Mark Zegarelli - SAT Math For Dummies with Online Practice

Fractions, ratios, decimals, and percentages are four complementary ways of describing rational numbers — that is, the values that lie between the integers on the number line. In this section, you get a quick review of how to work with these important mathematical values.

A fraction is composed of two integers: a numerator (top number) divided by a denominator (bottom number). For example:

The reciprocal (or inverse ) of a fraction is the result when you exchange the numerator and denominator. For example:

A proper fraction has a numerator that’s less than its denominator. In contrast, an improper fraction has a numerator that’s greater than or equal to its denominator.

Improper fractions can be awkward, because in many real-world cases, an improper fraction doesn’t provide easy-to-understand numerical information. For example, if I tell you that I bought gallons of gasoline, you may have a hard time interpreting that information.

However, if I convert the improper fraction to its mixed number of , you now know that I bought a little more than 9 gallons.

To change an improper fraction to a mixed number, divide the numerator by the denominator. If the result has a remainder, use the remainder as the numerator of the answer. For example, to convert to a mixed number, divide , so .

To convert a mixed number to an improper fraction, multiply the denominator by the whole number, add the numerator, and then use this number as the numerator of the answer. For example, to convert to an improper fraction, calculate , so .

Sometimes when a fraction has a large numerator and denominator, you can simplify it by dividing both of these numbers by the same value, resulting in an equivalent fraction. For example:

The most simplified form of a fraction is usually the form that an SAT answer will take.

You can also reverse this process to increase the denominator of a fraction by multiplying the numerator and denominator by the same value.

Increasing the denominator of a fraction is often useful for adding and subtracting fractions, which I discuss in the next section.

When a pair of fractions both have the same denominator, you can add or subtract them by adding or subtracting their numerators and keeping the denominator the same. For example:

When a pair of fractions have different denominators, you need to get the denominators the same — that is, find a common denominator for both fractions. In some cases, you can do this by increasing the lesser denominator to the greater one. For example:

In other cases, you need to increase the denominators of both fractions. For example: