Skill: Divide mixed numbers

To divide mixed numbers:

1. Estimate to predict about how large the answer should be.
2. Rewrite each mixed number as an improper fraction.
3. Keep the first fraction, change division to multiplication, and flip only the divisor (the second fraction).
4. Multiply and simplify.
5. Check that the answer is reasonable.

Example:

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

First, estimate:

$$2\frac{1}{4}\approx 2,\qquad 1\frac{1}{2}\approx 1.5$$

Since $2\div 1.5$ is a little more than $1$, we expect an answer near $1\frac{1}{2}$.

Rewrite the mixed numbers as improper fractions:

$$2\frac{1}{4}=\frac{9}{4}$$

because $2\times 4+1=9$, and

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

because $1\times 2+1=3$.

Now divide:

$$\frac{9}{4}\div\frac{3}{2}$$

Keep the first fraction, change $\div$ to $\times$, and flip only the divisor:

$$\frac{9}{4}\times\frac{2}{3}$$

Multiply and simplify:

$$\frac{9\times2}{4\times3}=\frac{18}{12}=\frac{3}{2}=1\frac{1}{2}$$

Therefore,

$$2\frac{1}{4}\div 1\frac{1}{2}=1\frac{1}{2}.$$

The answer is reasonable because it is close to our estimate.