numerator (top)  _
  denominator (bottom)

A fraction actually means: divide the top by the bottom.

1/2 means "1 divided by 2." 

This is why working with fractions can be confusing. We are adding, subtracting, multiplying, and dividing divisions.

to add ½ + ½  

just use 2 as the denominator of the answer because both fractions have same denominator.

So ½ + ½= 2/2 = 1

Add 1/2 + 1/3 

you have to convert each fraction to another fraction so that each has the same (or 'common') denominator. 

The easiest way to find a common denominator is to multiply the first denominator by the second.

In this case, 2 x 3 = 6, so we convert 1/2 and 1/3 to fractions with six in the denominator.

1/2 = 3/6  and 1/3 = 2/6

so

1/2 + 1/3 =

3/6 + 2/6 =

5/6

Subtract 1/2 - 1/3 

you have to convert each fraction so that each has the same (or 'common') denominator. 

The easiest way to find a common denominator is to multiply the first denominator by the second.

In this case, 2 x 3 = 6, so we convert 1/2 and 1/3 to fractions with six in the denominator.

1/2 = 3/6  and 1/3 = 2/6

so

1/2 - 1/3 =

3/6 - 2/6 =

1/6

Multiplying fractions is the easiest. 

Multiply the top by the top, and the bottom by the bottom

1/2 times 1/3 = 1/6

'Flip-it-over' and multiply.

1. Change the ÷ sign to x and invert the second fraction.

2. Multiply the numerators.

3. Multiply the denominators.

4. Reduce the results.

1/2  ÷  1/3  =  1/2  X  3/1  =  3/2 =   1½

 

To divide a fraction by a whole number, make the whole number 'over 1', and then 'flip-it-over'.

1. Convert the whole number to a fraction (3 becomes 3/1).

2. 'Flip-over' the new fraction (now 1/3).

3. Multiply the numerators.

4. Multiply the denominators.

5. Reduce the results.

To divide a whole number by a fraction, make the whole number 'over 1', and then 'flip-over'.

1. Convert the whole number to a fraction (3 becomes 3/1).

2. 'Flip-over' the other fraction.

3. Multiply the numerators.

4. Multiply the denominators.

5. Reduce the results.

Remember: A fraction is a division. Look at the division sign on your calculator. It is actually a fraction. So dividing fractions is dividing divisions.

Good Site: VISUAL FRACTIONS