# Verify whether the given statement is true or false:

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

Solution:

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

LHS

$\frac{13}{5} \div \frac{26}{10}$

$=\frac{13}{5} \times \frac{10}{26}$

$=\frac{130}{130}$

$=1$

RHS

$\frac{26}{10} \div \frac{13}{5}$

$=\frac{26}{10} \times \frac{5}{13}$

$=\frac{130}{130}$

$=1$

TRUE

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

LHS

$-9 \div \frac{3}{4}$

$=-9 \times \frac{4}{3}$

$=\frac{-36}{3}$

$=-12$

RHS

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

$=\frac{3}{4} \times \frac{1}{-9}$

$=\frac{3}{-36}$

$=\frac{-1}{12}$

FALSE

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

LHS

$\frac{-8}{9} \div \frac{-4}{3}$

$=\frac{-8}{9} \times \frac{3}{-4}$

$=\frac{24}{36}$

$=\frac{2}{3}$

RHS

$\frac{-4}{3} \div \frac{-8}{9}$

$=\frac{-4}{3} \times \frac{9}{-8}$

$=\frac{36}{24}$

$=\frac{3}{2}$

FALSE

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

LHS

$\frac{-7}{24} \times \frac{-16}{3}$

$=\frac{112}{72}$

RHS

$\frac{3}{-16} \div \frac{-7}{24}$

$=\frac{3}{-16} \times \frac{24}{-7}$

$=\frac{72}{112}$

FALSE