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Solve the following: 1) 7 2/5 + 8 4/5, 2) 2 5/9 + 7 1/3, 3) 9 3/5 + 5 3/4. Home Work: Solve the following: 1) 2 3/5 - 1 1/2, 2) 9 1/6 - 7 3/5, 3) 3 3/5 - 2 2/3

Mathematics

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Exercise

  1. To solve 725+8437\frac{2}{5} + 8\frac{4}{3}:
  1. Convert the mixed numbers to improper fractions.

    $$
    7\frac{2}{5} = \frac{7 \times 5 + 2}{5} = \frac{37}{5}
    $$
    $$
    8\frac{4}{3} = \frac{8 \times 3 + 4}{3} = \frac{28}{3}
    $$
    
  2. Find a common denominator, which is 15.

    $$
    \frac{37}{5} = \frac{37 \times 3}{5 \times 3} = \frac{111}{15}
    $$
    $$
    \frac{28}{3} = \frac{28 \times 5}{3 \times 5} = \frac{140}{15}
    $$
    
  3. Add the fractions.

    $$
    \frac{111}{15} + \frac{140}{15} = \frac{111 + 140}{15} = \frac{251}{15}
    $$
    
  4. Convert the improper fraction back to a mixed number.

    $$
    \frac{251}{15} = 16\frac{11}{15}
    $$
    The answer is $\boxed{\mathbf{16\frac{11}{15}}}$.
    

    2. To solve 259+7132\frac{5}{9} + 7\frac{1}{3}:

  5. Convert the mixed numbers to improper fractions.

    $$
    2\frac{5}{9} = \frac{2 \times 9 + 5}{9} = \frac{23}{9}
    $$
    $$
    7\frac{1}{3} = \frac{7 \times 3 + 1}{3} = \frac{22}{3}
    $$
    
  6. Find a common denominator, which is 9.

    $$
    \frac{22}{3} = \frac{22 \times 3}{3 \times 3} = \frac{66}{9}
    $$
    
  7. Add the fractions.

    $$
    \frac{23}{9} + \frac{66}{9} = \frac{23 + 66}{9} = \frac{89}{9}
    $$
    
  8. Convert the improper fraction back to a mixed number.

    $$
    \frac{89}{9} = 9\frac{8}{9}
    $$
    The answer is $\boxed{\mathbf{9\frac{8}{9}}}$.
    

    3. To solve 935+5349\frac{3}{5} + 5\frac{3}{4}:

  9. Convert the mixed numbers to improper fractions.

    $$
    9\frac{3}{5} = \frac{9 \times 5 + 3}{5} = \frac{48}{5}
    $$
    $$
    5\frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{23}{4}
    $$
    
  10. Find a common denominator, which is 20.

    $$
    \frac{48}{5} = \frac{48 \times 4}{5 \times 4} = \frac{192}{20}
    $$
    $$
    \frac{23}{4} = \frac{23 \times 5}{4 \times 5} = \frac{115}{20}
    $$
    
  11. Add the fractions.

    $$
    \frac{192}{20} + \frac{115}{20} = \frac{192 + 115}{20} = \frac{307}{20}
    $$
    
  12. Convert the improper fraction back to a mixed number.

    $$
    \frac{307}{20} = 15\frac{7}{20}
    $$
    The answer is $\boxed{\mathbf{15\frac{7}{20}}}$.
    

    Home Work

    1. To solve 235−1122\frac{3}{5} - 1\frac{1}{2}:
  13. Convert the mixed numbers to improper fractions.

    $$
    2\frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{13}{5}
    $$
    $$
    1\frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2}
    $$
    
  14. Find a common denominator, which is 10.

    $$
    \frac{13}{5} = \frac{13 \times 2}{5 \times 2} = \frac{26}{10}
    $$
    $$
    \frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10}
    $$
    
  15. Subtract the fractions.

    $$
    \frac{26}{10} - \frac{15}{10} = \frac{26 - 15}{10} = \frac{11}{10}
    $$
    
  16. Convert the improper fraction back to a mixed number.

    $$
    \frac{11}{10} = 1\frac{1}{10}
    $$
    The answer is $\boxed{\mathbf{1\frac{1}{10}}}$.
    

    2. To solve 936−7359\frac{3}{6} - 7\frac{3}{5}:

  17. Simplify the first mixed number and convert both to improper fractions.

    $$
    9\frac{3}{6} = 9\frac{1}{2} = \frac{9 \times 2 + 1}{2} = \frac{19}{2}
    $$
    $$
    7\frac{3}{5} = \frac{7 \times 5 + 3}{5} = \frac{38}{5}
    $$
    
  18. Find a common denominator, which is 10.

    $$
    \frac{19}{2} = \frac{19 \times 5}{2 \times 5} = \frac{95}{10}
    $$
    $$
    \frac{38}{5} = \frac{38 \times 2}{5 \times 2} = \frac{76}{10}
    $$
    
  19. Subtract the fractions.

    $$
    \frac{95}{10} - \frac{76}{10} = \frac{95 - 76}{10} = \frac{19}{10}
    $$
    
  20. Convert the improper fraction back to a mixed number.

    $$
    \frac{19}{10} = 1\frac{9}{10}
    $$
    The answer is $\boxed{\mathbf{1\frac{9}{10}}}$.
    

    3. To solve 335−2233\frac{3}{5} - 2\frac{2}{3}:

  21. Convert the mixed numbers to improper fractions.

    $$
    3\frac{3}{5} = \frac{3 \times 5 + 3}{5} = \frac{18}{5}
    $$
    $$
    2\frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{8}{3}
    $$
    
  22. Find a common denominator, which is 15.

    $$
    \frac{18}{5} = \frac{18 \times 3}{5 \times 3} = \frac{54}{15}
    $$
    
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