 ÷ 3)`

First: Inside first bracket: `(3 + 9 ÷ 3)`

- `9 ÷ 3` = 3
- `3 + 3` = 6
- Then `6 · 2` = 12

Second part: `(2 · 6 ÷ 3)`

- `2 · 6` = 12
- `12 ÷ 3` = 4

Total: `12 + 4 = 16`

✔ Answer: 16

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Problem 7: Left column, fourth row

`[(3 + 9 ÷ (3 · 2) + 2] · 6 ÷ 3`

Wait — let me check original: It says:

`[(3 + 9 ÷ (3 · 2) + 2] · 6 ÷ 3`

Actually, looking again — it should be:

`[(3 + 9 ÷ (3 · 2) + 2)] · 6 ÷ 3`

Assume that’s what was meant.

Step 1: Innermost: `(3 · 2)` = 6

Then: `9 ÷ 6` = 1.5? Wait — but maybe we’re supposed to keep fractions or decimals? Let’s see.

But actually, let’s re-read carefully. Original is:

`[(3 + 9 ÷ (3 · 2) + 2] · 6 ÷ 3`

I think there might be a typo — probably meant:

`[(3 + 9 ÷ (3 · 2) + 2)] · 6 ÷ 3`

Proceeding:

- `(3 · 2)` = 6
- `9 ÷ 6` = 1.5
- Now: `3 + 1.5 + 2` = 6.5
- Then: `6.5 · 6` = 39
- Then: `39 ÷ 3` = 13

But wait — this gives decimal. Maybe I misread.

Looking back at image description — perhaps it's:

`[(3 + 9 ÷ (3 · 2) + 2)] · 6 ÷ 3`

Yes. But 9÷6=1.5 — okay, unless they expect fraction.

Alternatively — maybe it’s `(3 + 9) ÷ (3·2) + 2`? No, brackets are as written.

Wait — let me double-check the original problem from your list:

You wrote:

`[(3 + 9 ÷ (3 · 2) + 2] · 6 ÷ 3`

There’s an extra opening bracket? Probably typo. Likely:

`[(3 + 9 ÷ (3 · 2) + 2)] · 6 ÷ 3`

So:

Inner: `3·2=6`

Then: `9÷6 = 3/2 = 1.5`

Then: `3 + 1.5 + 2 = 6.5`

Then: `6.5 × 6 = 39`

Then: `39 ÷ 3 = 13`

✔ Answer: 13

*(Note: If fractional answer expected, 13 is still correct since 39/3=13)*

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Problem 8: Right column, fourth row

`3 + (9 ÷ 3) · (2 + 2 · 6 ÷ 3)`

Break it down.

First: `(9 ÷ 3)` = 3

Second: Inside other parentheses: `(2 + 2 · 6 ÷ 3)`

Do multiplication/division left to right:

- `2 · 6` = 12
- `12 ÷ 3` = 4
- Then: `2 + 4` = 6

Now: `3 + 3 · 6`

Multiplication before addition: `3 · 6 = 18`

Then: `3 + 18 = 21`

✔ Answer: 21

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Problem 9: Left column, bottom row

`3 + {[(9 ÷ 3) · (2 + 2)] · (6 ÷ 3)}`

Start innermost:

- `(9 ÷ 3)` = 3
- `(2 + 2)` = 4
- `(6 ÷ 3)` = 2

Now: `{[3 · 4] · 2}`

→ `[12] · 2` = 24

Then: `3 + 24 = 27`

✔ Answer: 27

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Problem 10: Right column, bottom row

`[(3 + 9) ÷ 3] · 2 + [(2 · 6) ÷ 3]`

Step 1: `(3 + 9)` = 12 → `12 ÷ 3` = 4 → `4 · 2` = 8

Step 2: `(2 · 6)` = 12 → `12 ÷ 3` = 4

Add: `8 + 4 = 12`

✔ Answer: 12

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Final Answers Summary:

Left Column:
1. 13
2. 2
3. 20
4. 13
5. 27

Right Column:
1. 6
2. 13
3. 16
4. 21
5. 12

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Final Answer:
Left Column (top to bottom): 13, 2, 20, 13, 27
Right Column (top to bottom): 6, 13, 16, 21, 12