Whole numbers

The set of whole numbers include the natural numbers and 0. Suppose we call this set W, then W = { 0,1,2,3,4,5,6,......}. Natural number, also called counting numbers, are 1, 2, 3, 4...

The number line below only shows whole numbers from 0 to 10.

However, not all numbers are shown!

50 is also a whole number.

Similarly, 2000 is also a whole number as the following figure shows.

See below two graphs showing what whole numbers are

Whole numbers
Definition of whole numbers

Physical representations of whole numbers

Cubes can be used to represent numbers

 1 cube: physical representation of 1


1 long : physical representation of 10

 Made of 10 cubes.

1 flat : physical representation of 100

 Made of 100 cubes.

One hundred

 1 block: physical representation of 1000

 Made of 1000 cubes.

One thousand

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

What whole 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

Why do we need whole numbers?

Everybody counts, adds or subtracts 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 we need numbers.

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

FourRepresentation of 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 number down using a symbol and we call the symbol a numeral.

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.

What types of numbers are out there besides whole 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

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, division, and many others.

Before knowing how to add, subtract, multiply and so forth, it is important to understand place value. Next, take the quiz and then study the lesson about place value.

Whole numbers quiz. Check your understanding of this lesson.

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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