SAT Math For Dummies with Online Practice. Mark Zegarelli
The square root of a negative number is called an imaginary number — that is, a real number multiplied by
Only a few SAT questions include imaginary numbers. You learn more about imaginary numbers in Chapter 12, where I focus on the roots of quadratic functions, and in Chapter 15, where I discuss operations with imaginary numbers.
Complex numbers
The complex numbers are the set of all numbers of the form
The complex numbers include the set of real numbers, the set of imaginary numbers, and other values. Like the rational numbers and real numbers, the complex numbers are closed under the basic four operations. They’re also closed under square roots and a variety of other operations.
Very few questions on the SAT require knowledge of the complex numbers. I discuss the specific points you need to know about them in Chapters 12 and 15.
Fractions, Ratios, Decimals, and Percentages
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.
Review of fractions and ratios
A fraction is composed of two integers: a numerator (top number) divided by a denominator (bottom number). For example:
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The reciprocal (or inverse) of a fraction is the result when you exchange the numerator and denominator. For example:
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Converting between improper fractions and mixed numbers
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
However, if I convert the improper fraction
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
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:
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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.
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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.