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Rational Numbers — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSRational Numbers2 Marks
Question
Solve
(i) $\frac{4}{7}+\left(-\frac{4}{9}\right)+\frac{3}{7}+\left(-\frac{13}{9}\right)$
(ii) $\left(\frac{-3}{7}+\frac{9}{14}\right)+\left(\frac{-5}{2}\right)$
(iii) $\frac{18}{19}+\left(\frac{-37}{19}+\frac{74}{57}\right)$
✓

Answer


$\begin{array}{l}\text{(i) We have,} \quad \frac{4}{7}+\left(-\frac{4}{9}\right)+\frac{3}{7}+\left(-\frac{13}{9}\right) \\ =\left(\frac{4}{7}+\frac{3}{7}\right)+\left(-\frac{4}{9}+\frac{-13}{9}\right)=\frac{7}{7}+\left(-\frac{4}{9}-\frac{13}{9}\right) \\ =1+\left(-\frac{17}{9}\right)=1-\frac{17}{9}=\frac{9-17}{9}=-\frac{8}{9} \end{array}$
$\text{(ii) We have, }\left(-\frac{3}{7}÷ \frac{9}{14}\right) ÷\left(\frac{-5}{2}\right)$
$=\left(-\frac{3}{7} \times \frac{14}{9}\right) \times\left(\frac{-2}{5}\right)=\left(-\frac{2}{3}\right) \times\left(\frac{-2}{5}\right)=\frac{4}{15}$
$\text{(iii) We have, }\frac{18}{19} ÷\left(\frac{-37}{19} ÷ \frac{74}{57}\right)$
$=\frac{18}{19}÷(\frac{-37}{19}\times\frac{57}{74})=\frac{18}{19}÷(\frac{-3}{2})$
$=\frac{18}{19}\times(\frac{-2}{3})=\frac{-12}{19}$

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