- Topics At a Glance
- Different Types of Numbers
- Natural Numbers
- Whole Numbers
- Integers and Negative Numbers
- Integers and Absolute Value
- Rational Numbers
- Irrational Numbers
- Real Numbers and Imaginary Numbers
- Different Ways to Represent Numbers
- Fractions
- Equivalent Fractions
- Mixed Numbers
- Reducing Fractions
- Comparing Fractions
- Least Common Denominator
- Addition and Subtraction of Fractions
- Multiplication of Fractions
- Equivalent Fractions and Multiplication by 1
- Multiplication by Clever Form of 1
- Multiplicative Inverses
- Division of Fractions
- Multiplication and Division with Mixed Numbers
- Decimals
- Converting Fractions into Decimals
- Converting Decimals into Fractions
- Comparing Decimals
- Adding and Subtracting Decimals
- Multiplication and Division by Powers of 10
- Multiplying Decimals
- Dividing Decimals
- Infinite Decimals
- Percents
- Portion of the Whole
**Things to Do with Real Numbers**- Addition and Subtraction of Real Numbers
- Properties of Addition
- Subtraction
- Multiplication
- Division
- Long Division Remainder
- Exponents and Powers - Whole Numbers
- Properties of Exponents
- Prime Factorization
- Order of Operations
- Even and Odd Numbers
- Infinity
- Sequences
- is Irrational
- Counting Rational Numbers
- Counting Real Numbers?
- Counting Irrational Numbers
- In the Real World
- Decimals in Use
- How to Solve a Math Problem
- I Like Abstract Things: Summary

When comparing real numbers, it can help to think of the number line. Ah, how fondly we remember it. Our favorite line of all the lines.

The numbers on a number line get bigger as we go further right on the number line, and smaller as we go further left on the number line.

So then why doesn't a number line look like this?

Good question. Write your congressman.

All positive numbers are bigger than zero, and all negative numbers are less than zero. Doesn't mean they can't be friends.

Example 1

Since -200 is to the left of 5 on the number line, we say that -200 is less than 5. This is abbreviated in symbols by: |

Example 2

Remember that the absolute value of a number is the number of steps it takes to reach that number from zero. (You can only take one step at a time. We're very impressed that you can jump all the way from 3 to 7 in a single bound, but you're going to have to pull it back a skosh.) |-200| = 200 so, the absolute value of (-200) is greater than 5. Show this as an inequality. |

Example 3

Show n in an inequality if |

Exercise 1

Fill in the blank with <, >, or =.

2 __ 3

Exercise 2

Fill in the blank with <, >, or =.

|-4.5| __ -5

Exercise 3

Fill in the blank with <, >, or =.

-3 __ -2

Exercise 4

Fill in the blank with <, >, or =.

|-17.2| __ 17.2

Exercise 5

Fill in the blank with <, >, or =.

-(-pi) __ pi

Exercise 6

Fill in the blank with <, >, or =.

-4 __ -89

Exercise 7

Suppose *n* is a negative number and *p* is a positive number. Fill in the blank with <, >, or =.

*n __ p *

Exercise 8

Suppose *n* is a negative number and *p* is a positive number. Fill in the blank with <, >, or =.

*n* __ 0

Exercise 9

Suppose *n* is a negative number and *p* is a positive number. Fill in the blank with <, >, or =.

*p* __ 0

Exercise 10

Suppose *n* is a negative number and *p* is a positive number. Fill in the blank with <, >, or =.

|*p*| __ *p *

Exercise 11

Suppose *n* is a negative number and *p* is a positive number. Fill in the blank with <, >, or =.

|*n*| __ *n *