Order of Operations: PEMDAS | Interactive Worksheet - Free Printable

Let’s solve each expression one by one using PEMDAS:
Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

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1. 9 + 7 × 8

→ Multiplication first: 7 × 8 = 56
→ Then addition: 9 + 56 = 65

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2. 46 ÷ 19 – 4²

→ Exponent first: 4² = 16
→ Division next: 46 ÷ 19 ≈ 2.421… but let’s keep it as a fraction for accuracy: 46/19
→ Now subtract: 46/19 – 16 = 46/19 – 304/19 = -258/19 ≈ -13.578...

Wait — maybe we should check if this is meant to be exact or decimal? Since other problems are whole numbers, perhaps there’s a typo? But let’s stick with what’s written.

Actually, let me recalculate carefully:

46 ÷ 19 = 2.42105263...

Then 4² = 16

So 2.42105263 – 16 = -13.57894737

But since this is likely for middle school, maybe they expect rounding? Or perhaps I misread?

Wait — looking back at the image, it says “46 ÷ 19 – 4²” — yes.

But let’s hold on — maybe it’s 46 ÷ (19 – 4)²? No, no parentheses shown.

We’ll go with exact value unless told otherwise. But in school worksheets, sometimes they use nice numbers. Let me double-check all problems again.

Actually, let’s do them all step by step and see.

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3. 16 ÷ 4 × 7

→ Left to right: division then multiplication
→ 16 ÷ 4 = 4
→ 4 × 7 = 28

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4. 10² × 2 + 40 ÷ 8

→ Exponent: 10² = 100
→ Multiply: 100 × 2 = 200
→ Divide: 40 ÷ 8 = 5
→ Add: 200 + 5 = 205

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5. 8 × 12 ÷ (30 – 6)

→ Parentheses first: 30 – 6 = 24
→ Left to right: 8 × 12 = 96; then 96 ÷ 24 = 4

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6. 64 ÷ (8 + 10) × 3

→ Parentheses: 8 + 10 = 18
→ Left to right: 64 ÷ 18 = 32/9 ≈ 3.555...
→ Then × 3: (32/9) × 3 = 96/9 = 32/3 ≈ 10.666...

Again, not a whole number. Hmm.

Wait — maybe it’s 64 ÷ [(8 + 10) × 3]? But no, order is left to right after parentheses.

Let’s write it clearly:

64 ÷ 18 × 3 = (64 × 3) ÷ 18 = 192 ÷ 18 = 32 ÷ 3 = 10.666...

Still same.

Perhaps the worksheet expects fractions? Or maybe I made a mistake?

Let’s continue.

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7. 21 ÷ (3 + 4) × 6

→ Parentheses: 3 + 4 = 7
→ Left to right: 21 ÷ 7 = 3; then 3 × 6 = 18

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8. (9 – 5) × 7 – 2 × 8

→ Parentheses: 9 – 5 = 4
→ Multiply both: 4 × 7 = 28; 2 × 8 = 16
→ Subtract: 28 – 16 = 12

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9. 48 ÷ 6 × 2² – (3 + 5)

→ Parentheses: 3 + 5 = 8
→ Exponent: 2² = 4
→ Left to right: 48 ÷ 6 = 8; then 8 × 4 = 32
→ Subtract: 32 – 8 = 24

Okay, that one worked out nicely.

Now going back to #2 and #6 — maybe they’re supposed to be solved as decimals rounded? Or perhaps there’s a typo in the original problem?

But since we must solve what’s given, let’s present accurate answers.

For #2: 46 ÷ 19 – 4² = 46/19 – 16 = (46 – 304)/19 = -258/19 = -13.5789... → If rounding to two decimals: -13.58

For #6: 64 ÷ (8 + 10) × 3 = 64 ÷ 18 × 3 = (64 × 3) ÷ 18 = 192 ÷ 18 = 32 ÷ 3 = 10.666... → Rounded to two decimals: 10.67

But wait — let me check if any of these can be simplified as fractions.

In many schools, they prefer exact fractions unless specified.

So:

#2: -258/19 → already simplified? 258 ÷ 19 = 13.578..., and 19 is prime, so yes.

#6: 32/3

But looking at the rest of the problems, most give whole numbers. Maybe I misread #2?

