Math worksheet designed to help students practice identifying the first step in the order of operations.

Let’s solve each problem step by step. We’re looking for the first expression to evaluate in each — that means we follow the order of operations (PEMDAS/BODMAS):

- Parentheses first
- Then Exponents
- Then Multiplication and Division (left to right)
- Then Addition and Subtraction (left to right)

We’ll go one by one.

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1) 5 + 9 + 10 + 16 ÷ 4

→ Division comes before addition → 16 ÷ 4 is first.

✔ First: 16 ÷ 4

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2) (7 + 90 ÷ 9) + 56 ÷ 7

→ Inside parentheses first: inside, division before addition → 90 ÷ 9

✔ First: 90 ÷ 9

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3) 10 - 7 + 12 ÷ 6 + 60 ÷ 6

→ Division before subtraction/addition → both divisions are equal priority, left to right → 12 ÷ 6 is first.

✔ First: 12 ÷ 6

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4) 10 + 5 + 7² + 6² + 8

→ Exponents come before addition → 7² is first (leftmost exponent).

✔ First: 7²

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5) 10 + 7 + 8³ + (10 + 50 ÷ 10)

→ Parentheses first → inside: division before addition → 50 ÷ 10

✔ First: 50 ÷ 10

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6) 9 + 5 + 36 ÷ 4 + 54 ÷ 9

→ Division before addition → leftmost division: 36 ÷ 4

✔ First: 36 ÷ 4

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7) 10 + 12 ÷ 6 + 6³ + 2³

→ Exponents and division — exponents come before division? Wait! Actually, exponents come before multiplication/division in PEMDAS.

Wait — correction: PEMDAS = Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction.

So exponents come BEFORE division.

Leftmost exponent: 6³

But wait — let’s check: 10 + 12 ÷ 6 + 6³ + 2³

Exponents: 6³ and 2³ — which is first? Left to right → 6³ is encountered first.

Actually, no — when evaluating expressions, you do ALL exponents before moving to multiplication/division. But since we’re asked for the *first expression to evaluate*, meaning the very first operation you perform according to order of operations...

In this case, there are no parentheses, so next is exponents. The leftmost exponent is 6³.

But hold on — actually, in standard evaluation, you scan left to right and apply precedence. So even though 6³ appears after 12÷6, because exponent has higher precedence than division, you do exponents first.

BUT — here’s the key: if multiple operations have same precedence level, you go left to right. But exponents are higher than division, so you must do all exponents before any division.

However, in this expression: 10 + 12 ÷ 6 + 6³ + 2³

The exponents are at positions: 6³ and 2³ — but 6³ comes before 2³ from left to right.

So first operation to evaluate is 6³

Wait — actually, let me double-check with a reliable source or logic.

Standard rule: Evaluate all exponents before doing multiplication/division.

So yes — even though “12 ÷ 6” appears earlier in the string, because exponentiation has higher precedence, you evaluate exponents first.

And among exponents, you go left to right → so 6³ is first.

✔ First: 6³

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8) 6 + 12 ÷ 3 + 8 - 8

→ Division before addition/subtraction → 12 ÷ 3

✔ First: 12 ÷ 3

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9) 5 + 20 ÷ 4 + 56 ÷ 8

→ Division first → leftmost: 20 ÷ 4

✔ First: 20 ÷ 4

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10) 5 + 3² + (4 + 9) + 8 + 4

→ Parentheses first → (4 + 9)

✔ First: 4 + 9

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11) 5 + (3² - 8) + 10 + 7

→ Parentheses first → inside: exponent before subtraction → 3²

✔ First: 3²

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12) 6 - 4 + 54 ÷ 6 × 3

→ Division and multiplication left to right → 54 ÷ 6 is first (then multiply by 3)

