Fractions

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FractionsFractionsBy. Maxx Kim

A fraction is a numerical quantity that is not a whole number. Such as 1/2, or 1/5. 3/10.

What is a Fraction?What is a Fraction?

The most important part in a fraction is that it has a numerator and a denominator.

Example. 1 Numerator 2 Denominator The top part is the numerator ( 1 ) the bottom part is the denominator ( 2 )

Parts of a FractionParts of a Fraction

Okay so now that you know all the parts to a fraction first lets learn how to multiply fractions

In order to do that here’s an example 1 X 4 2 7 So in order to do this all you have to do is

multiply the numerators and denominators together. If you do it yourself you should get 4/14

Multiplying FractionsMultiplying Fractions

Dividing fractions is easy! It's very very similar to multiplying except it has one extra step.

So as an example lets use the last problem we did to make things easy. 1 4 2 7 Step 1 Flip the 2nd fraction so that the numerator is now the denominator,

and the denominator is the numerator 1 7 2 4 Step 2 Turn the division sign into a multiplication sign 1 X 7 2 4 Step 3 Solve If you do these steps you should get 7/8

Dividing FractionsDividing Fractions

For Adding and subtracting fractions the first step you have to do is trying to find something called the least common denominator, also known as LCD.

To find the least common denominator, simply list the multiples of each denominator (multiply by 2, 3, 4, etc.) then look for the smallest number that appears in each list.

Adding FractionsAdding Fractions

Example: Suppose we wanted to add 1/5 + 1/6. We would find the least common denominator as follows.

First we list the multiples of each denominator.

Multiples of 5 are 10, 15, 20, 25, 30, 35, 40,...

Multiples of 6 are 12, 18, 24, 30, 36, 42, 48,...

Adding Fraction cont.Adding Fraction cont.

Now, when you look at the list of multiples, you can see that 30 is the smallest number that appears in each list

Therefore, the least common denominator of 1/5, 1/6 is 30 so now that we found the LCD there’s also another rule that follows up

which is, “what you do to the bottom you do to the top.” For the first fraction 1/5 and the common denominator is 30 so that means you multiplied 5, 6 times in order to get 30. So you also multiply 6 to the top number to. Giving you 6/30.

Lets do the same for 1/6. The LCD was 30, so you multiplied 6, 5 times in order to get 30. And you also multiply that by the top giving you 5/30.

So far this is what we have so far. 6 + 5 30 30 when you get here all you have to do now is add the numerators together

but just carry over the 30. (DO NOT TOUCH THE DENOMINATOR!) Giving you 11/30 which is the answer.

L.C.DL.C.D

Subtracting fractions is almost the same as addition. Lets use the same problem in adding fractions.

1 - 1 5 6 Step 1 so again you find the common denominator

which was 30 right? 6 - 5 30 30 Step 2 you then just subtract only the numerators

again and just carry over the denominator which gives you 1/30.

Subtracting FractionsSubtracting Fractions

So basically this time I’m going to show you how to do fractions using variables. This makes things a little more trickier because instead of dealing with numbers were dealing with letters. Don’t let them confuse you though. Here’s the

X+3 - x X-1 x+1

Fractions w/variblesFractions w/varibles

Ok so Step 1 just like any other subtraction fraction problem you have to find the LCD. Except this time finding it is a bit different.

To find the Common Denominator this time look at this formula

a*b=b*a so knowing this take a look at what I’ve done

so far. (x+3) (x+1) - x(x-1) (x-1) (x+1) (x+1) (x-1)

Fractions w/Varibles cont.Fractions w/Varibles cont.

If you noticed I added a few numbers to the equation making it look confusing.

So to find the denominator I multiplied “a” by “b”, and “b” by “a” using a FOIL

method. a=x-1 b=x+1 Also don’t forget the rule where what you do

to the top you do to the bottom. (x+3) (x+1) - x(x-1) (x-1) (x+1) (x+1) (x-1)


So now that you know that if you do FOIL you get this

x2+x+3x+3 - x2-x x2+x-x-1 x2-x+x-1

Here I just combined like terms. x2+4x+3 - x2+x x2-1 x2-1


x2+4x+3 – x2 + x x2-1 x2-1

Now all you do is subtract the Numerators up top.

So if you do that you get the answer at the bottom. Again you just carry over the common denominator. (DO NOT SUBTRACT THE DENOMINATORS!)

5x+3 x2-1


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Fractions