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Solve the following fraction addition and subtraction problems:

Mathematics

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Step-by-step solution

19 steps

Here are the solutions to the fraction problems:

  1. : 27+37−27\frac{2}{7} + \frac{3}{7} - \frac{2}{7}
  1. Combine the numerators since the denominators are the same.

    $$
    \frac{2+3-2}{7}
    $$
    
  2. Perform the arithmetic in the numerator.

    $$
    \frac{5-2}{7} = \frac{3}{7}
    $$
    The simplified answer is $\boxed{\frac{3}{7}}$.
    

    2. : 29+49−79\frac{2}{9} + \frac{4}{9} - \frac{7}{9}

  3. Combine the numerators.

    $$
    \frac{2+4-7}{9}
    $$
    
  4. Perform the arithmetic in the numerator.

    $$
    \frac{6-7}{9} = \frac{-1}{9}
    $$
    The simplified answer is $\boxed{-\frac{1}{9}}$.
    

    3. : 712−512−312+812\frac{7}{12} - \frac{5}{12} - \frac{3}{12} + \frac{8}{12}

  5. Combine the numerators.

    $$
    \frac{7-5-3+8}{12}
    $$
    
  6. Perform the arithmetic in the numerator from left to right.

    $$
    \frac{2-3+8}{12} = \frac{-1+8}{12} = \frac{7}{12}
    $$
    The simplified answer is $\boxed{\frac{7}{12}}$.
    

    4. : 810+710−910\frac{8}{10} + \frac{7}{10} - \frac{9}{10}

  7. Combine the numerators.

    $$
    \frac{8+7-9}{10}
    $$
    
  8. Perform the arithmetic in the numerator.

    $$
    \frac{15-9}{10} = \frac{6}{10}
    $$
    
  9. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2.

    $$
    \frac{6 \div 2}{10 \div 2} = \frac{3}{5}
    $$
    The simplified answer is $\boxed{\frac{3}{5}}$.
    

    5. : 1215−715−515+1115\frac{12}{15} - \frac{7}{15} - \frac{5}{15} + \frac{11}{15}

  10. Combine the numerators.

    $$
    \frac{12-7-5+11}{15}
    $$
    
  11. Perform the arithmetic in the numerator from left to right.

    $$
    \frac{5-5+11}{15} = \frac{0+11}{15} = \frac{11}{15}
    $$
    The simplified answer is $\boxed{\frac{11}{15}}$.
    

    6. : 98−58−38+108\frac{9}{8} - \frac{5}{8} - \frac{3}{8} + \frac{10}{8}

  12. Combine the numerators.

    $$
    \frac{9-5-3+10}{8}
    $$
    
  13. Perform the arithmetic in the numerator from left to right.

    $$
    \frac{4-3+10}{8} = \frac{1+10}{8} = \frac{11}{8}
    $$
    The simplified answer is $\boxed{\frac{11}{8}}$.
    

    7. : 79−19\frac{7}{9} - \frac{1}{9}

  14. Combine the numerators.

    $$
    \frac{7-1}{9}
    $$
    
  15. Perform the arithmetic in the numerator.

    $$
    \frac{6}{9}
    $$
    
  16. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3.

    $$
    \frac{6 \div 3}{9 \div 3} = \frac{2}{3}
    $$
    The simplified answer is $\boxed{\frac{2}{3}}$.
    

    8. : 1015−815+715−415\frac{10}{15} - \frac{8}{15} + \frac{7}{15} - \frac{4}{15}

  17. Combine the numerators.

    $$
    \frac{10-8+7-4}{15}
    $$
    
  18. Perform the arithmetic in the numerator from left to right.

    $$
    \frac{2+7-4}{15} = \frac{9-4}{15} = \frac{5}{15}
    $$
    
  19. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5.

    $$
    \frac{5 \div 5}{15 \div 5} = \frac{1}{3}
    $$
    The simplified answer is $\boxed{\frac{1}{3}}$.
    
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