Operations with Rational Numbers Worksheets - Free Printable

Let's solve each problem step by step, following the rules for adding and subtracting positive and negative mixed numbers. We’ll convert mixed numbers to improper fractions when needed, perform operations, simplify, and convert back to mixed numbers if necessary.

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1. $ 2\frac{2}{9} + (-3\frac{7}{9}) $

Convert both to improper fractions:
- $ 2\frac{2}{9} = \frac{20}{9} $
- $ -3\frac{7}{9} = -\frac{34}{9} $

Add:
$ \frac{20}{9} + (-\frac{34}{9}) = \frac{-14}{9} $

Convert to mixed number:
$ -\frac{14}{9} = -1\frac{5}{9} $

✔ Answer: $ -1\frac{5}{9} $

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2. $ 7\frac{4}{5} - 2\frac{3}{5} $

Subtract whole numbers and fractions:
- Whole: $ 7 - 2 = 5 $
- Fraction: $ \frac{4}{5} - \frac{3}{5} = \frac{1}{5} $

✔ Answer: $ 5\frac{1}{5} $

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3. $ 5\frac{1}{6} + 1\frac{1}{6} $

Add whole numbers and fractions:
- Whole: $ 5 + 1 = 6 $
- Fraction: $ \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3} $

✔ Answer: $ 6\frac{1}{3} $

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4. $ 3\frac{3}{10} - (-4\frac{1}{10}) $

Subtracting a negative is adding:
$ 3\frac{3}{10} + 4\frac{1}{10} $

Add:
- Whole: $ 3 + 4 = 7 $
- Fraction: $ \frac{3}{10} + \frac{1}{10} = \frac{4}{10} = \frac{2}{5} $

✔ Answer: $ 7\frac{2}{5} $

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5. $ -4\frac{7}{8} + 3\frac{5}{8} $

Convert to improper fractions:
- $ -4\frac{7}{8} = -\frac{39}{8} $
- $ 3\frac{5}{8} = \frac{29}{8} $

Add:
$ -\frac{39}{8} + \frac{29}{8} = -\frac{10}{8} = -\frac{5}{4} $

Convert: $ -\frac{5}{4} = -1\frac{1}{4} $

✔ Answer: $ -1\frac{1}{4} $

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6. $ -2\frac{5}{12} - 5\frac{1}{12} $

Subtract:
- Whole: $ -2 - 5 = -7 $
- Fraction: $ \frac{5}{12} - \frac{1}{12} = \frac{4}{12} = \frac{1}{3} $

But since it's negative:
$ -7 + \frac{1}{3} = -6\frac{2}{3} $? Wait — let's do this carefully.

Actually:
$ -2\frac{5}{12} - 5\frac{1}{12} = -(2\frac{5}{12} + 5\frac{1}{12}) $

Add:
- Whole: $ 2 + 5 = 7 $
- Fraction: $ \frac{5}{12} + \frac{1}{12} = \frac{6}{12} = \frac{1}{2} $

So: $ -7\frac{1}{2} $

✔ Answer: $ -7\frac{1}{2} $

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7. $ -3\frac{1}{4} + (-6\frac{1}{2}) $

Add two negatives:
$ -3\frac{1}{4} - 6\frac{1}{2} $

Convert to improper:
- $ -3\frac{1}{4} = -\frac{13}{4} $
- $ -6\frac{1}{2} = -\frac{13}{2} = -\frac{26}{4} $

Add:
$ -\frac{13}{4} - \frac{26}{4} = -\frac{39}{4} $

Convert: $ -\frac{39}{4} = -9\frac{3}{4} $

✔ Answer: $ -9\frac{3}{4} $

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8. $ 4\frac{2}{3} + (-1\frac{5}{6}) $

Convert to improper:
- $ 4\frac{2}{3} = \frac{14}{3} = \frac{28}{6} $
- $ -1\frac{5}{6} = -\frac{11}{6} $

Add:
$ \frac{28}{6} - \frac{11}{6} = \frac{17}{6} $

Convert: $ \frac{17}{6} = 2\frac{5}{6} $

✔ Answer: $ 2\frac{5}{6} $

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9. $ -5\frac{3}{4} - (-2\frac{3}{8}) $

Subtracting a negative is adding:
$ -5\frac{3}{4} + 2\frac{3}{8} $

Convert to improper:
- $ -5\frac{3}{4} = -\frac{23}{4} = -\frac{46}{8} $
- $ 2\frac{3}{8} = \frac{19}{8} $

Add:
$ -\frac{46}{8} + \frac{19}{8} = -\frac{27}{8} $

Convert: $ -\frac{27}{8} = -3\frac{3}{8} $

✔ Answer: $ -3\frac{3}{8} $

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10. $ -6\frac{8}{9} - (-3\frac{2}{3}) $

