Question

Answer 1

a) \(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}\)

\(=\dfrac{3}{6}+\dfrac{2}{6}+\dfrac{1}{6}\)

\(=1\)

b) \(\dfrac{4}{7}+\dfrac{3}{4}+\dfrac{2}{7}\)

\(=\left(\dfrac{4}{7}+\dfrac{2}{7}\right)+\dfrac{3}{4}\)

\(=\dfrac{6}{7}+\dfrac{3}{4}\)

\(=\dfrac{24}{28}+\dfrac{21}{28}\)

\(=\dfrac{45}{28}\)

c) \(\dfrac{1}{6}+\dfrac{5}{24}+\dfrac{2}{3}\)

\(=\dfrac{4}{24}+\dfrac{5}{24}+\dfrac{16}{24}\)

\(=\dfrac{25}{24}\)

d) \(\dfrac{1}{2}+\dfrac{5}{16}-\dfrac{1}{4}\)

\(=\dfrac{8}{16}+\dfrac{5}{16}-\dfrac{4}{16}\)

\(=\dfrac{9}{16}\)

e) \(1-\left(\dfrac{1}{5}+\dfrac{1}{2}\right)\)

\(=1-\dfrac{7}{10}\)

\(=\dfrac{3}{10}\)

f) \(\dfrac{2}{3}+\dfrac{1}{2}-\dfrac{5}{6}\)

\(=\dfrac{4}{6}+\dfrac{3}{6}-\dfrac{5}{6}\)

\(=\dfrac{1}{3}\)

g) \(\dfrac{5}{12}+\dfrac{5}{6}-\dfrac{3}{4}\)

\(=\dfrac{5}{12}+\dfrac{10}{12}-\dfrac{9}{12}\)

\(=\dfrac{1}{2}\)

h) \(\dfrac{7}{5}-\dfrac{4}{15}-\dfrac{2}{3}\)

\(=\dfrac{21}{15}-\dfrac{4}{15}-\dfrac{10}{15}\)

\(=\dfrac{7}{15}\)