Question

a)5/11-1/2+2/5+6/11+15/25+3/4+5/16      b)5/9.7/13+5/9.34/13-5/9.2/13

Answer 1

a: \(\dfrac{5}{11}-\dfrac{1}{2}+\dfrac{2}{5}+\dfrac{6}{11}+\dfrac{15}{25}+\dfrac{3}{4}+\dfrac{5}{16}\)

\(=\left(\dfrac{5}{11}+\dfrac{6}{11}\right)+\left(\dfrac{2}{5}+\dfrac{3}{5}\right)+\left(-\dfrac{1}{2}+\dfrac{3}{4}+\dfrac{5}{16}\right)\)

\(=1+1+\dfrac{-8+12+5}{16}\)

\(=2+\dfrac{9}{16}=\dfrac{2\cdot16+9}{16}=\dfrac{41}{16}\)

b: \(\dfrac{5}{9}\cdot\dfrac{7}{13}+\dfrac{5}{9}\cdot\dfrac{34}{13}-\dfrac{5}{9}\cdot\dfrac{2}{13}\)

\(=\dfrac{5}{9}\left(\dfrac{7}{13}+\dfrac{34}{13}-\dfrac{2}{13}\right)\)

\(=\dfrac{5}{9}\cdot3=\dfrac{5}{3}\)