Operation 
Explanation 
Example 
Multiply fractions 
Multiply both numerators and
denominators. You don't need the same
denominators. 
1 3 1 X 3 3
 X  =  = 
2 5 2 X 5 10

Fraction addition  Same denominators 
Just add the numerators. Keep the same denominator. 
1 2 1 + 2 3
 +  =  = 
8 8 8 8
Note:Don't add
denominators.

Changing denominators 
Divide the denominator you want by the denominator you have, then multiply by the numerator to get your new numerator. 
3 ? 8/4 = 2; 6
 =  = 
4 8 2 x 3 = 6 8

Fraction addition with different
denominators 
If one denominator divides evenly into the
other, change to the higher denominator and add. 
1 1 2 1 3
 +  =  +  = 
2 4 4 4 4

If the denominators don't divide evenly, then
multiply them
together to get your new denominator. Change denominators, then add 
Note: Since 3 doesn't go
into 5, use 3 x 5 = 15.
1 3 5 9 14
 +  =  +  = 
3 5 15 15 15

Changing mixed numbers to improper
fractions 
Find the number of unit fractions in the whole number, then add the fractional part of the mixed number. 
2 6 2 8
2  =  +  = 
3 3 3 3
Note: 2 is 6 thirds.

Changing improper fractions to mixed
numbers 
Divide the numerator by the denominator to get the whole number. Then the fraction is the remainder over the denominator. 
8 8/3 = 2 with a
For  remainder of 2 so
3 the mixed number
is 2 2/3

Dividing fractions 
To divide one fraction by another, invert (turn upsidedown) the second fraction, then multiply. 
3/4 3 8 24
 =  X  =  = 6
1/8 4 1 4
Note: This means there are
6 eighths in 3/4.
