- 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

If someone lived in ancient Egypt and wanted to count how many cats she had (cat ladies were in large supply back then), all she would need in order to do so would be the set of **natural numbers**, also known as **counting numbers**. These are, as the second name implies, the numbers 1, 2, 3, 4, etc. These numbers are very useful for counting things, as you might imagine. Who would've guessed, right? We'll try to make things a bit more interesting from here on out.

**Natural Numbers on a Number Line**

Let's try to answer the following questions using just the natural numbers:

John has 3 sheep. Mary gives him 4 more sheep. How many sheep does John have now? Do a little addition, and 3 + 4 = 7. Don't worry about Mary though...she held onto a little lamb.

John has 5 goats. He gives Mary 2 goats. How many goats does John have now? Answer: 5 - 2 = 3 goats. And he's got those listed on eBay, so hopefully he will soon be 100% goat-free.

John has 5 cows. He gives Mary 5 cows. How many cows does John have?

Whoa, there, Bessie! Before you get a little too cocky and start shouting "zero" from the rooftops (which is dangerous, by the way...why not just open a window?), notice that 0 is not a counting number. We can't really answer this question as written. Unfortunately, in order to list 0 as an answer, we would need to be able to include **whole numbers**, which aren't all that different from natural numbers. Read on...