# Subtracting Fractions

In this instructables we will learn how to subtract fractions.
What is a fraction you ask? Well its simple! (trust me)

A fraction is the ratio of two whole numbers. Simply put, its one whole number divided by another whole number. We write a fraction like this:
5 (numerator)
---
7 (denominator)

The top part of the fraction is called the numerator.The bottom part is called the denominator

Normally the numerator is smaller than the denominator, this is called a 'Proper Fraction'. If the numerator is equal to or larger than the denominator then the fraction is called an 'Improper Fraction'.

A proper fraction is always less than the number 1 and we can relate proper fractions to a part of a whole object. We use the denominator to divide the object into that number of parts and then we take the numerator number of parts and we can say we have that fractions part of the whole object.

For example: 3/4's of an orange, that means we have taken the orange, cut it into 4 equal parts, and then taken 3 of these part.

Pretty simple huh?
No lets learn how to add them
Remove these ads by Signing Up

## Step 1: How To Subtract Fractions.

There are 3 simple steps to subtract fractions

Step 1. Make sure the denominators are the same

Step 2. Subtract the numerators. Put the answer over the same denominator as in step 1

Step 3. Simplify the fraction. (If needed)
(Note: 3/4 the 3 in the numerator, and the 4 is the denominator.)
Let me explain....

Lets say we have the problem...
3/4 - 1/4

Since the denominators are the same, you can go straight to step 2, and add the top 2 numbers.
You will get 2/4, and now you simplify.

--HOW TO SIMPLIFY --
To simplify you divide both the top and bottom of the fraction by the Greatest Common Factor.

What is a "Greatest Common Factor" AKA: GCF?
Well lets look at what a factor is first, A factor is any of the numbers that can be multiplied together to make another number. Example: The factors of 12 are 1,2,3,4,6 and 12 ...because 2 * 6 = 12, or 4 * 3 = 12, or 1 * 12 = 12.

Now, what makes a Factor a "Common Factor"?
A factor is a common factor if it is a factor of two or more numbers.
For example:
The factors of 12 are 1, 2, 3, 4, "6" and 12
The factors of 30 are 1, 2, 3, 5, "6", 10, 15 and 30

Notice that 1,2,3 and 6 appear in both lists? So, the common factors of 12 and 30 are: 1, 2, 3 and 6

Ok, now we know what a common factor is but what on earth is the "Greatest Common Factor"?

It is simply the largest of the common factors. In our example above, the largest of the common factors is 6, so the Greatest Common Factor is 6!

To find the GCF, you just play around with the numbers, lets try with 4 and 10!
4: 1, "2", 4
10: 1, "2", 5, 10
The GFC is 2!

Ok? Now lets get back to the subtracting

2/4
The GCF of the two numbers is 2, so divide both numbers by 2 and you get...
1
---
2
Done, We have now subtracted, and simplified a fraction.
Simple right? Well it gets harder

If you have a problem like 1/2 - 1/10, you have to make the denominators the same before you can subtract.
In this case we need to multiply 1/2 by 5, so you get 5/10
Now we have 5/10 - 1/10.
Subtract the numerators, and leave the denominators alone and we get
5 - 1
-- --
10 10
And that equals 4/10, now we simplify, and get 2/5

It's that simple!

If you have a question, feel free to ask