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

Автор: Mark Zegarelli

Издательство: John Wiley & Sons Limited

Жанр: Математика

Серия:

isbn: 9781119867265

isbn:

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Understanding Inequalities

Sometimes you want to talk about when two quantities are different. These statements are called inequalities. In this section, I discuss six types of inequalities: ≠ (doesn’t equal), < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), and ≈ (approximately equals).

Doesn’t equal (≠)

The simplest inequality is ≠, which you use when two quantities are not equal. For example,

You can read ≠ as “doesn’t equal” or “is not equal to.” Therefore, read math as “two plus two doesn’t equal five.”

Less than (<) and greater than (>)

The symbol < means less than. For example, the following statements are true:

Similarly, the symbol > means greater than. For example,

Tip The two symbols < and > are similar and easily confused. Here are two simple ways to remember which is which:

Notice that the < looks sort of like an L. This L should remind you that it means 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:

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

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,

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

Example Q. 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.

A. math Sam worked 7 hours for $8 an hour, so here’s how much he earned:

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:

Now it’s easy to add math

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

(a) math

(b) math

(c) math

(d) math

16 Change the ≠ signs to either > or <: