Find the difference in these mixed number subtraction problems.

Let's solve each of these mixed number subtraction problems step by step. We'll convert the mixed numbers to improper fractions, find a common denominator if needed, subtract, and then simplify.

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1. $ 16 \frac{3}{9} - 10 \frac{2}{5} $

First, simplify $ \frac{3}{9} = \frac{1}{3} $, so:
$$
16 \frac{1}{3} - 10 \frac{2}{5}
$$

Convert to improper fractions:
- $ 16 \frac{1}{3} = \frac{49}{3} $
- $ 10 \frac{2}{5} = \frac{52}{5} $

Find common denominator: LCM of 3 and 5 is 15.
$$
\frac{49}{3} = \frac{245}{15}, \quad \frac{52}{5} = \frac{156}{15}
$$
$$
\frac{245}{15} - \frac{156}{15} = \frac{89}{15} = 5 \frac{14}{15}
$$

✔ Answer: $ \boxed{5 \frac{14}{15}} $

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2. $ 7 \frac{5}{12} - 2 \frac{1}{2} $

Convert:
- $ 7 \frac{5}{12} = \frac{89}{12} $
- $ 2 \frac{1}{2} = \frac{5}{2} = \frac{30}{12} $

$$
\frac{89}{12} - \frac{30}{12} = \frac{59}{12} = 4 \frac{11}{12}
$$

✔ Answer: $ \boxed{4 \frac{11}{12}} $

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3. $ 8 \frac{9}{10} - 3 \frac{2}{3} $

Convert:
- $ 8 \frac{9}{10} = \frac{89}{10} $
- $ 3 \frac{2}{3} = \frac{11}{3} $

LCM of 10 and 3 is 30:
- $ \frac{89}{10} = \frac{267}{30} $
- $ \frac{11}{3} = \frac{110}{30} $

$$
\frac{267}{30} - \frac{110}{30} = \frac{157}{30} = 5 \frac{7}{30}
$$

✔ Answer: $ \boxed{5 \frac{7}{30}} $

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4. $ 19 \frac{2}{3} - 11 \frac{5}{8} $

Convert:
- $ 19 \frac{2}{3} = \frac{59}{3} $
- $ 11 \frac{5}{8} = \frac{93}{8} $

LCM of 3 and 8 is 24:
- $ \frac{59}{3} = \frac{472}{24} $
- $ \frac{93}{8} = \frac{279}{24} $

$$
\frac{472}{24} - \frac{279}{24} = \frac{193}{24} = 8 \frac{1}{24}
$$

✔ Answer: $ \boxed{8 \frac{1}{24}} $

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5. $ 13 \frac{1}{8} - 12 \frac{10}{12} $

Simplify $ \frac{10}{12} = \frac{5}{6} $, so:
$$
13 \frac{1}{8} - 12 \frac{5}{6}
$$

Convert:
- $ 13 \frac{1}{8} = \frac{105}{8} $
- $ 12 \frac{5}{6} = \frac{77}{6} $

LCM of 8 and 6 is 24:
- $ \frac{105}{8} = \frac{315}{24} $
- $ \frac{77}{6} = \frac{308}{24} $

$$
\frac{315}{24} - \frac{308}{24} = \frac{7}{24}
$$

✔ Answer: $ \boxed{\frac{7}{24}} $

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6. $ 18 \frac{1}{2} - 17 \frac{2}{8} $

Simplify $ \frac{2}{8} = \frac{1}{4} $, so:
$$
18 \frac{1}{2} - 17 \frac{1}{4}
$$

Convert:
- $ 18 \frac{1}{2} = \frac{37}{2} $
- $ 17 \frac{1}{4} = \frac{69}{4} $

LCM of 2 and 4 is 4:
- $ \frac{37}{2} = \frac{74}{4} $
- $ \frac{69}{4} = \frac{69}{4} $

$$
\frac{74}{4} - \frac{69}{4} = \frac{5}{4} = 1 \frac{1}{4}
$$

✔ Answer: $ \boxed{1 \frac{1}{4}} $

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7. $ 14 \frac{4}{10} - 13 \frac{1}{3} $

