On this page, we hope to clear up problems that you
might have with fractions and their uses in Algebra. Fractions
are continually being utilized in math, so they're quite
an important subject to understand. Click any
of the links below to start understanding fractions better!
LCM, or Lowest Common Multiple
Addition of fractions
Quiz on Fractions
In this section we will help you understand how to multiply fractions that contain rational expressions (expressions containing variables). If you still need help with fractions that only contain numbers, click here.
When fractions are multiplied, they are multiplied by multiplying the numerators by each other and the denominators by each other. No cross-multiplication is involved! Always remember that variables stand for numbers! Because of that fact, nothing changes when dealing with variables in a multiplication problem with fractions that have rational expressions in them.
_ _ 1. Expand: x^2| x^2 3y^3 | ---| --- - ---- | y^2|_ y m _|
or subtracting fractions from other numbers, and especially other
fractions, you must have the denominators of each fraction be
the same expression. Addition and subtraction are discussed
further down on this page, but we will help you understand
the Lowest Common Multiple in this section.
1. Find the LCM of 15a2b and 10ab3.
The addition or subtraction of fractions is complicated by the fact that the denominators must be the same before the fractions can be added or subtracted. As we move toward more complex Algebra, you will come across fractions that have polynomials in them. If the denominator is a polynomial, this polynomial must be a factor in the least common multiple.
1. Add: a b - + ------- x (x + y) Solution: First, find the LCM of the denominators, which will become the new denominator. -------- + -------- x(x + y) x(x + y) So that the problem does not change, the numerator of each term has to be multiplied by the same quantity that its respective denominator was. The original denominator of the first term was x, and it has been multiplied by (x + y), so the original numerator, a, must be multiplied by (x + y), too. a(x + y) -------- + -------- x(x + y) x(x + y) The original denominator of the second term was (x + y), but it was multiplied by x, so the original numerator must also be multiplied by x. Now, the fractions can be added together. a(x + y) xb a(x + y) + xb -------- + -------- = ------------- x(x + y) x(x + y) x(x + y) This is one of the rare times in Algebra that there are multiple forms of the correct answer. In this case, you can multiply out the numerator and/or denominator if you want, and since doing that does not help you simplify the answer any further, they are also correct forms of the answer.
for a fraction divided by a fraction is a complex fraction. Complex
fractions are typically shown as follows:
1. Simplify: a - b --- c (b, c do not equal 0)
Take the Quiz on fractions. (Very useful to review or to see if you've really got this topic down.) Do it!