Order of Operations Worksheets - Free Printable Math PDFs - Free Printable

Let’s solve each problem step by step, following the order of operations: Parentheses first, then Exponents (none here), then Multiplication and Division from left to right, then Addition and Subtraction from left to right. We’ll handle innermost parentheses or brackets first.

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Problem 1:
{4 + [(8 – 7) × 6 – 55 ÷ 11]} × 2

Step 1: Solve inside the innermost parentheses:
(8 – 7) = 1

Now we have:
{4 + [1 × 6 – 55 ÷ 11]} × 2

Step 2: Do multiplication and division inside the brackets from left to right:
1 × 6 = 6
55 ÷ 11 = 5

Now:
{4 + [6 – 5]} × 2

Step 3: Subtract inside the brackets:
6 – 5 = 1

Now:
{4 + 1} × 2

Step 4: Add inside the braces:
4 + 1 = 5

Step 5: Multiply by 2:
5 × 2 = 10

✔ Final Answer for Problem 1: 10

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Problem 2:
7 × 9 – 8 + 11 – 6[5 + 2(–3)]

Note: The “6[...]” means 6 multiplied by whatever is in the brackets.

Step 1: Start with the innermost parentheses:
2 × (–3) = –6

Now:
7 × 9 – 8 + 11 – 6[5 + (–6)]

Step 2: Simplify inside the brackets:
5 + (–6) = –1

Now:
7 × 9 – 8 + 11 – 6 × (–1)

Step 3: Do all multiplications:
7 × 9 = 63
6 × (–1) = –6 → but since it’s minus that, it becomes: – (–6) = +6? Wait — let’s be careful.

Actually, the expression is:
... – 6 × (–1)

So: 6 × (–1) = –6
Then subtracting that: – (–6) = +6

Wait — no! Let’s rewrite clearly:

Original after simplifying brackets:
7 × 9 – 8 + 11 – 6 × (–1)

Multiplication first:
7 × 9 = 63
6 × (–1) = –6

So now:
63 – 8 + 11 – (–6)? No — wait, the “– 6 × (–1)” is one term.

Actually, think of it as:
63 – 8 + 11 + [because –6 × –1 = +6?]

No — let’s parse the expression correctly:

It’s:
7 × 9 – 8 + 11 – [6 × (5 + 2×(–3))]

We already did: 5 + 2×(–3) = 5 – 6 = –1
Then 6 × (–1) = –6
Then the whole thing is: ... – (–6)? No!

The original is:
7 × 9 – 8 + 11 – 6[5 + 2(–3)]
= 63 – 8 + 11 – 6*(–1)
= 63 – 8 + 11 – (–6) ??? No — 6*(–1) is –6, so subtracting that is: – (–6) = +6

Yes! Because it’s “minus 6 times negative one”, which is minus a negative, so plus positive.

So:
63 – 8 = 55
55 + 11 = 66
66 + 6 = 72

Wait — let me write it step by step without skipping:

After computing multiplications:

Expression becomes:
63 – 8 + 11 – (–6) ? No — actually, 6 × (–1) = –6, and the operation before it is subtraction, so:

It’s: 63 – 8 + 11 – (–6) → no, that’s not right.

Let me use proper grouping:

The term is: – 6 × (–1)

Which equals: – [6 × (–1)] = – [–6] = +6

Yes.

So:

Start over:

7 × 9 = 63
Then: 63 – 8 = 55
Then: 55 + 11 = 66
Then: 66 – [6 × (–1)] = 66 – (–6) = 66 + 6 = 72

✔ Final Answer for Problem 2: 72

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Problem 3:
25 + {2[3 + 8 – 7(25 ÷ 5) + 11]}

Step 1: Innermost parentheses:
25 ÷ 5 = 5

Now:
25 + {2[3 + 8 – 7×5 + 11]}

Step 2: Multiplication inside brackets:
7 × 5 = 35

Now:
25 + {2[3 + 8 – 35 + 11]}

Step 3: Inside the brackets, do addition/subtraction left to right:
3 + 8 = 11
11 – 35 = –24
–24 + 11 = –13

Now:
25 + {2 × (–13)}

Step 4: Multiply:
2 × (–13) = –26

Step 5: Add to 25:
25 + (–26) = –1

✔ Final Answer for Problem 3: –1

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Problem 4:
84 ÷ {12 + [(6 – 3 × 3) – 7] + 4}

Step 1: Handle innermost parentheses:
First, inside (6 – 3 × 3): multiplication first!
3 × 3 = 9
Then: 6 – 9 = –3

Now:
84 ÷ {12 + [(–3) – 7] + 4}

Step 2: Inside the brackets:
(–3) – 7 = –10

Now:
84 ÷ {12 + (–10) + 4}

Step 3: Inside the braces, left to right:
12 + (–10) = 2
2 + 4 = 6

Now:
84 ÷ 6 = 14

✔ Final Answer for Problem 4: 14

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Final Answer:
10
72
-1
14