PEMDAS Worksheet: Simplify using the PEMDAS rule.

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

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Problem 1:

20 ÷ {4 – (10 – 8)}

Step 1: Innermost parentheses → (10 – 8) = 2
→ 20 ÷ {4 – 2}

Step 2: Braces → 4 – 2 = 2
→ 20 ÷ 2

Step 3: Division → 20 ÷ 2 = 10

✔ Final Answer for #1: 10

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Problem 2:

9 × (40 – 29) – (28 – 23)

Step 1: Parentheses → (40 – 29) = 11; (28 – 23) = 5
→ 9 × 11 – 5

Step 2: Multiplication → 9 × 11 = 99
→ 99 – 5

Step 3: Subtraction → 99 – 5 = 94

✔ Final Answer for #2: 94

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Problem 3:

{21 – [2 × (7 + 2²)]} + 14

Step 1: Exponent inside innermost → 2² = 4
→ {21 – [2 × (7 + 4)]} + 14

Step 2: Parentheses → 7 + 4 = 11
→ {21 – [2 × 11]} + 14

Step 3: Brackets → 2 × 11 = 22
→ {21 – 22} + 14

Step 4: Braces → 21 – 22 = -1
→ -1 + 14

Step 5: Addition → -1 + 14 = 13

✔ Final Answer for #3: 13

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Problem 4:

6² ÷ [(–7) – (–5) + 4]² × 9

Step 1: Exponents first → 6² = 36
Also, handle inside brackets: (–7) – (–5) = –7 + 5 = –2
Then: –2 + 4 = 2
So now: 36 ÷ [2]² × 9

Step 2: Exponent on bracket → 2² = 4
→ 36 ÷ 4 × 9

Step 3: Left to right: 36 ÷ 4 = 9
→ 9 × 9 = 81

✔ Final Answer for #4: 81

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Problem 5:

8 × (11 – 3) – (4 × 9 – 5)

Step 1: Parentheses → (11 – 3) = 8; inside second: 4 × 9 = 36 → 36 – 5 = 31
→ 8 × 8 – 31

Step 2: Multiplication → 8 × 8 = 64
→ 64 – 31

Step 3: Subtraction → 64 – 31 = 33

✔ Final Answer for #5: 33

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Problem 6:

(12 – 7) × (33 – 26) – 45 ÷ 5

Step 1: Parentheses → (12 – 7) = 5; (33 – 26) = 7
→ 5 × 7 – 45 ÷ 5

Step 2: Multiplication and Division left to right → 5 × 7 = 35; 45 ÷ 5 = 9
→ 35 – 9

Step 3: Subtraction → 35 – 9 = 26

✔ Final Answer for #6: 26

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Problem 7:

2 × 6 ÷ (8 – 2) – 2³ + 3 × 4

Step 1: Parentheses → (8 – 2) = 6
Exponent → 2³ = 8
→ 2 × 6 ÷ 6 – 8 + 3 × 4

Step 2: Multiplication/Division left to right:
2 × 6 = 12 → 12 ÷ 6 = 2
3 × 4 = 12
Now: 2 – 8 + 12

Step 3: Addition/Subtraction left to right:
2 – 8 = -6 → -6 + 12 = 6

✔ Final Answer for #7: 6

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Problem 8:

{5 + [2³ × 4 – (1 + 2)²]} – 80

Step 1: Innermost parentheses → (1 + 2) = 3 → 3² = 9
Exponent → 2³ = 8
→ {5 + [8 × 4 – 9]} – 80

Step 2: Brackets → 8 × 4 = 32 → 32 – 9 = 23
→ {5 + 23} – 80

Step 3: Braces → 5 + 23 = 28
→ 28 – 80 = -52

✔ Final Answer for #8: -52

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Problem 9:

(66 ÷ 11) × [26 + (27 ÷ 9) – 9]

Step 1: Parentheses → 66 ÷ 11 = 6; 27 ÷ 9 = 3
→ 6 × [26 + 3 – 9]

Step 2: Inside brackets → 26 + 3 = 29 → 29 – 9 = 20
→ 6 × 20

Step 3: Multiplication → 6 × 20 = 120

✔ Final Answer for #9: 120

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Problem 10:

(4² ÷ 2⁴) × [5 + (16 × 3)]

Step 1: Exponents → 4² = 16; 2⁴ = 16
Parentheses → 16 × 3 = 48
→ (16 ÷ 16) × [5 + 48]

Step 2: Division → 16 ÷ 16 = 1
Brackets → 5 + 48 = 53
→ 1 × 53

Step 3: Multiplication → 1 × 53 = 53

✔ Final Answer for #10: 53

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