Evaluate expressions using the PEMDAS rule with this math worksheet.

Let's solve each problem step by step using the PEMDAS rule:

> Parentheses
> Exponents
> Multiplication and Division (from left to right)
> Addition and Subtraction (from left to right)

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1) $ 35 \div 7 + 2^2 $

- Exponent: $ 2^2 = 4 $
- Division: $ 35 \div 7 = 5 $
- Addition: $ 5 + 4 = 9 $

✔ Answer: 9

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2) $ 2.5 \times (13 - 5) $

- Parentheses: $ 13 - 5 = 8 $
- Multiplication: $ 2.5 \times 8 = 20 $

✔ Answer: 20

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3) $ 45 \div (6 + 3) \times 3 - 6 \div 2 $

- Parentheses: $ 6 + 3 = 9 $
- Division: $ 45 \div 9 = 5 $
- Multiplication: $ 5 \times 3 = 15 $
- Division: $ 6 \div 2 = 3 $
- Subtraction: $ 15 - 3 = 12 $

✔ Answer: 12

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4) $ 48 - 3(16 + 15 \div 5 \times 3 - 2 \times 3) + 8 $

We simplify inside the parentheses first, following PEMDAS.

Inside the parentheses:
- $ 15 \div 5 = 3 $
- $ 3 \times 3 = 9 $
- $ 2 \times 3 = 6 $
- Now: $ 16 + 9 - 6 = 19 $

So now:
$ 48 - 3(19) + 8 $

Now:
- Multiplication: $ 3 \times 19 = 57 $
- Expression becomes: $ 48 - 57 + 8 $
- Left to right: $ 48 - 57 = -9 $, then $ -9 + 8 = -1 $

✔ Answer: -1

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5) $ 7 + [(25 - 1) \div (3^2 - 3)] - 3 $

- Inside brackets:
- $ 25 - 1 = 24 $
- $ 3^2 = 9 $, so $ 9 - 3 = 6 $
- $ 24 \div 6 = 4 $
- Now: $ 7 + 4 - 3 $
- $ 7 + 4 = 11 $, $ 11 - 3 = 8 $

✔ Answer: 8

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6) $ (63 \div 7) + 22 \times (9 + 1) \div 11 $

- $ 63 \div 7 = 9 $
- $ 9 + 1 = 10 $
- $ 22 \times 10 = 220 $
- $ 220 \div 11 = 20 $
- Now: $ 9 + 20 = 29 $

✔ Answer: 29

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7) $ (146 - 2) \div (3 \times 4) - 15 + 9 $

- $ 146 - 2 = 144 $
- $ 3 \times 4 = 12 $
- $ 144 \div 12 = 12 $
- Now: $ 12 - 15 + 9 $
- $ 12 - 15 = -3 $, $ -3 + 9 = 6 $

✔ Answer: 6

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8) $ 78 \div 13 + (24 - 12) \times 5 $

- $ 78 \div 13 = 6 $
- $ 24 - 12 = 12 $
- $ 12 \times 5 = 60 $
- $ 6 + 60 = 66 $

✔ Answer: 66

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9) $ (24 + 1) \times 2 \div (13 - 3) - 19 $

- $ 24 + 1 = 25 $
- $ 13 - 3 = 10 $
- $ 25 \times 2 = 50 $
- $ 50 \div 10 = 5 $
- $ 5 - 19 = -14 $

✔ Answer: -14

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10) $ [12 - 36 \div (4^2 - 4) \div 3 + 2] \times 5 $

Work inside the brackets:

- $ 4^2 = 16 $
- $ 16 - 4 = 12 $
- $ 36 \div 12 = 3 $
- $ 3 \div 3 = 1 $
- Now: $ 12 - 1 + 2 = 13 $
- Multiply by 5: $ 13 \times 5 = 65 $

✔ Answer: 65

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✔ Final Answers:

1) 9
2) 20
3) 12
4) -1
5) 8
6) 29
7) 6
8) 66
9) -14
10) 65

Let me know if you'd like this in a printable format or with more explanation on any step!