Operations with Unlike Fractions Worksheets - 15 Worksheets Library - Free Printable

You’ve uploaded a worksheet titled “Operations with Unlike Denominators”, specifically asking to subtract improper fractions with different denominators.

To solve each problem, we follow these steps:

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✔ Step-by-Step Method:

1. Find the Least Common Denominator (LCD) of the two fractions.
2. Convert both fractions to equivalent fractions with the LCD.
3. Subtract the numerators, keeping the denominator the same.
4. Simplify the result (if possible) — reduce to lowest terms or convert to a mixed number if needed.

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Let’s solve all 18 problems one by one.

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🔢 Problem 1:

$\frac{9}{4} - \frac{15}{7}$

- LCD of 4 and 7 = 28
- $\frac{9}{4} = \frac{63}{28}$, $\frac{15}{7} = \frac{60}{28}$
- $\frac{63}{28} - \frac{60}{28} = \frac{3}{28}$

✔ Answer: $\frac{3}{28}$

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🔢 Problem 2:

$\frac{15}{6} - \frac{9}{4}$

- LCD of 6 and 4 = 12
- $\frac{15}{6} = \frac{30}{12}$, $\frac{9}{4} = \frac{27}{12}$
- $\frac{30}{12} - \frac{27}{12} = \frac{3}{12} = \frac{1}{4}$

✔ Answer: $\frac{1}{4}$

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🔢 Problem 3:

$\frac{20}{6} - \frac{9}{4}$

- LCD of 6 and 4 = 12
- $\frac{20}{6} = \frac{40}{12}$, $\frac{9}{4} = \frac{27}{12}$
- $\frac{40}{12} - \frac{27}{12} = \frac{13}{12} = 1\frac{1}{12}$

✔ Answer: $1\frac{1}{12}$

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🔢 Problem 4:

$\frac{7}{3} - \frac{15}{9}$

- Simplify $\frac{15}{9} = \frac{5}{3}$
- Now: $\frac{7}{3} - \frac{5}{3} = \frac{2}{3}$

✔ Answer: $\frac{2}{3}$

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🔢 Problem 5:

$\frac{25}{7} - \frac{15}{6}$

- LCD of 7 and 6 = 42
- $\frac{25}{7} = \frac{150}{42}$, $\frac{15}{6} = \frac{105}{42}$
- $\frac{150}{42} - \frac{105}{42} = \frac{45}{42} = \frac{15}{14} = 1\frac{1}{14}$

✔ Answer: $1\frac{1}{14}$

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🔢 Problem 6:

$\frac{18}{7} - \frac{21}{14}$

- $\frac{21}{14} = \frac{3}{2}$
- LCD of 7 and 2 = 14
- $\frac{18}{7} = \frac{36}{14}$, $\frac{3}{2} = \frac{21}{14}$
- $\frac{36}{14} - \frac{21}{14} = \frac{15}{14} = 1\frac{1}{14}$

✔ Answer: $1\frac{1}{14}$

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🔢 Problem 7:

$\frac{33}{9} - \frac{25}{18}$

- $\frac{33}{9} = \frac{11}{3}$
- LCD of 3 and 18 = 18
- $\frac{11}{3} = \frac{66}{18}$, $\frac{25}{18} = \frac{25}{18}$
- $\frac{66}{18} - \frac{25}{18} = \frac{41}{18} = 2\frac{5}{18}$

✔ Answer: $2\frac{5}{18}$

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🔢 Problem 8:

$\frac{7}{3} - \frac{15}{9}$

- $\frac{15}{9} = \frac{5}{3}$
- $\frac{7}{3} - \frac{5}{3} = \frac{2}{3}$

✔ Answer: $\frac{2}{3}$

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🔢 Problem 9:

$\frac{21}{15} - \frac{24}{18}$

- Simplify: $\frac{21}{15} = \frac{7}{5}$, $\frac{24}{18} = \frac{4}{3}$
- LCD of 5 and 3 = 15
- $\frac{7}{5} = \frac{21}{15}$, $\frac{4}{3} = \frac{20}{15}$
- $\frac{21}{15} - \frac{20}{15} = \frac{1}{15}$

✔ Answer: $\frac{1}{15}$

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🔢 Problem 10:

