Adding and Subtracting Fractions with Uncommon Denominators

There are 3 steps to adding and subtracting fractions with uncommon denominators. We will go over each step one at a time.

The first step is to make sure the denominators are common.

If the denominators are not common, we have to make them that way. This is known as step 1A (not quite step 2 but still part of step 1)

Well we have to multiply! First we have to find a number to multiply it by though.

Let's try this example:

What number could we multiply the the first fraction by to get the same number at the bottom of both fractions? Answer the question in the next poll

2 would be a good number to multiply the first fraction by because it would make both bottom numbers 8. 2 is the least common denominator of 4 and 8.

Let us go back to our example problem:

In order to completely change it, not only do we multiply the bottom number by two but also the top number.  It wouldn't make a whole lot of sense to multiply just the bottom number.  

 $\frac{2}{4}\times\frac{2}{2}=\frac{4}{8}$  

 $\frac{4}{8}+\frac{4}{8}=\frac{8}{8}\ or\ 1$  

The first step is to make sure the denominators are common

Step 1A if they are not common we have to find a way to make them common (by multiplying each denominator by their least common denominator.

It is better to choose the fraction that has the smallest denominator (for example, I chose to multiply the first fraction in our practice problem by the least common denominator since that was the smallest).

Finally, we add.

Now that we know how to add fractions with uncommon denominators, we know how to subtract them to.

The only difference between adding and subtracting is that at the end, you subtract the two numbers rather than add.

Let's look at a quick example

Here is our problem:

Our denominators aren't common so we have to find a number that when multiplied by 5 could make 10.  The least common denominator.

Let's try 5:  $\frac{2}{5}\times\frac{5}{5}=\frac{10}{25}$  

Hmmm...that doesn't look right. How about 2?

 $\frac{2}{5}\times\frac{2}{2}=\frac{4}{10}$  

So now that we have multiplied one of our fractions by 2 so that the denominators are the same, we have a new equation.

 $\frac{7}{10}-\frac{4}{10}$  

Now we subtract the top numbers and we end up with  

 $\frac{3}{10}$  

 $\frac{5}{8}+\frac{1}{16}=$  

 $\frac{10}{14}-\frac{11}{28}=$  

Answer the following equations on a sheet of paper. You have the rest of the hour to do it. If you don't finish, I'll hold onto it and you could finish it during study hall

 $\frac{1}{3}+\frac{1}{6}=$  

 $\frac{2}{10}-\frac{4}{20}=$  

 $\frac{4}{5}+\frac{1}{10}=$  

 $\frac{6}{7}-\frac{8}{14}=$  

For Tuesday, we will still be looking at fractions but we will be focusing on dividing and multiplying them

Have a great weekend!