What it means to multiply two fractions together might not be as clear as what it means to multiply two whole numbers together, but knowing how to multiply fractions is a very important skill in math, and believe it or not, sometimes multiplying fractions is even simpler than adding them. Let's take a quick look at what the steps are.

The first step is to set up your multiplication problem. Next, use cross cancellation, if needed, to reduce the original fractions given in the problem. Then multiply the numerators together, and then the denominators. Lastly, make sure that your answer is in its simplest, reduced form.

Let's walk through these steps before we try a couple of examples. Take this problem here: five twelfths times nine tenths. Now that we have set up our multiplication problem we determine if we can use the process of cross cancellation. To do that, we take the numerator for one of the fractions and pair it with the denominator of the other fraction. So we can take the numerator of 5 and the denominator of 10. Find their greatest common factor, and divide both numbers by that GCF. In this case, their GCF is 5, so 5 divided by 5 is 1, and 10 divided by 5 is 2. Notice that when we divide out the common factor of 5 from both the numerator and denominator, we replace both of them with the quotient of this division. Now do the exact same process with the other pair. The GCF of 12 and 9 is 3. 12 divided by 3 is 4 and 9 divided by 3 is 3. Now, its important to note that one fourth is not an equivalent fraction to five twelfths, just as 3 halves is not and equivalent fraction to 9 tenths. But this multiplication expression – one fourth times three halves – is equivalent to our original expression of 5 twelfths times 9 tenths, it's just simpler.

Now that we've simplified the problem, we perform the actual multiplication. First, we multiply the numerators together. 1 times 3 is 3, so our numerator is 3. Next we multiply the denominators. 4 times 2 is 8, so our denominator is 8.

Lastly, we check to see that our answer is in its simplest form. Since 3 and 8 have no common factors, this answer is in its simplest reduced form

Now let's head over to the whiteboard to do a couple of examples.

This first problem reads, "Find the product of 9/10 and 20 thirds. Well, let's write that expression out.

Nine tenths times twenty thirds. Now let's do cross cancellation. Let's look at nine and three. The greatest common factor of nine and three is 3, so 9 divided by 3 gives us 3, and 3 divided by 3 gives us 1. Now let's look at the other pair, 10 and 20. The greatest common factor of 10 and 20 is 10, so 10 divided 10 is 1, and 20 divided 10 is 2. Now let's multiply this out. Three times 2 gives us a numerator of 6, and 1 times 1 gives us a denominator of 1. Six over one is just six, so the product of nine tenths and 20 thirds is 6. Let's look at another.

This question reads, "What is the product of 12, five sixths and 3 twenty-fifths?" Well, let's start by writing our whole number, 12, as a fraction. We can do that by just putting the denominator as one, so 12 over 1 times 5 over 6 times 3 over 25.

When we have more than two fractions, we still do cross cancellation and we can just pick any numerator denominator pair. So let's start by paring 12 and six. Together they have a greatest common factor of 6, so 12 divided by 6 leaves us 2 and 6 divided by 6 leaves us 1. 5 and 25 also share a common factor of 5. 5 divided by 5 is 1 and 25 divided by 5 is 5. There aren't any more numerators that have a common factor with any of the denominators, so now you multiply these out. Two times 1 times 3 is 6, and 1 times 1 times 5 is 5, so the product of 12, five sixths and 3 twenty-fifths is 6 fifths.

Now, there's another way we can do this problem, and still get the exact same answer. Let's begin by setting it up the exact same way: 12 over 1 times 5 over 6 times 3 over 25. Instead of doing cross cancellation with the 12 and the 6, let's start by doing it between the 6 and the 3. 6 and 3 have a greatest common factor of 3. 6 divided by 3 leaves us 2, and 3 divided by 3 leaves us 1. Now we can do cross cancellation between the 12 and the 2. 12 and 2 have a greatest common factor of 2, so 12 divided by 2 is 6, and 2 divided by 2 leaves us 1. 5 and 25 still have a greatest common factor of five, so dividing the five out leaves 1 in the numerator and 5 in that denominator. 6 times 1 times 1 gives us 6, and 1 times 1 times 5 gives us 5. So even though we did the cross cancellation differently, we arrived at the exact same result. Let's look at one more problem.

This problem reads, "The zoo has ordered 320 pounds of frozen vegetables to use in their animals' meal. Over the next two weeks. If the tortoises need to have 3/8 of the frozen vegetable order for their food needs, how many pounds of frozen vegetables will the tortoises eat over the next two weeks?" Well, let's start by writing the total amount, 320, as a fraction. We can write that as 320 over 1. The word "of" tells us that this is going to be multiplication, so it's 320 over 1 times 3 over 8. Now let's see if we can perform cross cancellation. 1 and 3 don't have any common factors, but 320 and 8 do. They have a greatest common factor of 8. 320 divided by 8 is 40, and 8 divided by 8 is 1. So, when we multiply this out, 40 times 3 is 120, and 1 times 1 is 1. And 120 over 1 is just the whole number 120. So the question of how many pounds of frozen vegetables will do tortoises eat: it is 120 pounds.