Simplify $ \frac{4}{10} = \frac{2}{5} $, so:
$$
14 \frac{2}{5} - 13 \frac{1}{3}
$$

Convert:
- $ 14 \frac{2}{5} = \frac{72}{5} $
- $ 13 \frac{1}{3} = \frac{40}{3} $

LCM of 5 and 3 is 15:
- $ \frac{72}{5} = \frac{216}{15} $
- $ \frac{40}{3} = \frac{200}{15} $

$$
\frac{216}{15} - \frac{200}{15} = \frac{16}{15} = 1 \frac{1}{15}
$$

✔ Answer: $ \boxed{1 \frac{1}{15}} $

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8. $ 19 \frac{7}{12} - 19 \frac{1}{5} $

Same whole number, subtract fractions:
$$
\frac{7}{12} - \frac{1}{5}
$$

LCM of 12 and 5 is 60:
- $ \frac{7}{12} = \frac{35}{60} $
- $ \frac{1}{5} = \frac{12}{60} $

$$
\frac{35}{60} - \frac{12}{60} = \frac{23}{60}
$$

✔ Answer: $ \boxed{\frac{23}{60}} $

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9. $ 20 \frac{3}{4} - 18 \frac{2}{3} $

Convert:
- $ 20 \frac{3}{4} = \frac{83}{4} $
- $ 18 \frac{2}{3} = \frac{56}{3} $

LCM of 4 and 3 is 12:
- $ \frac{83}{4} = \frac{249}{12} $
- $ \frac{56}{3} = \frac{224}{12} $

$$
\frac{249}{12} - \frac{224}{12} = \frac{25}{12} = 2 \frac{1}{12}
$$

✔ Answer: $ \boxed{2 \frac{1}{12}} $

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10. $ 19 \frac{7}{10} - 13 \frac{4}{10} $

Same denominator:
$$
(19 - 13) + \left( \frac{7}{10} - \frac{4}{10} \right) = 6 + \frac{3}{10} = 6 \frac{3}{10}
$$

✔ Answer: $ \boxed{6 \frac{3}{10}} $

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11. $ 17 \frac{5}{6} - 1 \frac{3}{5} $

Convert:
- $ 17 \frac{5}{6} = \frac{107}{6} $
- $ 1 \frac{3}{5} = \frac{8}{5} $

LCM of 6 and 5 is 30:
- $ \frac{107}{6} = \frac{535}{30} $
- $ \frac{8}{5} = \frac{48}{30} $

$$
\frac{535}{30} - \frac{48}{30} = \frac{487}{30} = 16 \frac{7}{30}
$$

✔ Answer: $ \boxed{16 \frac{7}{30}} $

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12. $ 9 \frac{1}{5} - 5 \frac{4}{6} $

Simplify $ \frac{4}{6} = \frac{2}{3} $, so:
$$
9 \frac{1}{5} - 5 \frac{2}{3}
$$

Convert:
- $ 9 \frac{1}{5} = \frac{46}{5} $
- $ 5 \frac{2}{3} = \frac{17}{3} $

LCM of 5 and 3 is 15:
- $ \frac{46}{5} = \frac{138}{15} $
- $ \frac{17}{3} = \frac{85}{15} $

$$
\frac{138}{15} - \frac{85}{15} = \frac{53}{15} = 3 \frac{8}{15}
$$

✔ Answer: $ \boxed{3 \frac{8}{15}} $

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✔ Final Answers:

1. $ 5 \frac{14}{15} $
2. $ 4 \frac{11}{12} $
3. $ 5 \frac{7}{30} $
4. $ 8 \frac{1}{24} $
5. $ \frac{7}{24} $
6. $ 1 \frac{1}{4} $
7. $ 1 \frac{1}{15} $
8. $ \frac{23}{60} $
9. $ 2 \frac{1}{12} $
10. $ 6 \frac{3}{10} $
11. $ 16 \frac{7}{30} $
12. $ 3 \frac{8}{15} $

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