Teaching Models

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-fourths + two-fourths, three unit fractions of one-fourth plus two unit fractions of one-fourth equals five unit fractions of one-fourth. So the sum is five-fourths.

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.


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

[a/b] + [c/d]

Subtract. [a/b] - [c/d]

Note that for the subtraction of fractions in this chapter, only the case where a over b>c over d is being considered. The study of cases in which a over b<c over d 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.


Add five-sixths + seven-ninths. Write then answer in simplest form. Add by using the product of the denominators as the common denominator.

Add by using the product of the denominators as the common denominator

Add by using the LCM of 6 and 9

Add by using the LCM of 6 and 9

Proper and Improper Fractions
A fraction like five-sevenths is said to be proper because the numerator is less than the denominator. A fraction like four-thirds 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 = five-fifths and 2 = four-halves. The improper fraction four-thirds can be written as the mixed number 1one-third.

Teaching Model 5.3: Add With Unlike Denominators

Houghton Mifflin Math Grade 6