## Add and Subtract Fractions

In dealing with operations with fractions in this chapter, only whole numbers are considered as numerators and denominators. The use of integers or other fractions are much more advanced concepts. However, the concepts and rules for operations on fractions also hold true for rational numbers and complex fractions. Thus, it is important for students to understand operations with fractions.

**Addition and Subtraction of Fractions**

To add or subtract fractions with a common denominator, find the sum or difference of the numerators and keep the common denominator. For example, in + , three unit fractions of plus two unit fractions of equals five unit fractions of . So the sum is .

When adding and subtracting fractions with unlike denominators, a common denominator must be found. One way to find a common denominator is to use the product of the denominators.

Examples:

Add + where b ≠ 0, d ≠ 0 (because division by 0 is undefined)

Subtract.

Note that for the subtraction of fractions in this chapter, only the case where > is being considered. The study of cases in which < is left to a more advanced study of rational numbers.

Using the least common multiple of the denominators to get the least common denominator is another way of adding or subtracting fractions.

Example:

Add + . Write then answer in simplest form. Add by using the product of the denominators as the common denominator.

Add by using the LCM of 6 and 9

**Proper and Improper Fractions**

A fraction like is said to be proper because the numerator is less than the denominator. A fraction like is said to be improper because the numerator is not less than the denominator. Whole numbers can also be written as improper fractions, such as 1 = and 2 = . The improper fraction can be written as the mixed number 1.

**Teaching Model 5.3:** Add With Unlike Denominators