Simplify expressions using the PEMDAS rule with this math worksheet from Math Monks.

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. $ 20 \div [4 - (10 - 8)] $

- First, solve innermost parentheses:
$10 - 8 = 2$
- Now: $20 \div [4 - 2] = 20 \div 2 = 10$

✔ Answer: 10

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2. $ 9 \times (40 - 29) - (28 - 23) $

- Parentheses:
$40 - 29 = 11$, $28 - 23 = 5$
- Now: $9 \times 11 - 5 = 99 - 5 = 94$

✔ Answer: 94

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3. $ \{21 - [2 \times (7 + 2^2)]\} + 14 $

- Exponent first: $2^2 = 4$
- Then inside parentheses: $7 + 4 = 11$
- Multiplication: $2 \times 11 = 22$
- Now: $21 - 22 = -1$
- Then: $-1 + 14 = 13$

✔ Answer: 13

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4. $ 6^2 \div [(-7) - (-5) + 4]^2 \times 9 $

- Exponent: $6^2 = 36$
- Inside brackets: $(-7) - (-5) = -7 + 5 = -2$, then $-2 + 4 = 2$
- So: $[2]^2 = 4$
- Now: $36 \div 4 = 9$
- Then: $9 \times 9 = 81$

✔ Answer: 81

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5. $ 8 \times (11 - 3) - (4 \times 9 - 5) $

- Parentheses:
$11 - 3 = 8$, so $8 \times 8 = 64$
$4 \times 9 = 36$, $36 - 5 = 31$
- Now: $64 - 31 = 33$

✔ Answer: 33

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6. $ (12 - 7) \times (33 - 26) - 45 \div 5 $

- Parentheses:
$12 - 7 = 5$, $33 - 26 = 7$
- Multiplication: $5 \times 7 = 35$
- Division: $45 \div 5 = 9$
- Then: $35 - 9 = 26$

✔ Answer: 26

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7. $ 2 \times 6 \div (8 - 2) - 2^3 + 3 \times 4 $

- Parentheses: $8 - 2 = 6$
- Exponent: $2^3 = 8$
- Now expression: $2 \times 6 \div 6 - 8 + 3 \times 4$
- Left to right for multiplication/division:
$2 \times 6 = 12$, $12 \div 6 = 2$
$3 \times 4 = 12$
- Now: $2 - 8 + 12$
- Left to right: $2 - 8 = -6$, $-6 + 12 = 6$

✔ Answer: 6

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8. $ [5 + \{2^3 \times 4 - (1 + 2)^2\}] - 80 $

- Exponents:
$2^3 = 8$, $(1 + 2)^2 = 3^2 = 9$
- Inside braces: $8 \times 4 = 32$, $32 - 9 = 23$
- Now: $5 + 23 = 28$
- Then: $28 - 80 = -52$

✔ Answer: -52

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9. $ (66 \div 11) \times [26 + (27 \div 9) - 9] $

- $66 \div 11 = 6$
- $27 \div 9 = 3$
- Inside brackets: $26 + 3 - 9 = 20$
- Now: $6 \times 20 = 120$

✔ Answer: 120

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10. $ (4^2 \div 2^4) \times [5 + (16 \times 3)] $

- Exponents:
$4^2 = 16$, $2^4 = 16$
- Division: $16 \div 16 = 1$
- Inside brackets: $16 \times 3 = 48$, $5 + 48 = 53$
- Now: $1 \times 53 = 53$

✔ Answer: 53

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✔ Final Answers:

1. 10
2. 94
3. 13
4. 81
5. 33
6. 26
7. 6
8. -52
9. 120
10. 53

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