✔ First: 54 ÷ 6

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13) (4 + 30 ÷ 6) + 40 ÷ 8

→ Parentheses first → inside: division before addition → 30 ÷ 6

✔ First: 30 ÷ 6

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14) 4 + 3 + 18 ÷ 9 + 40 ÷ 5

→ Division first → leftmost: 18 ÷ 9

✔ First: 18 ÷ 9

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15) (10 + 4²) + 10 + 10 + 56 ÷ 7

→ Parentheses first → inside: exponent before addition → 4²

✔ First: 4²

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16) 4 + 36 ÷ 9 + 5 + 8

→ Division first → 36 ÷ 9

✔ First: 36 ÷ 9

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17) 9 + (10 ÷ 2 + 3²) + 5

→ Parentheses first → inside: division and exponent — exponent has higher precedence → 3²

Wait — inside parentheses: 10 ÷ 2 + 3²

Exponent before division? No — exponent before multiplication/division? Yes!

PEMDAS: Exponents before Multiplication/Division.

So inside parentheses: 3² is evaluated before 10 ÷ 2.

So first operation overall is 3²

✔ First: 3²

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18) 8 + (90 ÷ 9 × 5) × 6

→ Parentheses first → inside: division and multiplication left to right → 90 ÷ 9

✔ First: 90 ÷ 9

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19) 8 + 7² + 2 × 2 + 14 ÷ 2

→ Exponents first → 7²

✔ First: 7²

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20) 2 + 3² + 2³ + (7 × 4)

→ Exponents and parentheses — parentheses and exponents are same level? Actually, parentheses are done first, but only if they contain something to evaluate.

Here, (7 × 4) is a group — but it contains multiplication, which is lower than exponents? No — parentheses override everything.

Wait — important: You evaluate what’s inside parentheses first, regardless of content.

But in this case, (7 × 4) — you would evaluate that as a unit, but since it's just multiplication, and exponents are higher precedence... Hmm.

Actually, no: Parentheses are evaluated first — meaning you compute the entire expression inside them before using it elsewhere.

But within the parentheses, you still follow order of operations.

In (7 × 4), it’s just multiplication — so you do that.

But compare to exponents outside: 3² and 2³.

Which comes first?

Rule: Parentheses first — so you must evaluate (7 × 4) before anything else? Not exactly.

Actually, the rule is: evaluate expressions inside parentheses first — but if there are multiple groups or operations, you handle them based on precedence.

In this expression: 2 + 3² + 2³ + (7 × 4)

There are no nested parentheses. The (7 × 4) is a single grouped term.

But according to order of operations, you evaluate exponents before multiplication — unless the multiplication is inside parentheses.

Since (7 × 4) is enclosed in parentheses, you evaluate that entire group first — but within the group, it’s just multiplication, so you do 7 × 4.

However, exponents like 3² and 2³ are not inside parentheses — so should you do exponents first?

This is tricky.

Let me clarify with an example:

Consider: 2 + 3² + (4 × 5)

Do you do 3² first or (4×5) first?

Answer: It doesn’t matter numerically, but by strict order of operations, parentheses are evaluated first — meaning you compute the value inside the parentheses before combining with other terms.

But technically, in terms of "which operation to perform first", if we think of scanning left to right with precedence:

- Exponents have higher precedence than multiplication, but parentheses force their contents to be evaluated as a unit.

Actually, the correct interpretation is: you evaluate the contents of parentheses first — so even if it contains low-precedence operations, you do them before outer high-precedence ones.

For example: 2 + 3² + (4 + 5) — you do 4+5 first, even though exponent is higher, because it’s inside parentheses.

Similarly, here: (7 × 4) — you do that multiplication first, because it’s inside parentheses.

But wait — in our case, the parentheses contain only multiplication, which is fine.

However, let’s look back at the expression: 2 + 3² + 2³ + (7 × 4)

If we strictly follow PEMDAS:

Step 1: Parentheses → evaluate (7 × 4) = 28

Step 2: Exponents → 3²=9, 2³=8

Step 3: Addition

So the very first operation to evaluate is 7 × 4

Is that correct?

I think I made a mistake earlier.

