Whole numbers

The set of whole numbers include the natural numbers and 0. Call this set W, then W = { 0,1,2,3,4,5,6,......}




Natural number, also called counting numbers, are 1, 2, 3, 4...

Just so you know, there are other types of numbers.

These are integers, rational numbers, irrational numbers real numbers, and complex numbers.

We will not cover these here, we will only focus on whole numbers in this unit, but be aware that they exist.

If you are really curious, visit the following website: Wikipedia

Everybody counts, add or subtract on a daily basis from the time we started counting toys on the floor when we were 2 or 3 years old to when we count the cost of our groceries.

A child counting cubes for instance may want to know how many cubes the following set has:

4 cubesA representation of the number 4
When we count, we use a number to represent a quantity. A number is an idea that we use to represent that quantity

We write the numbers down using symbols and these are called numerals.

The numeral that we use to represent the set above is   4

When using numbers to count how many elements a set has, it is referred to as cardinal numbers

For instance, 4 or four is a cardinal number

Besides counting how many elements a set has, we use numbers to order objects

Our team is second in group A

I am fifty-sixth in line

The first president of the United States is George Washington

Numbers used in this way are called ordinal numbers

For example, first, second, and fifty-sixth are ordinal numbers

For cardinal numbers, we can use the symbol n(A) to represent the number of elements in a finite set A

For example, the set made of cubes has 4 elements. We can write n(cubes) = 4

If A = {1, 2, 3, 4, 5, 6}, n(A) = 6

If B = {♠,♠,♠,♠,♠,♠,♠,♠,♠}

n(B) = 9



Physical representations of numbers

Cubes can be used to represent numbers

 1 cube: physical representation of 1

1 cube = 1


1 long : physical representation of 10

 Made of 10 cubes.

1 long = 10 cubes  = 10


1 flat : physical representation of 100

 Made of 100 cubes.

1 flat  = 100 cubes  = 100


 1 block: physical representation of 1000

 Made of 1000 cubes.

1 block  = 1000 cubes  = 1000
Let's say you have 4 blocks, 8 flats, 5 longs, and 8 cubes.

What number is this?

1 block represents 1000, so 4 blocks represent 4000

1 flat represents 100, so 8 flats represent 800

1 long represents 10, so 5 longs represent 50

1 cube represents 1, so 8 cubes represent 8

4000 + 800 + 50 + 8 = 4858

Knowing about operations with numbers can be an invaluable tool as we go about our daily routine.

My goal is to help you discover the similarities among addition, subtraction, multiplication, and division.

Before knowing how to add, subtract, multiply and so forth, it is important to understand place value. Now time to take a quiz

Whole numbers quiz. Check your understanding of this lesson.


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Pre-algebra lessons

Place value    
Start with this lesson. Then, study the following lessons in the order listed here from top to bottom.

Reading and writing whole numbers
Learn how to read and write numbers.

Adding whole numbers 
Learn to add numbers with or without regrouping.

Subtracting whole numbers
Learn to subtract numbers with or without regrouping.

Multiplying whole numbers
Learn to multiply numbers with some great illustrations.

Lattice method for multiplication
After you learn the standard multiplication algorithm, entertain yourself with this fun and old way of doing multiplication.

Russian peasant multiplication
Learn to multiply with the Russian peasant algorithm.

Duplication algorithm for multiplication
Learn to multiply with the duplication algorithm.

Dividing whole numbers
Learn to divide numbers with good illustrations.

How to interpret the remainder
Learn 4 ways to interpret the remainder

Finding the average
A crystal clear lesson on how to find the average of numbers.

Weighted mean 
How to find the weighted mean.

Harmonic mean
Find out what the harmonic mean is and how to calculate it.

Even and odd numbers
Learn the difference between even and odd numbers and see formal definitions for even and odd numbers.

Extras topics

Multiplication table

Addition table

Subtraction table




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