SAT Math For Dummies with Online Practice. Mark Zegarelli

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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 .

      Finding simplified and increased forms of fractions

      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.

      Adding and subtracting fractions

      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:

      Multiplying and dividing fractions

      Multiplying and dividing fractions is often easier than adding or subtracting them, because you don’t need to find a common denominator.

To multiply two or more fractions, first multiply the numerators across to find the numerator of the answer, then multiply the denominators across to find the denominator of the answer. For example:

      In some cases, you can make multiplying fractions easier by canceling pairs of equivalent factors in the numerator and denominator. For example, when multiplying and , begin by canceling a factor of 4 in both the numerator and denominator:

      Next, cancel a factor of 5:

      Now when you multiply, the result is already the most simplified form of the answer:

      To divide one fraction by another, change the division to multiplication using the mnemonic Keep-Change-Flip: Keep the first fraction as it is, Change the division sign to a multiplication sign, and Flip

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