Let me confirm with a trusted source or logical reasoning.

Actually, no — in standard mathematical convention, when you have an expression like A + B^C + (D * E), you evaluate the parentheses first — meaning you compute D*E before doing the exponentiation? No, that’s not right.

Wait — let’s think differently.

The expression is: 2 + 3² + 2³ + (7 × 4)

The parentheses around (7 × 4) mean that this product is treated as a single entity, but the evaluation order is still governed by precedence.

Actually, the correct way is: you evaluate all operations inside parentheses first, then exponents, then multiplication/division, etc.

But in this case, the parentheses contain only a multiplication, so you do that multiplication as part of evaluating the parenthetical group.

However, exponents outside the parentheses have higher precedence than the addition, but the parenthetical group is evaluated as a whole before being added.

But for the purpose of "which operation to perform first", we need to see which atomic operation is executed first during evaluation.

In practice, calculators and computers evaluate expressions by parsing and applying precedence.

According to standard rules:

- Parentheses are evaluated first — so any operation inside parentheses is done before operations outside, regardless of precedence.

Therefore, in (7 × 4), you do 7 × 4 first.

Even though 3² has higher precedence than multiplication, since the multiplication is inside parentheses, it gets priority.

Yes, that’s correct.

Example: 2 + 3 * (4 + 5) — you do 4+5 first, even though multiplication has higher precedence than addition, because it’s inside parentheses.

Similarly, here: (7 × 4) is inside parentheses, so you evaluate that multiplication first.

Moreover, in the expression, the parentheses are present, so you must evaluate their contents before proceeding.

Therefore, for problem 20, the first operation is 7 × 4

But let’s double-check with another approach.

Suppose we write the expression without spaces: 2+3^2+2^3+(7*4)

When parsed, the parser sees the parentheses and knows to evaluate the subexpression inside first.

Inside, it’s 7*4, which is a single operation.

Whereas 3^2 and 2^3 are exponents outside.

So yes, (7*4) is evaluated first.

To confirm, imagine if it was (7 + 4) — you’d definitely do 7+4 first.

Same logic applies.

So for 20, first is 7 × 4

But earlier I thought exponents, but no — parentheses take precedence.

Let me verify with a simple example.

Take: 1 + 2^2 + (3 * 4)

What is evaluated first? 3*4, because it’s in parentheses.

Then 2^2, then additions.

Yes.

So for 20: 7 × 4

✔ First: 7 × 4

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Now, compiling all answers:

1. 16 ÷ 4
2. 90 ÷ 9
3. 12 ÷ 6
4. 7²
5. 50 ÷ 10
6. 36 ÷ 4
7. 6³
8. 12 ÷ 3
9. 20 ÷ 4
10. 4 + 9
11. 3²
12. 54 ÷ 6
13. 30 ÷ 6
14. 18 ÷ 9
15. 4²
16. 36 ÷ 9
17. 3²
18. 90 ÷ 9
19. 7²
20. 7 × 4

Note: For #7, I said 6³, but let me reconfirm.

Problem 7: 10 + 12 ÷ 6 + 6³ + 2³

Order of operations: exponents before division.

Leftmost exponent is 6³, so yes.

Some might argue that since 12÷6 is written first, but no — precedence rules say exponents first.

Similarly, for #17: 9 + (10 ÷ 2 + 3²) + 5

Inside parentheses: 10 ÷ 2 + 3²

Exponent before division → 3² first.

Yes.

All seem correct.

Final Answer:
1. 16 ÷ 4
2. 90 ÷ 9
3. 12 ÷ 6
4. 7²
5. 50 ÷ 10
6. 36 ÷ 4
7. 6³
8. 12 ÷ 3
9. 20 ÷ 4
10. 4 + 9
11. 3²
12. 54 ÷ 6
13. 30 ÷ 6
14. 18 ÷ 9
15. 4²
16. 36 ÷ 9
17. 3²
18. 90 ÷ 9
19. 7²
20. 7 × 4