Question 2

To divide by a fraction, we multiply by its reciprocal.

Step 1 — Understanding Reciprocals

Let us think about reciprocals. The reciprocal of a fraction is its inverse. We flip the numerator and the denominator. For example, the reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$. Multiply a fraction by its reciprocal. The answer is always 1. Let us check this with an example. We multiply $\frac{2}{3}$ by $\frac{3}{2}$.

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

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

$= \frac{6}{6}$

$\boxed{1}$

Step 2 — The Division Rule

Now, let us divide two fractions. Consider dividing $\frac{1}{2}$ by $\frac{3}{4}$. We keep the first fraction as it is. We change the division sign to a multiplication sign. We then take the reciprocal of the second fraction. The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$. Now we multiply the two fractions.

$\frac{1}{2} \div \frac{3}{4}$

$= \frac{1}{2} \times \frac{4}{3}$

$= \frac{1 \times 4}{2 \times 3}$

$= \frac{4}{6}$

$= \frac{2}{3}$

$\boxed{\frac{2}{3}}$

This is the rule for dividing fractions. We keep the first fraction. We change the division to multiplication. We flip the second fraction (take its reciprocal). Then we multiply the fractions.

Answer

(i) To divide two fractions, multiply the first fraction by the reciprocal of the second fraction.