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Add the following fractions: a) 1/2 + 1/2, b) 2/5 + 1/5, c) 3/8 + 2/8, d) 2/7 + 3/7, e) 2/9 + 5/9, f) 3/10 + 2/10, g) 3/11 + 5/11 + 2/11

Mathematics

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Step-by-step solution

43 steps

Here are the solutions to the fraction problems:

1. Add the following fractions.

a)

  1. Add the numerators since the denominators are the same.

    12+12=1+12\frac{1}{2} + \frac{1}{2} = \frac{1+1}{2}
  2. Simplify the fraction.

    22=1\frac{2}{2} = 1

    1

    b)

  3. Add the numerators since the denominators are the same.

    25+15=2+15\frac{2}{5} + \frac{1}{5} = \frac{2+1}{5}
  4. Simplify the fraction.

    35\frac{3}{5}

    \frac{3}{5}

    c)

  5. Add the numerators since the denominators are the same.

    38+28=3+28\frac{3}{8} + \frac{2}{8} = \frac{3+2}{8}
  6. Simplify the fraction.

    58\frac{5}{8}

    \frac{5}{8}

    d)

  7. Add the numerators since the denominators are the same.

    27+37=2+37\frac{2}{7} + \frac{3}{7} = \frac{2+3}{7}
  8. Simplify the fraction.

    57\frac{5}{7}

    \frac{5}{7}

    e)

  9. Add the numerators since the denominators are the same.

    29+59=2+59\frac{2}{9} + \frac{5}{9} = \frac{2+5}{9}
  10. Simplify the fraction.

    79\frac{7}{9}

    \frac{7}{9}

    f)

  11. Add the numerators since the denominators are the same.

    310+210=3+210\frac{3}{10} + \frac{2}{10} = \frac{3+2}{10}
  12. Simplify the fraction.

    510=12\frac{5}{10} = \frac{1}{2}

    \frac{1}{2}

    g)

  13. Add the numerators since the denominators are the same.

    311+511+211=3+5+211\frac{3}{11} + \frac{5}{11} + \frac{2}{11} = \frac{3+5+2}{11}
  14. Simplify the fraction.

    1011\frac{10}{11}

    \frac{10}{11}

    h)

  15. Add the numerators since the denominators are the same.

    712+112+312=7+1+312\frac{7}{12} + \frac{1}{12} + \frac{3}{12} = \frac{7+1+3}{12}
  16. Simplify the fraction.

    1112\frac{11}{12}

    \frac{11}{12}

    2. Subtract the following fractions.

    a)

  17. Subtract the numerators since the denominators are the same.

    34−24=3−24\frac{3}{4} - \frac{2}{4} = \frac{3-2}{4}
  18. Simplify the fraction.

    14\frac{1}{4}

    \frac{1}{4}

    b)

  19. Subtract the numerators since the denominators are the same.

    45−35=4−35\frac{4}{5} - \frac{3}{5} = \frac{4-3}{5}
  20. Simplify the fraction.

    15\frac{1}{5}

    \frac{1}{5}

    c)

  21. Subtract the numerators since the denominators are the same.

    67−47=6−47\frac{6}{7} - \frac{4}{7} = \frac{6-4}{7}
  22. Simplify the fraction.

    27\frac{2}{7}

    \frac{2}{7}

    d)

  23. Subtract the numerators since the denominators are the same.

    78−18=7−18\frac{7}{8} - \frac{1}{8} = \frac{7-1}{8}
  24. Simplify the fraction.

    68=34\frac{6}{8} = \frac{3}{4}

    \frac{3}{4}

    e)

  25. Subtract the numerators since the denominators are the same.

    56−46=5−46\frac{5}{6} - \frac{4}{6} = \frac{5-4}{6}
  26. Simplify the fraction.

    16\frac{1}{6}

    \frac{1}{6}

    f)

  27. Subtract the numerators since the denominators are the same.

    1011−811=10−811\frac{10}{11} - \frac{8}{11} = \frac{10-8}{11}
  28. Simplify the fraction.

    211\frac{2}{11}

    \frac{2}{11}

    g)

  29. Subtract the numerators since the denominators are the same.

    49−19=4−19\frac{4}{9} - \frac{1}{9} = \frac{4-1}{9}
  30. Simplify the fraction.

    39=13\frac{3}{9} = \frac{1}{3}

    \frac{1}{3}

    h)

  31. Subtract the numerators since the denominators are the same.

    712−212=7−212\frac{7}{12} - \frac{2}{12} = \frac{7-2}{12}
  32. Simplify the fraction.

    512\frac{5}{12}

    \frac{5}{12}

    3. Insert the correct symbol (+ or -).

    a)

  33. Determine the operation that makes the equation true.

    25_15=35\frac{2}{5} \_ \frac{1}{5} = \frac{3}{5}

    Since 2+1=32+1=3, the symbol is ++.
    +

    b)

  34. Determine the operation that makes the equation true.

    49_29=29\frac{4}{9} \_ \frac{2}{9} = \frac{2}{9}

    Since 4−2=24-2=2, the symbol is −-.

    c)

  35. Determine the operation that makes the equation true.

    12_12=0\frac{1}{2} \_ \frac{1}{2} = 0

    Since 1−1=01-1=0, the symbol is −-.

    d)

  36. Determine the operation that makes the equation true.

    813_513=1313=1\frac{8}{13} \_ \frac{5}{13} = \frac{13}{13} = 1

    Since 8+5=138+5=13, the symbol is ++.
    +

    e)

  37. Determine the operation that makes the equation true.

    710_310=1\frac{7}{10} \_ \frac{3}{10} = 1

    Since 7+3=107+3=10, and 1010=1\frac{10}{10}=1, the symbol is ++.
    +

    4. What fraction of the pizza is eaten? What fraction is left?

    a) (This example is done for you in the image)
    Fraction eaten: 14\boxed{\frac{1}{4}}
    Fraction left: 34\boxed{\frac{3}{4}}

    b)

  38. Observe the pizza.

    It is divided into 4 equal parts, and 1 part is missing.
    Fraction eaten: 14\boxed{\frac{1}{4}}

  39. Calculate the fraction left.

    1−14=44−14=341 - \frac{1}{4} = \frac{4}{4} - \frac{1}{4} = \frac{3}{4}

    Fraction left: 34\boxed{\frac{3}{4}}

    c)

  40. Observe the pizza.

    It is divided into 2 equal parts, and 1 part is missing.
    Fraction eaten: 12\boxed{\frac{1}{2}}

  41. Calculate the fraction left.

    1−12=22−12=121 - \frac{1}{2} = \frac{2}{2} - \frac{1}{2} = \frac{1}{2}

    Fraction left: 12\boxed{\frac{1}{2}}

    d)

  42. Observe the pizza.

    It is divided into 2 equal parts, and 1 part is missing.
    Fraction eaten: 12\boxed{\frac{1}{2}}

  43. Calculate the fraction left.

    1−12=22−12=121 - \frac{1}{2} = \frac{2}{2} - \frac{1}{2} = \frac{1}{2}

    Fraction left: 12\boxed{\frac{1}{2}}

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