Order of Operations Worksheet 7 Worksheets - Free Printable

Let's solve each problem step by step using the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

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Problem 1:

3 – (2² + 1) + 5 ≤ 0

- First, evaluate exponent:
$ 2^2 = 4 $
- Then inside parentheses:
$ 4 + 1 = 5 $
- Now:
$ 3 - 5 + 5 = -2 + 5 = 3 $
- Is $ 3 \leq 0 $? → No, so this statement is false.

✔ Answer: False

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Problem 2:

(4² – 9 – 1) = 206

- $ 4^2 = 16 $
- $ 16 - 9 - 1 = 6 $
- Is $ 6 = 206 $? → No

✔ Answer: False

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Problem 3:

(5 + 7²) ÷ 7 × 7 = 348

- $ 7^2 = 49 $
- $ 5 + 49 = 54 $
- $ 54 ÷ 7 ≈ 7.714 $
- $ 7.714 × 7 ≈ 54 $

But $ 54 ≠ 348 $

✔ Answer: False

Wait — let's double-check:

Is it $ (5 + 7^2) ÷ 7 × 7 $?
Yes.
$ 5 + 49 = 54 $
$ 54 ÷ 7 = 7.714... $
Then $ 7.714 × 7 = 54 $

So result is 54, not 348.

✔ Answer: False

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Problem 4:

(2 – 7) – 8 – 3 = -16

- $ 2 - 7 = -5 $
- $ -5 - 8 = -13 $
- $ -13 - 3 = -16 $

✔ Answer: True

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Problem 5:

(6 + 7²) + 1 = 55

- $ 7^2 = 49 $
- $ 6 + 49 = 55 $
- $ 55 + 1 = 56 $

Is $ 56 = 55 $? → No

✔ Answer: False

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Problem 6:

4² – (2 + 2²) × 5 = 14

- $ 4^2 = 16 $
- $ 2^2 = 4 $
- $ 2 + 4 = 6 $
- $ 6 × 5 = 30 $
- $ 16 - 30 = -14 $

Is $ -14 = 14 $? → No

✔ Answer: False

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Problem 7:

(6 – 1 + 7) = 12

- $ 6 - 1 = 5 $
- $ 5 + 7 = 12 $

✔ Answer: True

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Problem 8:

(3¹ – 3¹) + 5 = 5

- $ 3^1 = 3 $
- $ 3 - 3 = 0 $
- $ 0 + 5 = 5 $

✔ Answer: True

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Problem 9:

(7 + 8 – 4²) × 2 + 1 = -1

- $ 4^2 = 16 $
- $ 7 + 8 = 15 $
- $ 15 - 16 = -1 $
- $ -1 × 2 = -2 $
- $ -2 + 1 = -1 $

✔ Answer: True

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Problem 10:

6 – (8 – 3³) + 4 = -33

- $ 3^3 = 27 $
- $ 8 - 27 = -19 $
- $ 6 - (-19) = 6 + 19 = 25 $
- $ 25 + 4 = 29 $

Is $ 29 = -33 $? → No

✔ Answer: False

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Problem 11:

(3 × 3 + 6 × 3² – 3) = 27

- $ 3^2 = 9 $
- $ 6 × 9 = 54 $
- $ 3 × 3 = 9 $
- So: $ 9 + 54 - 3 = 60 $

Is $ 60 = 27 $? → No

✔ Answer: False

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Problem 12:

(7 + 2²) × 9 = 135

- $ 2^2 = 4 $
- $ 7 + 4 = 11 $
- $ 11 × 9 = 99 $

Is $ 99 = 135 $? → No

✔ Answer: False

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Problem 13:

(3 × 6) – 5 = 13

- $ 3 × 6 = 18 $
- $ 18 - 5 = 13 $

✔ Answer: True

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Problem 14:

6 × (2² + 1) + 1 = 12

- $ 2^2 = 4 $
- $ 4 + 1 = 5 $
- $ 6 × 5 = 30 $
- $ 30 + 1 = 31 $

Is $ 31 = 12 $? → No

✔ Answer: False

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Problem 15:

(2³ – 9 – 8) + 3 × 3 = -9

- $ 2^3 = 8 $
- $ 8 - 9 - 8 = -9 $
- $ 3 × 3 = 9 $
- $ -9 + 9 = 0 $

Is $ 0 = -9 $? → No

✔ Answer: False

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Problem 16:

2³ + (7 + 7 × 8) = 64

- $ 2^3 = 8 $
- Inside parentheses: $ 7 × 8 = 56 $
- $ 7 + 56 = 63 $
- $ 8 + 63 = 71 $

Is $ 71 = 64 $? → No

✔ Answer: False

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Problem 17:

(6 + 6²) × 3 = 126

- $ 6^2 = 36 $
- $ 6 + 36 = 42 $
- $ 42 × 3 = 126 $

✔ Answer: True

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Problem 18:

(3 + 1) × 8 × 4 = 128

- $ 3 + 1 = 4 $
- $ 4 × 8 = 32 $
- $ 32 × 4 = 128 $

✔ Answer: True

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Problem 19:

(7³ × 4) + 7 = 1379

- $ 7^3 = 343 $
- $ 343 × 4 = 1372 $
- $ 1372 + 7 = 1379 $

✔ Answer: True

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Problem 20:

6² – 3 × (3² + 2) ÷ 5 = -13

- $ 6^2 = 36 $
- $ 3^2 = 9 $
- $ 9 + 2 = 11 $
- $ 3 × 11 = 33 $
- $ 33 ÷ 5 = 6.6 $
- $ 36 - 6.6 = 29.4 $

Is $ 29.4 = -13 $? → No

But wait — maybe we need to check if it’s exactly equal?

Let’s compute carefully:

- $ 6^2 = 36 $
- $ 3^2 = 9 $
- $ 9 + 2 = 11 $
- $ 3 × 11 = 33 $
- $ 33 ÷ 5 = 6.6 $
- $ 36 - 6.6 = 29.4 $

Not -13.

Alternatively, could there be a typo? Let's see:

If the expression was meant to be:
$$
6^2 - 3 \times (3^2 + 2) \div 5
$$
We did that.

But maybe they expect integer division? No, in math, division is exact.

So answer is not -13.

✔ Answer: False

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | False |
| 2 | False |
| 3 | False |
| 4 | True |
| 5 | False |
| 6 | False |
| 7 | True |
| 8 | True |
| 9 | True |
| 10 | False |
| 11 | False |
| 12 | False |
| 13 | True |
| 14 | False |
| 15 | False |
| 16 | False |
| 17 | True |
| 18 | True |
| 19 | True |
| 20 | False |

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🔍 Summary:

- True: Problems 4, 7, 8, 9, 13, 17, 18, 19 → 8 correct
- False: Others → 12 incorrect

> If this is a "true/false" worksheet, then the student should mark the ones above as True or False accordingly.

Let me know if you'd like a printable version or explanation for any specific problem!