Skill: Divide fractions using reciprocals

To divide by a fraction, multiply by the reciprocal of the divisor. The reciprocal is found by switching the numerator and denominator.

For example:

$$\frac{3}{4}\div\frac{2}{5}$$

1. Identify the divisor:
   The divisor is $\frac{2}{5}$ because it is the number you are dividing by.

2. Find its reciprocal:
   The reciprocal of $\frac{2}{5}$ is $\frac{5}{2}$.

3. Keep the dividend, change division to multiplication, and use the reciprocal of the divisor:

$$\frac{3}{4}\div\frac{2}{5} =\frac{3}{4}\times\frac{5}{2}$$

4. Multiply across:

$$\frac{3\times5}{4\times2}=\frac{15}{8}$$

5. Write the improper fraction as a mixed number:

$$\frac{15}{8}=1\frac{7}{8}$$

Therefore,

$$\boxed{\frac{3}{4}\div\frac{2}{5}=1\frac{7}{8}}$$

Remember: Keep the first fraction, change division to multiplication, and flip only the second fraction.