Dividing Fractions by Dividing Across

Dividing Fractions by Dividing Across: in this video we look at a different way how to divide fractions. In this method we are first getting a common denominator and then dividing across.

Dividing Fractions by Dividing Across


There are several ways to divide a fraction. This lesson will explore getting common denominators and then dividing across.

Let’s start by looking at this situation. Kenny has $1\frac{1}{2}$ pizzas. He wants to hand out slices that are an eighth of a whole pizza. How many slices can he give out?

To start with, let’s see if we can figure out the answer by using a model. First, we’ll divide the whole pizza into eighths. This will give us eight pieces. Then we will take the $\frac{1}{2}$ pizza and divide it into the same sized pieces. As you can see, it looks like we will be getting 4 slices out of that pizza. So, in all there will be 12 slices of pizza that are $\frac{1}{8}$ in size.

Now, let’s try solving the problem by getting a common denominator and just dividing across. In this scenario, we have $1\frac{1}{2}$ pizzas and we’re going to be making slices that are each the same size as $\frac{1}{8}$ of a whole pizza. That problem would be written as $1\frac{1}{2}$ divided by $\frac{1}{8}$. But remember: before we can divide, all the mixed numbers need to be written as fractions. Therefore we need to change $1\frac{1}{2}$ to $\frac{3}{2}$. Next, we need to get a common denominator for both fractions. So the problem becomes $\frac{12}{8}$ divided by $\frac{1}{8}$. Now, I can divide straight across. $\frac{12}{1}$ is 12 and $\frac{8}{8}$ is 1, so the final answer is indeed 12.

Dividing Fractions by Dividing Across example 2

Let’s try a second problem. Lea has a rope that is $1\frac{2}{3}$ feet long. She needs to cut it into pieces that are a $\frac{1}{4}$ of a foot in length in order to teach a magic trick. How many pieces of rope can she cut and how much is left over?

Let’s first try the problem on paper. To solve this problem we would divide $1\frac{2}{3}$ by $\frac{1}{4}$. Again, we will start by changing the mixed number into a fraction. Thus $1\frac{2}{3}$ becomes $\frac{5}{3}$. Now we have $\frac{5}{3}$ divided by $\frac{1}{4}$. Since the denominators are not the same, we need them to match up by using the common denominator of 12, giving us $\frac{20}{12}$ divided by $\frac{3}{12}$. When we divide across, we get 20 divided by 3, which is $6\frac{2}{3}$ and $\frac{12}{12}$, which is one. Since dividing by one does not change your answer, the final answer is $6\frac{2}{3}$.

Let’s check the problem by drawing out the situation. Before we start, let’s mark the rope into inches. $1\frac{2}{3}$ feet would be the same as 20 inches. Since $\frac{1}{4}$ of a foot is 3 inches, Lea needs 3 inch pieces. If we make a cut in the rope every 3 inches we will end up with 6 pieces of rope that can be used for the magic trick and a short unusable piece that is only 2 inches long or $\frac{2}{3}$ of the needed length.


Let’s consider one more situation. What if we had $\frac{3}{8}$ divided by $\frac{1}{4}$. Do we need to get a common denominator? Well, not really. 3 divided by 1 is 3 and 8 divided by 4 is 2, so the answer is $\frac{3}{2}$.

Usually you need to get a common denominator. Can you explain what makes this situation different?

A little confused?

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