Adding and Subtracting Fractions

Finding the Common Denominator

The first step in adding and subtracting fractions!

First we need to use the multiples...

But what are they???

Multiples of 4:

• 4

• 8

• 12

• 16

• 20

• 28

• 40

Open Ended

Based on the last slide, what are mutliples?

Good job!

They are just numbers that a given number (such as 4) can add or multiply up to over time. Four went into all of those numbers! Do you see it now?

Multiple Select

Which of the following are multiples of 3?

• 66

• 12

• 3

• 10

Now I know what you are thinking... how does this relate to common denominators...

Let's see!

Open Ended

Give me some multiples of 3 (maybe 5 or so).

Open Ended

Give me some multiples of 5 (maybe 4 or 5).

Multiple Choice

What is the lowest multiple that they have in common?

• 15

• 44

• 30

• 61

We can now use that as our LCD!

LCD=lowest common denominator

Remember we need a common denominator to add and subtract fractions, right?

Well we just found it! So now you need to multiply the bottom of each fraction by whatever it takes to get to that LCD (in this case 15). Keep in mind whatever you do to the bottom you must do to the top...

Multiple Choice

Which is the same fraction with a denominator of 15?

 $\frac{2}{3}$  

•  $\frac{3}{9}$  

•  $\frac{10}{15}$  

•  $\frac{11}{15}$  

•  $\frac{6}{9}$  

Multiple Choice

Which is the same fraction with a common denominator of 15?

 $\frac{4}{5}$  

•  $\frac{12}{15}$  

•  $\frac{8}{10}$  

• This is already right!

•  $\frac{6}{9}$  

So now we are here...

 $\frac{10}{15}+\frac{12}{15}=??$  

And you know we just need to add the tops...

And the bottoms stay the same...

Multiple Choice

What is this?

 $\frac{10}{15}+\frac{12}{15}=$  

•  $\frac{21}{15}$  

•  $\frac{7}{5}$  

•  $\frac{22}{15}$  

•  $\frac{22}{30}$  

Remember!

You always need to simplify your answer (we could not simplify the last one). Don't forget, we like small numbers!

Poll

Does that make sense? How do you feel?

• It makes sense but I feel eh

• I feel great and that makes complete sense!

• This makes no sense at all

• Not really sure

Time for practice!

You saw it coming didn't you...

Multiple Choice

 $\frac{3}{4}+\frac{4}{16}=$  

•  $\frac{20}{16}$  

•  $\frac{5}{4}$  

•  $\frac{4}{5}$  

•  $\frac{7}{20}$  

Multiple Choice

 $\frac{3}{4}+\frac{2}{6}=$  

•  $\frac{13}{12}$  

•  $\frac{5}{10}$  

•  $\frac{1}{2}$  

•  $\frac{26}{24}$  

Multiple Choice

Last one!

 $\frac{6}{7}+\frac{8}{9}=$  

•  $\frac{100}{63}$  

•  $\frac{14}{16}$  

•  $\frac{28}{3}$  

• I'm tired...

Poll

How do you feel?

• Great!

• Not too shabby!

• I need more practice!

• I have no clue what is going on

Open Ended

Any questions?