**Common fractions.**In section 1.2 we introduced the fraction notation,*a*/*b*, where*a*and*b*were both integers to describe a fraction or part of a whole object. For example ¾ meant that we had broken an object into 4 equal parts and we had 3 of those parts. Note that*a*/*b*was a number; the notation*a*/*b*had nothing to do with division. In section 1.2 we also learned how to reduce a fraction to lowest terms, how to add and subtract fractions, multiply fractions, divide fractions, and how to convert an improper fraction to a mixed fraction using long division.

**Division of numbers.**In section 2.4 we defined the division of two numbers in terms of multiplication. We said that dividing*a*by*b*produced a number*c*such that*c*multiplied by*b*gave back*a*. We used the same fraction notation,*a*/*b*, to denote the division of*a*by*b*because when*a*and*b*were both integers, then the division*a*/*b*resulted in the common fraction*a*/*b*. In any other case, though, the division resulted in a real number. In section 2.4 we also learned that the division of*a*by*b*could be replaced by the multiplication of*a*by the reciprocal of*b*. Finally, we learned the rules for division involving minus signs.

**Division of expressions.**In section 3.5 we saw that there were three different ways to divide expressions, depending on whether the numerator,*a*, and denominator,*b*, were monomials, multinomials or polynomials.- If they were monomials, then dividing
*a*by*b*simply amounted to writing down the algebraic fraction,*a*/*b*, and reducing it to lowest terms, just like a common fraction. - If they were polynomials, then
*a*could be divided by*b*using long division, just like an improper common fraction could be converted to a mixed fraction using long division. - If
*a*was a multinomial and*b*was a monomial then we placed*each term of**a*over*b*so that the result of the division was a sum of algebraic fractions.

- If they were monomials, then dividing

What remains to be discussed are

- section 11.1 - In this section we talk about the simplification of algebraic fractions. The main new result is that since we now know how to factor an expression, we can factor a numerator or denominator, and this opens up a new way to reduce an algebraic fraction to lowest terms.
- section 11.2 - In this section we talk about the multiplication and division of algebraic fractions.
- section 11.3 - In this section we talk about the addition and subtraction of algebraic fractions.
- section 11.4 - In this section we show how to solve equations containing algebraic fractions.