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

13 Multiply using distribution:

14 Multiply using distribution:

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).

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 as “two plus two doesn’t equal five.”

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

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

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.

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,

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.

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:

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

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

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

A. >.Because and 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. 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:

Q.Find an approximate solution to

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