Subtracting negative → add:
$ -6\frac{8}{9} + 3\frac{2}{3} $

Convert:
- $ -6\frac{8}{9} = -\frac{62}{9} $
- $ 3\frac{2}{3} = \frac{11}{3} = \frac{33}{9} $

Add:
$ -\frac{62}{9} + \frac{33}{9} = -\frac{29}{9} $

Convert: $ -\frac{29}{9} = -3\frac{2}{9} $

✔ Answer: $ -3\frac{2}{9} $

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11. $ 2\frac{3}{5} - (-2\frac{3}{4}) $

Subtracting negative → add:
$ 2\frac{3}{5} + 2\frac{3}{4} $

Convert:
- $ 2\frac{3}{5} = \frac{13}{5} $
- $ 2\frac{3}{4} = \frac{11}{4} $

LCM of 5 and 4 is 20:
- $ \frac{13}{5} = \frac{52}{20} $
- $ \frac{11}{4} = \frac{55}{20} $

Add: $ \frac{52}{20} + \frac{55}{20} = \frac{107}{20} $

Convert: $ \frac{107}{20} = 5\frac{7}{20} $

✔ Answer: $ 5\frac{7}{20} $

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12. $ -3\frac{1}{6} + (-4\frac{1}{4}) $

Add two negatives:
$ -3\frac{1}{6} - 4\frac{1}{4} $

Convert:
- $ -3\frac{1}{6} = -\frac{19}{6} $
- $ -4\frac{1}{4} = -\frac{17}{4} $

LCM of 6 and 4 is 12:
- $ -\frac{19}{6} = -\frac{38}{12} $
- $ -\frac{17}{4} = -\frac{51}{12} $

Add: $ -\frac{38}{12} - \frac{51}{12} = -\frac{89}{12} $

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

✔ Answer: $ -7\frac{5}{12} $

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13. $ 4\frac{7}{8} + (-2\frac{1}{6}) $

Convert:
- $ 4\frac{7}{8} = \frac{39}{8} $
- $ -2\frac{1}{6} = -\frac{13}{6} $

LCM of 8 and 6 is 24:
- $ \frac{39}{8} = \frac{117}{24} $
- $ -\frac{13}{6} = -\frac{52}{24} $

Add: $ \frac{117}{24} - \frac{52}{24} = \frac{65}{24} $

Convert: $ \frac{65}{24} = 2\frac{17}{24} $

✔ Answer: $ 2\frac{17}{24} $

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14. $ -8\frac{1}{2} + 3\frac{2}{3} $

Convert:
- $ -8\frac{1}{2} = -\frac{17}{2} $
- $ 3\frac{2}{3} = \frac{11}{3} $

LCM of 2 and 3 is 6:
- $ -\frac{17}{2} = -\frac{51}{6} $
- $ \frac{11}{3} = \frac{22}{6} $

Add: $ -\frac{51}{6} + \frac{22}{6} = -\frac{29}{6} $

Convert: $ -\frac{29}{6} = -4\frac{5}{6} $

✔ Answer: $ -4\frac{5}{6} $

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15. $ -7\frac{3}{4} + 9\frac{3}{10} $

Convert:
- $ -7\frac{3}{4} = -\frac{31}{4} $
- $ 9\frac{3}{10} = \frac{93}{10} $

LCM of 4 and 10 is 20:
- $ -\frac{31}{4} = -\frac{155}{20} $
- $ \frac{93}{10} = \frac{186}{20} $

Add: $ -\frac{155}{20} + \frac{186}{20} = \frac{31}{20} $

Convert: $ \frac{31}{20} = 1\frac{11}{20} $

✔ Answer: $ 1\frac{11}{20} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ -1\frac{5}{9} $ |
| 2 | $ 5\frac{1}{5} $ |
| 3 | $ 6\frac{1}{3} $ |
| 4 | $ 7\frac{2}{5} $ |
| 5 | $ -1\frac{1}{4} $ |
| 6 | $ -7\frac{1}{2} $ |
| 7 | $ -9\frac{3}{4} $ |
| 8 | $ 2\frac{5}{6} $ |
| 9 | $ -3\frac{3}{8} $ |
| 10 | $ -3\frac{2}{9} $ |
| 11 | $ 5\frac{7}{20} $ |
| 12 | $ -7\frac{5}{12} $ |
| 13 | $ 2\frac{17}{24} $ |
| 14 | $ -4\frac{5}{6} $ |
| 15 | $ 1\frac{11}{20} $ |

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