﻿ ABSOLUTE VALUE - Basic Arithmetic - TOPICS IN ARITHMETIC - SAT SUBJECT TEST MATH LEVEL 1 ﻿

## CHAPTER 2Basic 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.

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