## Add and Subtract Fractions

**Comparison of Fractions**

Which is greater, or ? When comparing fractions with like denominators, it is enough to compare the numerators. Since 4 unit fractions of is greater than 3 unit fractions of , is greater than . Which is greater, or ? When comparing fractions with unlike denominators, it is usually necessary to find a common denominator. In the example, any common multiple of 12 and 8 will do. For simplicity, choose 12 × 8 = 96.

Since 60 > 56, > .

Now, = 7 × × 8 = and = 5 × × 12 = .

Should students want to use only the least common denominator, suggest they try it both ways and decide for themselves which method is quicker or easier.

**Mixed Numbers**

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: 1 = and 2 = . The improper fraction can be written as the mixed number 1.

**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. Answers should be expressed in simplest form.

For example, in + , three unit fractions of plus two unit fractions of equals five unit fractions of . So the answer is , or 1 . In − , one unit fraction of is subtracted from three unit fractions of giving a result of two unit fractions of . So the answer is , or .

**Teaching Model 20.2:** Add and Subtract Mixed Numbers