Let's learn how to multiply any fraction by another fraction. We need to find 2/3 of 1/2 of the square. The square is divided into two equal columns. So one column is 1/2. The column has three equal parts. So each part is 1/3 of 1/2.
2/3 is two of these parts. So 2/3 of 1/2 is 26.
Let's try another one.
What is 2/3 of 3/4 of the square? First, let's find 3/4s. The square is divided into four columns, so each column is 1/4. Three of them are 3/4s.
Now, we need to find 2/3 of this section. Since there are three horizontal rows, each row is 1/3. 2/3 is six of the smaller parts. So, 2/3 of 3/4s is 6 12ths.
This illustrates the process. The three yellow columns are 3/4s of the square.
Taking 2/3 is the same as taking two of these rows colored green. There are six green pieces in total. So 2/3 * 3/4s is 6 12ths. Now let's find 3/5ths * 2s.
Remember that fraction multiplication is the same as asking what is 35ths of 2ths. First let's find two fths of the square. Since there are five columns, each column is 1/5.
The first two columns are two- fifths.
Now, let's find 3/5ths of this section.
Since there are five rows, we can shade three of them to find that 3/5ths * 2-5ths is 6 25ths.
Here, let's find 1/2 * 2/3. Let's represent 2/3 by shading two of the three horizontal rows. To find 1/2 of that area, take 1/2 of each rectangle.
So 1/2 * 2/3 is 26.
For our last problem, let's find 5/8 * 1/4. We can start by finding 1/4 of the square. This bottom right smaller square is 1/4 of the whole. It's divided into eight parts. So we can take five of these small triangles to represent 5/8 of 1/4. 5/8 * 1/4 is 532.
When you take a fraction of a fraction, you're finding a part of a part by dividing the whole into smaller equal pieces. You can see how the final fraction is formed.
