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Add the following rational numbers: a) -2/5 and 4/5, b) -7/3 and 1/3, c) -11/8 and 5/8, d) -6/11 and -4/11, e) 5/6 and -1/6, f) [omitted]

Mathematics

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Step-by-step solution

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Here are the solutions to your addition problems:

1. Add the following rational numbers:

a) −25\frac{-2}{5} and 45\frac{4}{5}

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

    −25+45=−2+45\frac{-2}{5} + \frac{4}{5} = \frac{-2+4}{5}
  2. Simplify the numerator.

    =25= \frac{2}{5}

    The sum is 25\boxed{\frac{2}{5}}.

    b) −73\frac{-7}{3} and 13\frac{1}{3}

  3. Add the numerators.

    −73+13=−7+13\frac{-7}{3} + \frac{1}{3} = \frac{-7+1}{3}
  4. Simplify the numerator.

    =−63= \frac{-6}{3}
  5. Simplify the fraction.

    =−2= -2

    The sum is −2\boxed{-2}.

    c) −118\frac{-11}{8} and 58\frac{5}{8}

  6. Add the numerators.

    −118+58=−11+58\frac{-11}{8} + \frac{5}{8} = \frac{-11+5}{8}
  7. Simplify the numerator.

    =−68= \frac{-6}{8}
  8. Simplify the fraction by dividing the numerator and denominator by 2.

    =−34= \frac{-3}{4}

    The sum is −34\boxed{\frac{-3}{4}}.

    d) −611\frac{-6}{11} and −411\frac{-4}{11}

  9. Add the numerators.

    −611+−411=−6−411\frac{-6}{11} + \frac{-4}{11} = \frac{-6-4}{11}
  10. Simplify the numerator.

    =−1011= \frac{-10}{11}

    The sum is −1011\boxed{\frac{-10}{11}}.

    e) 56\frac{5}{6} and −16\frac{-1}{6}

  11. Add the numerators.

    56+−16=5−16\frac{5}{6} + \frac{-1}{6} = \frac{5-1}{6}
  12. Simplify the numerator.

    =46= \frac{4}{6}
  13. Simplify the fraction by dividing the numerator and denominator by 2.

    =23= \frac{2}{3}

    The sum is 23\boxed{\frac{2}{3}}.

    f) −1715\frac{-17}{15} and −115\frac{-1}{15}

  14. Add the numerators.

    −1715+−115=−17−115\frac{-17}{15} + \frac{-1}{15} = \frac{-17-1}{15}
  15. Simplify the numerator.

    =−1815= \frac{-18}{15}
  16. Simplify the fraction by dividing the numerator and denominator by 3.

    =−65= \frac{-6}{5}

    The sum is −65\boxed{\frac{-6}{5}}.

    2. Add the following rational numbers:

    a) 34\frac{3}{4} and −35\frac{-3}{5}

  17. Find the least common multiple (LCM) of the denominators 4 and 5, which is 20.

  18. Convert the fractions to equivalent fractions with the common denominator.

    34+−35=3×54×5+−3×45×4=1520+−1220\frac{3}{4} + \frac{-3}{5} = \frac{3 \times 5}{4 \times 5} + \frac{-3 \times 4}{5 \times 4} = \frac{15}{20} + \frac{-12}{20}
  19. Add the numerators.

    =15−1220= \frac{15-12}{20}
  20. Simplify the numerator.

    =320= \frac{3}{20}

    The sum is 320\boxed{\frac{3}{20}}.

    b) 58\frac{5}{8} and −712\frac{-7}{12}

  21. Find the LCM of 8

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