Skill: Divide fractions

To divide fractions, use the relationship

$$a\div b=a\times \frac{1}{b}.$$

The number $\frac{1}{b}$ is called the reciprocal of $b$. So, to divide by a fraction, multiply by its reciprocal.

Example

Solve:

$$2\frac14\div\frac38$$

Step 1: Convert the mixed number to an improper fraction.

$$2\frac14=\frac{2\cdot4+1}{4}=\frac94$$

So the problem becomes

$$\frac94\div\frac38.$$

Step 2: Keep the first fraction, change division to multiplication, and flip the second fraction.

$$\frac94\div\frac38 = \frac94\times\frac83$$

Step 3: Multiply and simplify.

$$\frac{9\cdot8}{4\cdot3} = \frac{72}{12} = 6$$

Therefore,

$$\boxed{2\frac14\div\frac38=6}.$$

This means there are six groups of size $\frac38$ in $2\frac14$. The quotient can be larger than the numbers being divided because $\frac38$ is less than $1$. Dividing by zero is not defined.