How to add and subtract fractions

How to add and subtract fractions

Addition

Example 1
: In this example fractions 1/3 + 1/3 may be combined to give (1 + 1) / 3 since they have the same denominator, the new numerator is the sum of the old numerators, the new denominator is the common denominator 3.

Example 2:

In this example fractions 1/2 + 1/3 can not be combined as in example 1 because they do not have the same denominator. Fractions 1/2 and 1/3 have the least common denominator (LCD) of 6. Therefore, fraction 1/2 has to be multiplied by 3/3 to make 3/6 and fraction 1/3 has to be multiplied by 2/2 to make 2/6.

Subtraction

Example 1

In this example fractions 2/3 - 1/3 may be subtracted to give (2 - 1) / 3 since they have the same denominator, the new numerator is the difference of the old numerators, the new denominator is the common denominator 3.

Example 2:

In this example fractions 1/2 - 1/3 can not be subtracted as in example 1 because they do not have the same common denominator. Fractions 1/2 and 1/3 have the least common denominator (LCD) of 6. Therefore, fraction 1/2 has to be multiplied by 3/3 to make 3/6 and fraction 1/3 has to be multiplied by 2/2 to make 2/6.

Example 3:
In this example fractions 1/2 - 1/9 - 1/6 have the least common denominator (LCD) of 2 x 3 x 3 = 18. Therefore, fraction 1/2 has to be multiplied by 9/9 to make 9/18. Fraction 1/9 has to be multiplied by 2/2 to make 2/18 and fraction 1/6 has to be multiplied by 3/3 to make 3/18.

Example 1 :	In this example fractions 1/3 + 1/3 may be combined to give (1 + 1) / 3 since they have the same denominator, the new numerator is the sum of the old numerators, the new denominator is the common denominator 3.

Example 2:	In this example fractions 1/2 + 1/3 can not be combined as in example 1 because they do not have the same denominator. Fractions 1/2 and 1/3 have the least common denominator (LCD) of 6. Therefore, fraction 1/2 has to be multiplied by 3/3 to make 3/6 and fraction 1/3 has to be multiplied by 2/2 to make 2/6.

*Example 1*	In this example fractions 2/3 - 1/3 may be subtracted to give (2 - 1) / 3 since they have the same denominator, the new numerator is the difference of the old numerators, the new denominator is the common denominator 3.
*Example 2:*	In this example fractions 1/2 - 1/3 can not be subtracted as in example 1 because they do not have the same common denominator. Fractions 1/2 and 1/3 have the least common denominator (LCD) of 6. Therefore, fraction 1/2 has to be multiplied by 3/3 to make 3/6 and fraction 1/3 has to be multiplied by 2/2 to make 2/6.
*Example 3:*	In this example fractions 1/2 - 1/9 - 1/6 have the least common denominator (LCD) of 2 x 3 x 3 = 18. Therefore, fraction 1/2 has to be multiplied by 9/9 to make 9/18. Fraction 1/9 has to be multiplied by 2/2 to make 2/18 and fraction 1/6 has to be multiplied by 3/3 to make 3/18.