1/2 1/4 3/8
(One-Half)
(One-Quarter)
(Three-Eighths)
     
The top number tells how many slices you have and the bottom number tells how many slices the pizza was cut into.

Numerator / Denominator

We call the top number the Numerator, it is the number of parts you have.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.

 

Numerator
 
Denominator

You just have to remember those names! (If you forget just think "Down"-ominator)

Equivalent Fractions

Some fractions may look different, but are really the same, for example:

 
4/8 = 2/4 = 1/2
(Four-Eighths)   Two-Quarters)   (One-Half)
   
It is usually best to show an answer using the simplest fraction ( 1/2 in this case ). That is called Simplifying, or Reducing the Fraction

Adding Fractions

You can add fractions easily if the bottom number (the denominator) is the same:

1/4 + 1/4 = 2/4 = 1/2
(One-Quarter)   (One-Quarter)   (Two-Quarters)   (One-Half)
     

Another example:

5/8 + 1/8 = 6/8 = 3/4
     

 

Adding Fractions with Different Denominators

But what if the denominators are not the same? As in this example:

 
3/8 + 1/4 = ?
   

You must somehow make the denominators the same. In this case it is easy, because we know that 1/4 is the same as 2/8 :

 
3/8 + 2/8 = 5/8
   

Equivalent Fractions

Equivalent Fractions have the same value, even though they may look different.

These fractions are really the same:
 
1  =  2  =  4
     
2 4 8

Why are they the same? Because when you multiply or divide both the top and bottom by the same number, the fraction keeps it's value. The rule to remember is:

What you do to the top of the fraction
you must also do to the bottom of the fraction !

So, here is why those fractions are really the same:

  × 2   × 2  
 
1  =  2  =  4
     
2 4 8
 
  × 2   × 2  
And visually it looks like this:

 
1/2   2/4   4/8
= =

 

Here are some more equivalent fractions, this time by dividing:

  ÷ 3   ÷ 6  
 
18  =  6  =  1
     
36 12 2
 
  ÷ 3   ÷ 6  
1/2 1/4 3/8
(One-Half)
(One-Quarter)
(Three-Eighths)

 

 

Improper Fractions

Quick Definition: An Improper fraction has a
numerator (top number) larger than or equal to
the denominator (bottom number),

such as 7/4 or 4/3

(It is "top-heavy")
7/4
(seven-fourths or seven-quarters)

Fractions

A Fraction (such as 7/4) has two numbers:
Numerator
 
Denominator

We call the top number the Numerator, it is the number of parts you have.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.

 

Fractions can have three different types :

Proper Fractions: The numerator is less than the denominator
Examples: 1/3, 3/4, 2/7
   
Improper Fractions: The numerator is greater than (or equal to) the denominator
Examples: 4/3, 11/4, 7/7
   
Mixed Fractions: A whole number and proper fraction together
Examples: 1 1/3, 2 1/4, 16 2/5

Improper Fractions

So, an improper fraction is just a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). In other words, it is top-heavy.

Examples

3/2 7/4 16/15

 

Improper Fractions = Mixed Fractions

You can use either an improper fraction or a mixed fraction to show the same amount. For example 1 3/4 = 7/4, shown here:
 

1 3/4   7/4
=

 

Are Improper Fractions Bad ?

NO, they aren't bad ! For mathematics they are actually better than mixed fractions. Mixed fractions can be confusing when you write them down in a formula:

Mixed Fraction: What is: 1 + 2 1/4   ?
  Is it: 1+2+1/4   = 3 1/4 ?
  Or is it: 1 + 2 × 1/4   = 1 1/2 ?
         
Improper Fraction: What is: 1 + 9/4   ?
  It is: 4/4 + 9/4 = 13/4  

But, for everyday use, people understand mixed fractions better. It is easier to say "I ate 2 1/4 sausages", than "I ate 9/4 sausages"

Can be Equal

What about when the numerator is equal to the denominator? For example 4/4 ?

Well, it is obviously the same as a whole, but it is written as a fraction, so most people agree that is a type of improper fraction.

Converting Improper Fractions to Mixed Fractions
 

To convert an improper fraction to a mixed fraction, follow these steps:

 
  • Divide the numerator by the denominator.
  • Write down the whole number answer
  • Then write down any remainder above the denominator.
 

Example: Convert 11/4 to a mixed fraction.

Divide: 11 ÷ 4 = 2 with a remainder of 3
Write down the 2 and then write down the remainder (3) above the denominator (4), like this:
2 3
 
4

Converting Mixed Fractions to Improper Fractions

To convert a mixed fraction to an improper fraction, follow these steps:

 
  • Multiply the whole number part by the fraction's denominator.
  • Add that to the numerator
  • Then write the result on top of the denominator.
 

Example: Convert 3 2/5 to an improper fraction.

Multiply the whole number by the denominator: 3 × 5 = 15
Add the numerator to that: 15 + 2 = 17
Then write that down above the denominator, like this:
17
 
5