Skill: Multiply two proper fractions

To multiply two proper fractions, multiply the numerators, multiply the denominators, and simplify the result if possible.

Example:

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

This means finding $\frac{2}{3}$ of $\frac{3}{4}$.

1. Multiply the numerators:

$$2\times 3=6$$

2. Multiply the denominators:

$$3\times 4=12$$

So,

$$\frac{2}{3}\times\frac{3}{4}=\frac{6}{12}$$

3. Simplify $\frac{6}{12}$. Both 6 and 12 can be divided by 6:

$$\frac{6\div 6}{12\div 6}=\frac{1}{2}$$

Therefore,

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

You can picture a whole divided into 3 rows and 4 columns, making 12 equal parts. Shading $\frac{3}{4}$ one way and $\frac{2}{3}$ another way leaves 6 overlapping parts out of 12, which is $\frac{6}{12}=\frac{1}{2}$. Since both factors are less than 1, the product $\frac{1}{2}$ is less than either factor.