Question 5

We will divide fractions by multiplying by the reciprocal of the divisor.

Step 1 — Find the first quotient

Let's find the quotient of $\frac{2}{3}$ and $\frac{3}{10}$. We change division to multiplication by the reciprocal. The reciprocal of $\frac{3}{10}$ is $\frac{10}{3}$. $\frac{2}{3} \div \frac{3}{10}$

$= \frac{2}{3} \times \frac{10}{3}$

$= \frac{2 \times 10}{3 \times 3}$

$= \frac{20}{9}$

$\boxed{\frac{20}{9}}$

Step 2 — Find the second quotient

Now, let's find the quotient of $\frac{7}{11}$ and $\frac{5}{8}$. We will multiply $\frac{7}{11}$ by the reciprocal of $\frac{5}{8}$. The reciprocal of $\frac{5}{8}$ is $\frac{8}{5}$. $\frac{7}{11} \div \frac{5}{8}$

$= \frac{7}{11} \times \frac{8}{5}$

$= \frac{7 \times 8}{11 \times 5}$

$= \frac{56}{55}$

$\boxed{\frac{56}{55}}$

Step 3 — Find the third quotient

Finally, let's find the quotient of $-\frac{4}{7}$ and $\frac{5}{14}$. We multiply $-\frac{4}{7}$ by the reciprocal of $\frac{5}{14}$. The reciprocal of $\frac{5}{14}$ is $\frac{14}{5}$. $-\frac{4}{7} \div \frac{5}{14}$

$= -\frac{4}{7} \times \frac{14}{5}$

$= \frac{-4 \times 14}{7 \times 5}$

$= \frac{-56}{35}$ We can simplify this fraction. Both $\textbf{56}$ and $\textbf{35}$ are divisible by $\textbf{7}$. $= \frac{-56 \div 7}{35 \div 7}$

$= -\frac{8}{5}$

$\boxed{-\frac{8}{5}}$

Answer

(i) $\frac{20}{9}$ (ii) $\frac{56}{55}$ (iii) $-\frac{8}{5}$