Order of Operations Practice Worksheet - Solve 20 equations using the correct mathematical order.

Let's solve each problem step by step using the order of operations (PEMDAS):

- Parentheses
- Exponents
- Multiplication / Division (from left to right)
- Addition / Subtraction (from left to right)

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① 50 ÷ (18 - 9) - 6 + 18

1. Parentheses: $18 - 9 = 9$
2. Division: $50 ÷ 9 ≈ 5.555...$ → But let’s keep it as a fraction or decimal? Let's compute exactly:
$50 ÷ 9 = \frac{50}{9}$
3. Then: $\frac{50}{9} - 6 + 18$

Convert 6 and 18 to ninths:
- $6 = \frac{54}{9}$, $18 = \frac{162}{9}$

So:
$\frac{50}{9} - \frac{54}{9} + \frac{162}{9} = \frac{50 - 54 + 162}{9} = \frac{158}{9} ≈ 17.56$

But wait — maybe we should use exact decimals or check if this is expected.

Alternatively, perhaps you want integer arithmetic? Let's recheck:

Wait — actually, 50 ÷ 9 is not an integer, but let's do it precisely:

$$
50 ÷ 9 = 5.\overline{5}
$$

Then:
$5.\overline{5} - 6 = -0.444...$, then $-0.444... + 18 = 17.555...$

So final answer: ≈ 17.56 or 158/9

But likely, the problem expects exact fractions or decimal approximation?

Let’s assume exact value:

✔ Answer: $ \frac{158}{9} $ or $ 17\frac{5}{9} $

But let's proceed with others and see if they are cleaner.

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② 48 × 2 + 9 - (48 ÷ 6)

1. Parentheses: $48 ÷ 6 = 8$
2. Multiplication: $48 × 2 = 96$
3. Now: $96 + 9 - 8 = 105 - 8 = 97$

✔ Answer: 97

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③ 36 - (14 × 2) + 22 ÷ 11

1. Parentheses: $14 × 2 = 28$
2. Division: $22 ÷ 11 = 2$
3. Now: $36 - 28 + 2 = 8 + 2 = 10$

✔ Answer: 10

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④ (28 - 4) + 9 × (8 ÷ 2)

1. Parentheses:
- $28 - 4 = 24$
- $8 ÷ 2 = 4$
2. Multiplication: $9 × 4 = 36$
3. Addition: $24 + 36 = 60$

✔ Answer: 60

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⑤ 74 - 20 ÷ 2 × (8 + 15)

1. Parentheses: $8 + 15 = 23$
2. Division: $20 ÷ 2 = 10$
3. Multiplication: $10 × 23 = 230$
4. Subtraction: $74 - 230 = -156$

✔ Answer: -156

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⑥ 36 + (12 - 8) × (20 - 3)

1. Parentheses:
- $12 - 8 = 4$
- $20 - 3 = 17$
2. Multiplication: $4 × 17 = 68$
3. Addition: $36 + 68 = 104$

✔ Answer: 104

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⑦ (30 + 5 × 3) - 48 ÷ 10

1. Inside parentheses:
- First: $5 × 3 = 15$
- Then: $30 + 15 = 45$
2. Division: $48 ÷ 10 = 4.8$
3. Subtraction: $45 - 4.8 = 40.2$

✔ Answer: 40.2 or $ \frac{201}{5} $

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⑧ 42 + 6 + 12 × (7 - 4)

1. Parentheses: $7 - 4 = 3$
2. Multiplication: $12 × 3 = 36$
3. Addition: $42 + 6 + 36 = 84$

✔ Answer: 84

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⑨ 25 ÷ 5 + 40 - 14 × 8

1. Division: $25 ÷ 5 = 5$
2. Multiplication: $14 × 8 = 112$
3. Now: $5 + 40 - 112 = 45 - 112 = -67$

✔ Answer: -67

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⑩ 80 - (20 + 4) × (24 ÷ 2)

1. Parentheses:
- $20 + 4 = 24$
- $24 ÷ 2 = 12$
2. Multiplication: $24 × 12 = 288$
3. Subtraction: $80 - 288 = -208$

✔ Answer: -208

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⑪ 25 × (10 - 5) ÷ (3 + 2)

