Verify whether the given statement is true or false: (i) 13/5 ÷ 26/10 ÷ 13/5 (iv) -9 ÷ 3/4 = 3/4 ÷ (-9)

Question

Verify whether the given statement is true or false:

(i) \(\frac{13}{5}\div\frac{26}{10}= \frac{26}{10}\div\frac{13}{5}\)

(ii) \(-9\div\frac{3}{4}= \frac{3}{4}\div(-9)\)

(iii) \(\frac{-8}{9}\div\frac{-4}{3}= \frac{-4}{3}\div\frac{-8}{9}\)

(iv) \(\frac{-7}{24}\div\frac{3}{-16}= \frac{3}{-16}\div\frac{-7}{24}\)

Answer 1

(i)

\(\frac{13}{5} \div\frac{26}{10}= \frac{26}{10}\div\frac{13}{5}\)

LHS = \(\frac{13}{5}\div\frac{26}{10}\)

= \(\frac{13}{5}\times\frac{10}{26}\)

= \(\frac{13\times10}{5\times26}\)

= \(\frac{130}{130}= 1\)

RHS = \(\frac{26}{10}\div\frac{13}{5}\)

= \(\frac{26}{10}\times\frac{5}{13}\)

= \(\frac{26\times5}{10\times13} \)

= \(\frac{130}{130}=1\)

Since, RHS = LHS 

Therefore, True

(ii)

\(-9\div\frac{3}{4}=\frac{3}{4}(-9)\)

LHS = \(-9\div\frac{4}{3}\)

= \(-9\times\frac{4}{3}\)

= \(\frac{-9\times4}{3}\)

= \(\frac{-36}{3}=-12\)

RHS = \(\frac{3}{4}\div(-9)\)

= \(\frac{3}{4}\times\frac{1}{-9}\)

= \(\frac{3\times1}{4\times-9}\)

= \(\frac{3}{-36}=\frac{-1}{12}\)

Since, RHS ≠ LHS

Therefore, False

(iii)

\(\frac{-8}{9}\div\frac{-4}{3}= \frac{-4}{3}\div\frac{-8}{9}\)

LHS = \(\frac{-8}{9}\div\frac{-4}{3}\)

= \(\frac{-8}{9}\times\frac{3}{-4}\)

= \(\frac{-8\times3}{9\times-4}\)

= \(\frac{-24}{-36} =\frac{2}{3}\)

RHS = \(\frac{-4}{3}\div\frac{-8}{9}\)

= \(\frac{-4}{9}\times\frac{9}{-8}\)

= \(\frac{-4\times9}{3\times-8}\)

= \(\frac{-36}{-24}=\frac{3}{2}\)

Since, RHS ≠ LHS

(iv)

\(\frac{-7}{24}\div\frac{3}{-16}=\frac{3}{-16}\div\frac{-7}{24}\)

LHS = \(\frac{-7}{24}\div\frac{3}{-16}\)

= \(\frac{-7}{24}\times\frac{-16}{3}\)

= \(\frac{-7\times-16}{24\times3}\)

= \(\frac{112}{72}=\frac{14}{9}\)

RHS = \(\frac{3}{-16}\div\frac{-7}{24}\)

= \(\frac{3}{-16}\times\frac{24}{-7}\)

= \(\frac{3\times24}{-16\times-7}\)

= \(\frac{72}{112}=\frac{9}{14}\)

Since, RHS ≠ LHS

Therefore, False