Question

calculați: a) |-0,(3)|-224*{(1/7-0,25)*(1/7+1/8)-[(1/7)^2-(1/8)^2]}​

Answer 1

$|-0,(3)|-224*\{(\frac{1}{7}-0,25)*(\frac{1}{7}+\frac{1}{8})-[(\frac{1}{7})^2-(\frac{1}{8})^2]\}= \\ =\frac{1}{3}-224*\[(\frac{1}{7}-\frac{1}{4})*\frac{15}{56}-(\frac{1}{49}-\frac{1}{64})]= \\ =\frac{1}{3}-224*(-\frac{3}{28}*\frac{15}{56}-\frac{15}{3136})=\frac{1}{3}-224*(-\frac{45}{1568}-\frac{15}{3136})= \\ =\frac{1}{3}-224*(-\frac{15}{448})=\frac{1}{3}+\frac{15}{2}=\bold{\frac{47}{6}}$