Wait — is it possible that “46 ÷ 19 – 4²” was meant to be “46 ÷ (19 – 4)²”? That would be 46 ÷ (15)² = 46 ÷ 225 ≈ 0.204 — still not nice.

Or “(46 ÷ 19 – 4)²”? That would be (2.421 – 4)² = (-1.579)² ≈ 2.49 — also not nice.

Alternatively, maybe it’s 46 ÷ 2 – 4²? 23 – 16 = 7 — that’s nice. But it says 19.

Hmm. Perhaps it’s a trick question? Or maybe I should just report the exact values.

Since the instruction is to solve accurately, I will provide exact fractional forms where needed.

Let me list all answers clearly:

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Final Answers:

1. 9 + 7 × 8 = 65
2. 46 ÷ 19 – 4² = -258/19 or approximately -13.58
3. 16 ÷ 4 × 7 = 28
4. 10² × 2 + 40 ÷ 8 = 205
5. 8 × 12 ÷ (30 – 6) = 4
6. 64 ÷ (8 + 10) × 3 = 32/3 or approximately 10.67
7. 21 ÷ (3 + 4) × 6 = 18
8. (9 – 5) × 7 – 2 × 8 = 12
9. 48 ÷ 6 × 2² – (3 + 5) = 24

But since this is likely for students who may not have learned fractions deeply yet, and considering common worksheet design, perhaps #2 and #6 were intended to have different numbers. However, based on what’s written, we proceed.

Wait — let me recheck #2: 46 ÷ 19 – 4²

Is 46 divisible by 19? 19×2=38, 19×3=57 → no. So fraction is correct.

Similarly, #6: 64 ÷ 18 × 3 = 64 × 3 / 18 = 192 / 18 = 32 / 3 — correct.

I think we have to accept non-integer answers here.

But let me verify once more with calculator-style steps:

#2:
4² = 16
46 ÷ 19 = 2.4210526315789473
2.4210526315789473 – 16 = -13.578947368421053 → rounds to -13.58

#6:
8+10=18
64÷18=3.5555555555555554
3.5555555555555554 × 3 = 10.666666666666666 → rounds to 10.67

Yes.

However, in some curricula, they might want mixed numbers:

-258/19 = -13 11/19
32/3 = 10 2/3

That might be better for student understanding.

Let me convert:

#2: -258 ÷ 19 = -13 remainder 11 → so -13 11/19
#6: 32 ÷ 3 = 10 remainder 2 → so 10 2/3

That could be acceptable.

But since the problem doesn’t specify format, and others are integers, I'll present both exact fraction and decimal approximation for clarity.

But for final answer box, perhaps just the exact value or simplest form.

Looking at the example in the image: they got integer answers. So maybe there's an error in my reading?

Wait — look again at the image description: "Evaluate each expression..." and the expressions are listed.

Another thought: in #2, is it 46 ÷ (19 – 4²)? But no, exponent comes before subtraction unless grouped.

PEMDAS says exponents before subtraction, so 4² is done first, then division and subtraction left to right.

Same for #6.

I think we have to go with what’s written.

So for Final Answer, I’ll list each result as calculated.

But the user asked to put final answer in boxed{} — probably meaning one box per problem? Or all together?

The instruction says: “If the question has a final answer, please place the answer in \boxed{}.”

Since there are multiple problems, I should box each answer separately.

Let me compile:

1. \boxed{65}
2. \boxed{-\dfrac{258}{19}} or \boxed{-13.58} — but to be precise, fraction is better.
Actually, let's use improper fraction unless specified.

But for consistency with typical math class expectations, I'll use decimals rounded to two places for non-integers, since the context seems to be arithmetic practice.

Alternatively, notice that in problem #9, they used 2² which is fine, and got integer.

Perhaps the worksheet assumes integer results, so maybe I made a mistake in #2 and #6.

Wait — let's try #2 again: 46 ÷ 19 – 4²

What if it's 46 ÷ (19) – (4^2) — same thing.

Unless 4^2 is interpreted as 4*2? No, exponent means power.

Another idea: maybe "4^2" is a typo and should be "4*2"? Then 46÷19 – 8 = 2.421 – 8 = -5.579 — still not nice.

Or "46 ÷ 2 – 4^2" = 23 – 16 = 7 — that works.

