Pre Algebra Finding Common Denominators
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Finding Common Denominators

 
 There is one normal pizza that is cut into 8 slices.
 
 
 Another pizza is cut into 6 slices:
 
 
 We have one slice from each. 
 How much pizza do we have ?
 

 
 We have a problem.
 To add fractions, the numbers on the bottom of both fractions 
 MUST be the same as each other.
 Here they're not.
 
 Swell! 
 Is there a way to make them the same.
 
 With math, there's always a way.
 In fact for this puppy, 
 there's a bunch of ways.
 
 Here's one now:
 
 On another page we looked at some fractions 
 and tried to make the numbers smaller. 
 Here we're going to do the opposite. 
 We start with fractions with kinda small numbers and make them bigger. 
 The trick is to end up with both of the bottom numbers being the same. 

 We don't really care what number they end up being, 

 just so they're the same.
 
 You can multiply something by 1 and it won't change the value. 
 The deal is, a 1 doesn't always look like a 1. 
 Sometimes it's a fraction where the number on top 
 and the number on the bottom are the same. 
 Like this:
 

 
 We can multiply ANYTHING we like by this fraction. 
 Since it's equal to 1, it won't change the value.
 OK, that's all we need to know. 
 Now here's the problem we're working on again 
 so you won't have to scroll to find it:
 

 

 
 Now we're ready. 
 Here's the plan:
 
 STEP 1: 
 Write down a fraction where both the top part and bottom part 
 are the same as the bottom part of the first fraction we want to add:
 

 
 STEP 2: 
 Multiply the second fraction in the problem by this:
 
Remember, the second
fraction here is equal to one
so this doesn't change the value
This is our NEW second fraction 
in the problem
 
 STEP 3: 
 Write down a fraction where both the top part and bottom part 
 are the same as the bottom part of the second fraction we want to add:
 

 

 
 STEP 4: 
 Multiply the first fraction in the problem by this:
 
Remember, the second
fraction here is equal to one
so this doesn't change the value
This is our NEW first fraction 
in the problem
 
 STEP 5: 
 The new fractions have the same bottom number so we can now add!
 
All we did 
was multiply the original fractions 
by something equal to 1 
so the values didn't change.
 
 STEP 6: 
 Simplify the answer if possible:
 

 
 This works with subtraction too!
 

 
 STEP 1:

 
 STEP 2:
 
This goes where the 1/6 was.
 
 STEP 3:

 
 STEP 4:
 
This goes where the 3/5 was.
 
 STEP 5:
 

 
 STEP 6:
 

 

   copyright 2005 Bruce Kirkpatrick

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