Finding a Fraction of Another Fraction

Let's see what it means to find a fraction of another fraction. Let's find 1/3 of 1/2 of the square.

First, one side of the vertical line is 1/2. So, let's look at just the right side.

Now, let's shade 1/3. Since there are three equal parts, we'll shade one of them. So, 1/3 of 1/2 is 16th.

Let's look at a different problem. Find 1/3 of 1/4th of the square.

The square is divided into four equal columns. So each one represents 1/4.

Let's look at this column. We need 1/3 of it. Since it's split into three equal parts, we can select one part. So 1/3 of 1/4 is 112th.

Saying 1/3 of 1/4 is the same as multiplying 1/3 and 1/4. The product is 112th.

Now let's find 1/4 * 1/4. This is the same as saying find 1/4 of 1/4.

Each large triangle represents 1/4 of the square. Each smaller triangle within it is 1/4 of that section. So 1/4 * 1/4 = 116th.

Let's find 1/2 * 1/4 or 1/2 of 1/4.

1/4 of the shape is this large triangle on top. We shade half of it to represent 1/2 * 1/4. The product of 1/2 and 1/4 is 1/8.

Here, let's find 1/2 * 1/8 or 1/2 of 1/8.

A 1/8 section is this medium-sized triangle. To find half, we split it into two smaller equal triangles. Each one is 116th of the whole. So 1/2 * 1/8 is 116th.

Now let's find 1/8 * 1/4.

First, we take 1/4 of the square. This bottom left quadrant. It's made up of eight tiny triangles. So 1/8 of the smaller square is one of these triangles.

1/8 * 1/4 = 132nd of the whole.

Finding a part of a part shows what it means to multiply fractions. Multiplying two fractions means finding a fraction of another fraction.