Similarly, #6: 64 ÷ (8+10) × 3 = 64÷18×3 — if it were 64 ÷ (8+10×3) = 64÷(8+30)=64÷38≈1.68 — not nice.

Or 64 ÷ 8 + 10 × 3 = 8 + 30 = 38 — nice, but not what's written.

Given that, and since this is a helper role, I should solve as written.

But to match educational level, perhaps present as mixed numbers.

Let me decide:

For #2: -258/19 = -13 11/19
For #6: 32/3 = 10 2/3

And box those.

Or since the example in the image uses integers, and these are outliers, maybe the student is expected to leave as fractions.

I think safest is to provide exact values.

So:

Final Answer for each:

1. \boxed{65}
2. \boxed{-\dfrac{258}{19}}
3. \boxed{28}
4. \boxed{205}
5. \boxed{4}
6. \boxed{\dfrac{32}{3}}
7. \boxed{18}
8. \boxed{12}
9. \boxed{24}

But to make it cleaner for a student, perhaps write as:

After careful calculation following PEMDAS:

- Problem 1: 65
- Problem 2: -258/19 (or -13 11/19)
- etc.

But the instruction is to box the final answer.

Since there are nine problems, I'll box each answer in sequence.

However, the user might expect a single box, but that doesn't make sense.

Looking back at the initial request: "solve the problem accurately" — and the problem is to evaluate each expression.

So I'll provide the answers in order, boxed individually.

But in text, I can write:

The solutions are:

1. \boxed{65}
2. \boxed{-\dfrac{258}{19}}
3. \boxed{28}
4. \boxed{205}
5. \boxed{4}
6. \boxed{\dfrac{32}{3}}
7. \boxed{18}
8. \boxed{12}
9. \boxed{24}

To avoid LaTeX issues, perhaps write as:

Final Answer:
1. 65
2. -258/19
3. 28
4. 205
5. 4
6. 32/3
7. 18
8. 12
9. 24

And box the entire list? But the instruction says "place the answer in \boxed{}", implying one box.

This is ambiguous.

Perhaps for such multi-part questions, we box each part.

I recall that in some formats, they expect the answers listed.

Another way: since the user said "the problem", singular, but it's a set, perhaps treat as one task with multiple answers.

I think best is to provide the answers in a clear list, and for the Final Answer section, box the key results.

But to comply, I'll assume that "Final Answer" refers to the complete solution set, and since it's multiple, I'll present them as above.

Perhaps the system expects only the last answer or something, but that doesn't make sense.

Let me read the user's message again: "Solve the problem accurately." and "if the question has a final answer, please place the answer in \boxed{}."

Since there are nine sub-problems, each has its own final answer.

In educational contexts, when solving multiple items, we often list them.

I will provide the answers in order, and for the Final Answer section, I'll box each one separately in the response.

But in the format specified, "Final Answer:" should contain the boxed answer.

Perhaps for this case, since it's a worksheet, the expected output is the list of answers.

I think I'm overcomplicating.

Let me just state the answers clearly, and for the box, since it's required, I'll box the first one as an example, but that's not right.

No — better to follow the spirit.

Upon second thought, in many AI responses for multi-part questions, they box each answer.

So I'll do that.

Also, for #2 and #6, to make it student-friendly, I'll use mixed numbers.

So:

2. -13 11/19
6. 10 2/3

But in boxed, how to write?

In text, I can write:

\boxed{65}, \boxed{-13\dfrac{11}{19}}, \boxed{28}, etc.

But for simplicity, since this is text-based, I'll write:

Final Answer:
1. \boxed{65}
2. \boxed{-13\frac{11}{19}}
3. \boxed{28}
4. \boxed{205}
5. \boxed{4}
6. \boxed{10\frac{2}{3}}
7. \boxed{18}
8. \boxed{12}
9. \boxed{24}

Yes, that seems appropriate for a student.

Confirming calculations once more:

#2: 46 ÷ 19 = 2 8/19, minus 16 = 2 8/19 - 16 = -13 11/19 — yes, because 16 - 2 8/19 = 13 11/19, so negative.

#6: 64 ÷ 18 = 32/9, times 3 = 96/9 = 32/3 = 10 2/3 — yes.

Perfect.

So here we go.