## SAT SUBJECT TEST MATH LEVEL 1

## TOPICS IN ARITHMETIC

**CHAPTER 2**

**Basic Arithmetic**

**ABSOLUTE VALUE**

The ** absolute value** of a number

*a*, denoted |

*a*|, is the distance between

*a*and 0 on the number line. Since 4 is 4 units to the right of 0 on the number line and –4 is 4 units to the left of 0, both have an absolute value of 4:

• |4| = 4

• |–4| = 4

Since 4 and –4 are the only numbers that are 4 units from 0, if |*x*| = 4, then *x* = 4 or *x* = –4. If |*x*| < 4, then *x* is less than 4 units from 0, which means –4 < *x* < 4. If |*x*| > 4, then *x* is more than 4 units from 0, which means either that *x* < –4 or *x* > 4.

**Remember**

The absolute value of a number is never negative.

**Key Fact A2**

**If b**

**is a positive number, then**

•

•

•

These results are displayed graphically on the three number lines below.

|** x**| =

*b*|** x**| <

*b*|** x**| >

*b*Given any two numbers *x* and *y*, you can *always* find their sum (*x* + *y*), difference (*x* – *y*), product (*xy*), and quotient (*x* *y*)—with your calculator, whenever necessary—except that you may *never divide by zero.* For example, 4 0 is meaningless. If you attempt to divide by 0 on your calculator, you will get an error message.