What happens when we multiply fractions?

Let’s think about what happens when we multiply whole numbers Let’s think about what happens when we multiply whole numbers. When we multiply three by four, we get the product of 12.

The product, 12…

…is larger than either of the whole numbers 3 and 4.

When we multiply 6 by 7, we get the product of 42 When we multiply 6 by 7, we get the product of 42. Again, the product is larger than the whole numbers 6 and 7.

This is true whenever we multiply two whole numbers This is true whenever we multiply two whole numbers. The product is never smaller than the two whole numbers being multiplied. One thousand is larger than 200 and 5.

When we multiply 18 by 1, the product is 18 When we multiply 18 by 1, the product is 18. The product is the same as one of the other numbers, but it is not smaller.

When we look at the table, we see that when we multiply two whole numbers, the product is never smaller than either of the two whole numbers being multiplied.

Now let’s see what happens when we multiply fractions Now let’s see what happens when we multiply fractions. When we multiply the proper fractions one half and one fourth, the product is one eighth.

The product 1/8…

…is smaller than either of the fractions being multiplied.

The product of 3/5 and one half is three tenths The product of 3/5 and one half is three tenths. Again, we see that that the product is smaller than either fraction being multiplied.

When we multiply 1/8 by 2/3, we get two twenty-fourths When we multiply 1/8 by 2/3, we get two twenty-fourths. This product is smaller than both 1/8 and 2/3.

Here’s one more. Four sixths times one fifth is four thirtieths Here’s one more. Four sixths times one fifth is four thirtieths. In each case we see that the product of two proper fractions is usually smaller than the fractions being multiplied.

Let's look at what happens when we multiply the whole numbers 3 and 4.

The model represents one set of 4 The model represents one set of 4. In this problem, we are finding three sets of four.

Now the model shows three sets of 4.

The model shows us that 3 times 4, or three sets of four…

…equals 12. 19

It’s important to remember that when we multiply two whole numbers, the product is never smaller than either of the whole numbers being multiplied.

We can use models to see what happens when we multiply two fractions, 1/2 times 2/3.

Another way we can say this problem is "What is 1/2 of 2/3 Another way we can say this problem is "What is 1/2 of 2/3?" First we start with a model that represents the fraction 2/3.

Then, we find 1/2 of the 2/3. We shade 1/2 using diagonal lines and look at where the shaded parts and the diagonal lines overlap.

The whole is six parts, This model shows one half…

…of two thirds. The part is represented by the squares that have both shading and diagonal lines. The part is 2.

So, 1/2 times 2/3 equals 2/6.

It’s also important to remember that when we multiply two fractions, we take a portion of a fraction.