*Basic Rule: Fractions can only be added or subtracted conveniently if they have like denominators. *

To see why this rule makes sense, let’s consider the problem of adding a quarter and a dime.

A quarter is
1414 size 12{ { {1} over {4} } } {} of a dollar.

A dime is
110110 size 12{ { {1} over {"10"} } } {} of a dollar.

We know that 1 quarter + 1 dime = 35 cents. How do we get to this answer by adding
1414 size 12{ { {1} over {4} } } {} and
110110 size 12{ { {1} over {"10"} } } {} ?

We convert them to quantities of the same denomination.

A quarter is equivalent to 25 cents, or
2510025100 size 12{ { {"25"} over {"100"} } } {}.

A dime is equivalent to 10 cents, or
1010010100 size 12{ { {"10"} over {"100"} } } {}.

By converting them to quantities of the same denomination, we can add them easily:

2510025100 size 12{ { {"25"} over {"100"} } } {} +
1010010100 size 12{ { {"10"} over {"100"} } } {} =
3510035100 size 12{ { {"35"} over {"100"} } } {}.

*Same denomination*
*
→
→
size 12{ rightarrow } {}
*
*same denominator*

If the denominators are not the same, make them the same by building up the fractions so that they both have a common denominator. A common denominator can always be found by multiplying all the denominators, but it is not necessarily the Least Common Denominator.