Q:

# 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 =

Accepted Solution

A:
$$\dfrac{7}{4} - \dfrac{3}{2} - \dfrac{2}{5}$$

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

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

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

$$= \dfrac{3}{20}$$

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

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

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

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

$$= \dfrac{9}{16}$$

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

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

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

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

$$= -\dfrac{2}{12}$$

$$= -\dfrac{1}{6}$$

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

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

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

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

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

$$= - \dfrac{11}{18}$$