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Power of a Power Property of Exponents
Adding and Subtracting Rational Numbers
Point
Solving Equations with Radicals and Exponents
Quadratic Equations
Using Intercepts for Graphing Linear Equations
Graphing Linear Equations in Two
Exponents
Multiplying Fractions
Solving Linear Equations Containing Fractions
Evaluating Polynomials
Multiplication Property of Square and Cube  Roots
Writing a Fraction in Simplest Form
Square Roots
Inequalities
The Pythagorean Theorem
Factoring The Difference of 2 Squares
Solving Polynomial Equations
Roots and Powers
Writing Linear Equations in Standard Form
Solving Nonlinear Equations by Substitution
Straight Lines
The Square of a Binomial
Solving Equations
Adding and Subtracting Like Fractions
Point
Finding the Equation of an Inverse Function
Slope of a Line
Rules for Nonnegative Integral Exponents

Writing a Fraction in Simplest Form

In the preceding section, we showed that and are equivalent fractions. Note that we could have written in its simplest form by dividing its numerator and denominator by 4.

To Simplify (Reduce) a Fraction

such as divide its numerator and denominator by the same number.

neither b nor n is 0

A fraction is said to be in simplest form (or reduced to lowest terms) when the only common factor of its numerator and its denominator is 1.

EXAMPLE 9

Express in simplest form.

Solution

To reduce this fraction, we can divide both its numerator and its denominator by 3.

To be sure that we have not made an error, let's check whether the cross products are equal:

3 · 5 = 15 and 1 · 15 = 15.

To reduce a fraction to lowest terms, we divide the numerator and denominator by all the factors that they have in common. To find these common factors, it is often helpful to express both the numerator and denominator as the product of prime factors. We can then divide out or cancel all common factors.

EXAMPLE 10

Write in lowest terms.

Solution

Express the numerator and denominator as the product of primes.

Cancel the common factors, noting that 1 remains.

Multiply the remaining factors.

EXAMPLE 11

Suppose that your annual income is $39,000. If you pay $9,000 for rent and $3,000 for food per year, rent and food account for what fraction of your income? Simplify your answer.

Solution

You must first find the total part of the income that you pay for rent and food per year.

The total part is $12,000 and the whole is $39,000, so the fraction is . You can simplify this fraction in the following way.

Note that canceling a 0 is the same as dividing by 10.

Therefore of your income goes for rent and food.