1. Parentheses:
- $10 - 5 = 5$
- $3 + 2 = 5$
2. Multiplication: $25 × 5 = 125$
3. Division: $125 ÷ 5 = 25$

✔ Answer: 25

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⑫ 54 - 6 × (13 + 9 - 14)

1. Parentheses: $13 + 9 - 14 = 22 - 14 = 8$
2. Multiplication: $6 × 8 = 48$
3. Subtraction: $54 - 48 = 6$

✔ Answer: 6

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⑬ 63 ÷ (24 - 16) × 9 + 10

1. Parentheses: $24 - 16 = 8$
2. Division: $63 ÷ 8 = 7.875$
3. Multiplication: $7.875 × 9 = 70.875$
4. Addition: $70.875 + 10 = 80.875$

Or as fraction:
- $63 ÷ 8 = \frac{63}{8}$
- $\frac{63}{8} × 9 = \frac{567}{8}$
- $\frac{567}{8} + 10 = \frac{567}{8} + \frac{80}{8} = \frac{647}{8} = 80.875$

✔ Answer: 80.875 or $ \frac{647}{8} $

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⑭ 63 ÷ (18 × 2 - 16 - 11)

1. Inside parentheses:
- $18 × 2 = 36$
- $36 - 16 = 20$
- $20 - 11 = 9$
2. Division: $63 ÷ 9 = 7$

✔ Answer: 7

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⑮ (55 - 21) + (18 + 9) × 2

1. Parentheses:
- $55 - 21 = 34$
- $18 + 9 = 27$
2. Multiplication: $27 × 2 = 54$
3. Addition: $34 + 54 = 88$

✔ Answer: 88

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⑯ 32 + (8 × 4 - 24) ÷ 20

1. Parentheses:
- $8 × 4 = 32$
- $32 - 24 = 8$
2. Division: $8 ÷ 20 = 0.4$
3. Addition: $32 + 0.4 = 32.4$

Or $ \frac{162}{5} $

✔ Answer: 32.4

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⑰ 91 - 21 × 2 ÷ (34 - 10)

1. Parentheses: $34 - 10 = 24$
2. Multiplication: $21 × 2 = 42$
3. Division: $42 ÷ 24 = 1.75$
4. Subtraction: $91 - 1.75 = 89.25$

Or $ \frac{357}{4} $

✔ Answer: 89.25

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⑱ 49 - 7 + 10 × (15 - 9)

1. Parentheses: $15 - 9 = 6$
2. Multiplication: $10 × 6 = 60$
3. Now: $49 - 7 + 60 = 42 + 60 = 102$

✔ Answer: 102

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⑲ 45 ÷ (5 × 3) + 10 - 7

1. Parentheses: $5 × 3 = 15$
2. Division: $45 ÷ 15 = 3$
3. Then: $3 + 10 - 7 = 13 - 7 = 6$

✔ Answer: 6

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⑳ 27 - 3 × (9 - 6 ÷ 2)

1. Inside parentheses:
- Division first: $6 ÷ 2 = 3$
- Then: $9 - 3 = 6$
2. Multiplication: $3 × 6 = 18$
3. Subtraction: $27 - 18 = 9$

✔ Answer: 9

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✔ Final Answers:

| Problem | Answer |
|--------|---------------|
| ① | $ \frac{158}{9} $ or $ 17\frac{5}{9} $ |
| ② | 97 |
| ③ | 10 |
| ④ | 60 |
| ⑤ | -156 |
| ⑥ | 104 |
| ⑦ | 40.2 or $ \frac{201}{5} $ |
| ⑧ | 84 |
| ⑨ | -67 |
| ⑩ | -208 |
| ⑪ | 25 |
| ⑫ | 6 |
| ⑬ | 80.875 or $ \frac{647}{8} $ |
| ⑭ | 7 |
| ⑮ | 88 |
| ⑯ | 32.4 or $ \frac{162}{5} $ |
| ⑰ | 89.25 or $ \frac{357}{4} $ |
| ⑱ | 102 |
| ⑲ | 6 |
| ⑳ | 9 |

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