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!