Skill: Multiply fractions greater than one

To multiply fractions greater than $1$, first rewrite any mixed numbers as improper fractions. Then multiply the numerators, multiply the denominators, and simplify.

Example:

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

Step 1: Convert the mixed numbers.

For $2\frac{1}{3}$:

$$2\frac{1}{3}=\frac{2\cdot 3+1}{3}=\frac{7}{3}$$

For $1\frac{3}{4}$:

$$1\frac{3}{4}=\frac{1\cdot 4+3}{4}=\frac{7}{4}$$

Now multiply:

$$\frac{7}{3}\times\frac{7}{4}$$

Step 2: Multiply the numerators and denominators.

$$\frac{7\cdot 7}{3\cdot 4}=\frac{49}{12}$$

Step 3: Simplify or rewrite as a mixed number.

Since $49\div 12=4$ remainder $1$,

$$\frac{49}{12}=4\frac{1}{12}$$

Therefore,

$$2\frac{1}{3}\times 1\frac{3}{4}=4\frac{1}{12}$$

Check your answer: Since $2\frac{1}{3}$ is about $2.3$ and $1\frac{3}{4}$ is about $1.8$,

$$2.3\times 1.8\approx 4.1$$

The answer $4\frac{1}{12}$, or about $4.08$, is reasonable. Also, multiplying by a number greater than $1$ makes the other positive factor larger, so the product should be greater than both original numbers.