Let's multiply fractions. We'll start by using a diagram to see what's happening.
The whole rectangle is divided into four equal rows. So each row is 1/4. In the top row, two out of three parts of the row are shaded. So this shaded part represents 1/4 * 2/3. There are 12 of these smaller equal parts in total. So the product of 1/4 * 2/3 is 2 12ths.
Let's look at a different problem. This shape is divided into five rows and two columns.
If we just look at the left column, we see that three out of five parts are shaded or 35ths of the column is shaded.
Since the column is 1/2 of the whole shape, that means we're taking 35ths of 1/2. So 3/5ths * 1/2 equals 3/10.
Here's another. This rectangle is divided into five columns and three rows. If we look at just the first four columns, two out of three rows or 2/3 of the section is shaded. Since we're looking at 2/3 of 4 out of 5 columns, that means we're taking 2/3 of 4 fths. So the equation is 2/3 * 4ths equals 8 15.
Here's the pattern. To multiply fractions, you multiply the numerators and multiply the denominators. Let's look at that last example again. For 2/3 * 4 fths, the number of colored parts is 2 * 4, which is 8. The total number of parts in the whole is 3 * 5, which is 15. This gives us our answer, 8.
Now, let's complete some equations.
First, 37 * 1/2. We multiply the numerators. 3 * 1 = 3. Then we multiply the denominators. 7 * 2 = 14. The answer is 34.
Here we're looking for what * 47 = 877.
2 * 4 = 8 and 11 * 7 = 77. So the missing fraction must be 2 11ths.
Now let's figure out which two fractions multiply to make 8 35ths. First, let's find two numbers that multiply to 8. Out of these numbers, we can use 2 and 4.
Next, what two numbers multiply to 35? We can use 5 and 7. So, 2 fths * 47th = 8 35ths. We could have also used 27th and 4 fths.
The key idea is that to multiply fractions, multiply the numerators and multiply the denominators.