$\frac{30}{9} - \frac{18}{12}$

- Simplify: $\frac{30}{9} = \frac{10}{3}$, $\frac{18}{12} = \frac{3}{2}$
- LCD of 3 and 2 = 6
- $\frac{10}{3} = \frac{20}{6}$, $\frac{3}{2} = \frac{9}{6}$
- $\frac{20}{6} - \frac{9}{6} = \frac{11}{6} = 1\frac{5}{6}$

✔ Answer: $1\frac{5}{6}$

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🔢 Problem 11:

$\frac{9}{5} - \frac{14}{10}$

- $\frac{14}{10} = \frac{7}{5}$
- $\frac{9}{5} - \frac{7}{5} = \frac{2}{5}$

✔ Answer: $\frac{2}{5}$

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🔢 Problem 12:

$\frac{20}{9} - \frac{25}{15}$

- $\frac{25}{15} = \frac{5}{3}$
- LCD of 9 and 3 = 9
- $\frac{20}{9} - \frac{15}{9} = \frac{5}{9}$

✔ Answer: $\frac{5}{9}$

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🔢 Problem 13:

$\frac{16}{9} - \frac{25}{15}$

- $\frac{25}{15} = \frac{5}{3}$
- LCD of 9 and 3 = 9
- $\frac{16}{9} - \frac{15}{9} = \frac{1}{9}$

✔ Answer: $\frac{1}{9}$

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🔢 Problem 14:

$\frac{12}{7} - \frac{16}{14}$

- $\frac{16}{14} = \frac{8}{7}$
- $\frac{12}{7} - \frac{8}{7} = \frac{4}{7}$

✔ Answer: $\frac{4}{7}$

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🔢 Problem 15:

$\frac{14}{5} - \frac{36}{15}$

- $\frac{36}{15} = \frac{12}{5}$
- $\frac{14}{5} - \frac{12}{5} = \frac{2}{5}$

✔ Answer: $\frac{2}{5}$

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🔢 Problem 16:

$\frac{28}{10} - \frac{15}{9}$

- Simplify: $\frac{28}{10} = \frac{14}{5}$, $\frac{15}{9} = \frac{5}{3}$
- LCD of 5 and 3 = 15
- $\frac{14}{5} = \frac{42}{15}$, $\frac{5}{3} = \frac{25}{15}$
- $\frac{42}{15} - \frac{25}{15} = \frac{17}{15} = 1\frac{2}{15}$

✔ Answer: $1\frac{2}{15}$

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🔢 Problem 17:

$\frac{18}{5} - \frac{20}{15}$

- $\frac{20}{15} = \frac{4}{3}$
- LCD of 5 and 3 = 15
- $\frac{18}{5} = \frac{54}{15}$, $\frac{4}{3} = \frac{20}{15}$
- $\frac{54}{15} - \frac{20}{15} = \frac{34}{15} = 2\frac{4}{15}$

✔ Answer: $2\frac{4}{15}$

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🔢 Problem 18:

$\frac{36}{14} - \frac{5}{2}$

- $\frac{36}{14} = \frac{18}{7}$
- LCD of 7 and 2 = 14
- $\frac{18}{7} = \frac{36}{14}$, $\frac{5}{2} = \frac{35}{14}$
- $\frac{36}{14} - \frac{35}{14} = \frac{1}{14}$

✔ Answer: $\frac{1}{14}$

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## 📝 Final Answers Summary:

| Problem | Answer |
|---------|----------------|
| 1 | $\frac{3}{28}$ |
| 2 | $\frac{1}{4}$ |
| 3 | $1\frac{1}{12}$ |
| 4 | $\frac{2}{3}$ |
| 5 | $1\frac{1}{14}$ |
| 6 | $1\frac{1}{14}$ |
| 7 | $2\frac{5}{18}$ |
| 8 | $\frac{2}{3}$ |
| 9 | $\frac{1}{15}$ |
| 10 | $1\frac{5}{6}$ |
| 11 | $\frac{2}{5}$ |
| 12 | $\frac{5}{9}$ |
| 13 | $\frac{1}{9}$ |
| 14 | $\frac{4}{7}$ |
| 15 | $\frac{2}{5}$ |
| 16 | $1\frac{2}{15}$ |
| 17 | $2\frac{4}{15}$ |
| 18 | $\frac{1}{14}$ |

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✔ All problems solved!
This worksheet reinforces skills in finding LCDs, converting fractions, subtracting, and simplifying — essential for mastering operations with unlike denominators.

Let me know if you’d like a printable answer key or step-by-step visuals for any specific problem!