Basic Math & Pre-Algebra All-in-One For Dummies (+ Chapter Quizzes Online). Mark Zegarelli

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Basic Math & Pre-Algebra All-in-One For Dummies (+ Chapter Quizzes Online) - Mark  Zegarelli


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less than.

       Remember that, in any true statement, the large open mouth of the symbol is on the side of the greater amount, and the small point is on the side of the lesser amount.

      Less than or equal to (≤) and greater than or equal to (≥)

      The symbol ≤ means less than or equal to. For example, the following statements are true:

math

      Similarly, the symbol ≥ means greater than or equal to. For example,

math

      Tip The symbols ≤ and ≥ are called inclusive inequalities because they include (allow) the possibility that both sides are equal. In contrast, the symbols < and > are called exclusive inequalities because they exclude (don’t allow) this possibility.

      Approximately equals (≈)

      In Chapter 3, I show you how rounding numbers makes large numbers easier to work with. In that chapter, I also introduce ≈, which means approximately equals.

      For example,

math

      You can also use ≈ when you estimate the answer to a problem:

math

      ExampleQ. Place the correct symbol (=, >, or <) in the blank: math

      A. <. Because math is less than 5, use the symbol that means is less than.

      Q. Place the correct symbol (=, >, or <) in the blank: math

      A. >. Because math and math is greater than 20, use the symbol that means is greater than.

      Q. Sam worked 7 hours for his parents at $8 an hour, and his parents paid him with a $50 bill. Use the symbol ≠ to point out why Sam was upset.

math

      He was upset because his parents didn’t pay him the correct amount: math

      Q. Find an approximate solution to math

      A. 8,000,000. The two numbers are both in the millions, so you can use ≈ to round them to the nearest million:

math

      Now it’s easy to add math

      15Your turn Place the correct symbol math in the blanks:

      (a) math

      (b) math

      (c) math

      (d) math

      16 Change the ≠ signs to either > or <:

      (a) math

      (b) math

      (c) math

      (d) math

      17 Tim’s boss paid him for 40 hours of work last week. Tim accounted for his time by saying that he spent 19 hours with clients, 11 hours driving, and 7 hours doing paperwork. Use ≠ to show why Tim’s boss was unhappy with Tim’s work.

      18 Find an approximate solution to 10,002 − 6,007.

      In this section, I introduce you to three new operations that you need as you move on with math: exponents, square roots, and absolute value. As with the Big Four operations, these three operations tweak numbers in various ways.

      Understanding exponents

      Exponents (also called powers) are shorthand for repeated multiplication. For example, math means to multiply 2 by itself three times. To do that, use the following notation:

math

      In this example, 2 is the base number and 3 is the exponent. You can read math as “2 to the third power” or “2 to the power of 3” (or even “2 cubed,” which has to do with the formula for finding the volume of a cube — see Chapter 19 for details).

      Here’s another example:

math

      That works out like this:

math

      This time, 10 is the


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