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iogann1982 [59]
3 years ago
14

Add and subtract rational numbers without common denominators. Show work! 1. 7/4 - 3/2 - 2/5 = 2. - 5/16 + 3/4 + 1/8 = 3. 3/4 -

1/3 - 7/12 = 4. 2/9 - 2/12 - 2/3 =
Mathematics
1 answer:
alukav5142 [94]3 years ago
6 0
\dfrac{7}{4}  -  \dfrac{3}{2} -  \dfrac{2}{5}

= \dfrac{7 \times 5}{4 \times 5}  -  \dfrac{3 \times 10}{2 \times 10} -  \dfrac{2 \times 4}{5 \times 4}

= \dfrac{35}{20}  -  \dfrac{30}{20} -  \dfrac{8}{20}

= \dfrac{35-30-8}{20}

= \dfrac{3}{20}

---------------------------------------------------------------

-\dfrac{5}{16}  + \dfrac{3}{4} + \dfrac{1}{8}

= -\dfrac{5}{16}  + \dfrac{3 \times 4}{4 \times 4} + \dfrac{1 \times 2}{8 \times 2}

= -\dfrac{5}{16}  + \dfrac{12}{16} + \dfrac{2}{16}

= \dfrac{-5+ 12 + 2}{16}

= \dfrac{9}{16}

---------------------------------------------------------------

\dfrac{3}{4} -  \dfrac{1}{3} - \dfrac{7}{12}

= \dfrac{3 \times 3}{4 \times 3} -  \dfrac{1 \times 4}{3 \times 4} - \dfrac{7}{12}

= \dfrac{9}{12} -  \dfrac{4}{12} - \dfrac{7}{12}

= \dfrac{9 - 4 - 7}{12}

= -\dfrac{2}{12}

= -\dfrac{1}{6}

---------------------------------------------------------------

\dfrac{2}{9}  -  \dfrac{2}{12} -  \dfrac{2}{3}

= \dfrac{2}{9}  -  \dfrac{1}{6} -  \dfrac{2}{3}

= \dfrac{2 \times 2}{9 \times 2}  -  \dfrac{1 \times 3}{6 \times 3} -  \dfrac{2 \times 6}{3 \times 6}

= \dfrac{4}{18}  -  \dfrac{3}{18} -  \dfrac{12}{18}

= \dfrac{4 - 3 - 12}{18}

= - \dfrac{11}{18}
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