Number and Arithmetic (Mathematics Curriculum)

Arithmetic

What Is Arithmetic?

Arithmetic is a branch of mathematics that studies numbers and the operations applied to numbers.

Dictionary Definition

The Oxford English Dictionary defines arithmetic as "the science of numbers; the art of computation by figures."
Here are some examples from arithmetic. We might be interested in adding, subtracting, multiplying and dividing numbers. We might be interested in doing several of these and have to do them in the correct order. Arithmetic allows us to do this.

arithmetic examples

Where Does the Word Arithmetic Come From?

Arithmetic comes from the Greek word "arithmētikḗ" meaning “counting”. 'Arithmos' is the Greek word for "number".

The Curriculum

The lessons are grouped into mini-curriculum to help you organise your learning. A brief description is given for each mini-curriculum. Click the MORE button to learn more.

Operations and Their Order

arithmetic about operations

Operations take numbers to create a new number. The most common operations in arithmetic are adding, subtracting, multiplying and dividing. In this mini-curriculum, you will learn about operations.

Operation
An operation takes values and calculates a new value from them.
The basic operations in arithmetic are addition, subtraction, multiplication and division.
arithmetic operations

Inverse Operations
An inverse operation is the opposite of an operation. It reverses an operation.
The inverse operation of addition is subtraction, and vice versa.
arithmetic addition subtraction inverse operations
The inverse operation of multiplication is division, and vice versa.
arithmetic multiplication division inverse operations

Order of Operations
The order of operations tells us what order to perform operations in.
arithmetic order of operations

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operations
inverse operations
the order of operations

Advanced Arithmetic

arithmetic advanced

When numbers get larger than a single numeral, we must use place value and 'long' arithmetic. In this mini-curriculum, you will learn about place value, long addition, long subtraction, long multiplication and long division.

Place Value
Place value tells us the value of a digit depending on what place it is in a number.
The same digit can have a different value depending on its place value.
A 1 placed here has a value of one.
arithmetic place value 1

A 1 placed a column to the left (before a 0) has a value of ten.
arithmetic place value 10

Long Addition
Numbers with more than one digit can be added using long addition.
arithmetic long addition

Long Subtraction
Numbers with more than one digit can be subtracted from each other using long subtraction.
arithmetic long subtraction

Long Multiplication
Numbers with more than one digit can be multiplied using long multiplication.
arithmetic long multiplication

Long Multiplication with Decimals
When numbers have a decimal point in them, they can be multiplied using long multiplication with decimals.
arithmetic long multiplication decimals

Long Division
Numbers with more than one digit can be divided using long division.
arithmetic long division

Long Division with a Remainder
Sometimes, a number will not divide exactly into another: there will be a remainder.
arithmetic long division remainder

Long Division with Decimals
When numbers have a decimal point in them, they can be divided using long division with decimals.
arithmetic long division decimals

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place value
long addition
long subtraction
long multiplication
long multiplication with decimals
long division
long division with a remainder
long division with decimals

Factors

arithmetic about factors

The factors of a number are those numbers that multiply to make that number. They divide exactly into the number. In this mini-curriculum, you will learn about factors.

Factor
A factor is a number which divides exactly into another number. The numbers that are multiplied together to make another number are factors.
2 and 3 are factors of 6 because they multiply to make 6.
arithmetic factors

Find Factors
To find the factors of a number, find pairs of numbers that multiply to make that number.
arithmetic find factors

Greatest Common Factor
The greatest common factor is the largest factor that is common to two or more numbers.
arithmetic greatest common factor

Find the Greatest Common Factor
To find the greatest common factor, list the factors of both numbers and find the largest number that appears in both lists.
Here is an example that shows that the greatest common factor of 4 and 6 is 2.
arithmetic find greatest common factor

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factors
how to find factors
the greatest common factor
how to find the greatest common factor

Multiples

arithmetic about multiples

Multiples are the result of multiplying a number by another whole number. In this mini-curriculum, you will learn about multiples.

Multiples
A multiple is the result of multiplying a number by an integer (a whole number).
The multiples of 3 are found by multiplying 3 by the integers: 1, 2, 3, 4, 5...
arithmetic multiples

Least Common Multiple
The least common multiple is the smallest multiple that is common to two or more numbers.
The multiples of 3 are found by multiplying 3 by the integers: 1, 2, 3, 4, 5...
arithmetic multiples

Find the Least Common Multiple
To find the least common multiple, list the multiples of both numbers and find the least number that appears in both lists.
Here is an example that shows that the least common multiple of 3 and 4 is 12.

Multiples of 3 = 3, 6, 9, 12, 15...
Multiples of 4 = 4, 8, 12, 16, 20...

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multiples
the least common multiple
how to find the least common multiple

Powers

arithmetic about powers

Powers are the result of multiplying a number by itself. In this mini-curriculum, you will learn about the parts of powers.

Powers
A power is the product of multiplying a number by itself. Here is an example of a power:
arithmetic power
This is 3 squared. 3 is multiplied by itself 2 times.

Base
The base is part of a power. It is the number that is multiplied by itself.
In our example, 3 is the base:
arithmetic base

Exponent
The exponent is part of a power. It tells you how many times a number is multiplied by itself.
In our example, 2 is the exponent:
arithmetic exponent

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powers
bases
exponents

Laws of Exponents

arithmetic about laws of exponents

The laws of exponents lets you do arithmetic with powers. In this mini-curriculum, you will learn about the laws of exponents.

Laws of Exponents
The laws of exponents are rules for using exponents. They tell us how to do arithmetic with powers.
arithmetic laws of exponents

Multiplying Powers
When the same numbers with different exponents are multiplied together, the exponents can be added.
arithmetic multiply exponent

Dividing Powers
When the same numbers with different exponents are divided, the exponents can be subtracted.
arithmetic divide exponent

Powers of Powers
A power of a power is where a number with an exponent is itself raised to an exponent. When a number with an exponent is raised to another exponent, the exponents can be multiplied.
arithmetic raise exponent

Negative Exponent
A number with a negative exponent is equal to 1 divided by the number with the exponent made positive.
arithmetic negative exponent

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the laws of exponents
how to multiply powers
how to divide powers
how to find a power of a power
how to find negative exponents

Reciprocals

arithmetic about reciprocals

Reciprocals of a number are 1 divided by the number. They can be denoted by an exponent of −1. In this mini-curriculum, you will learn about reciprocals.

Reciprocals
The reciprocal of a number is the result of dividing 1 by that number.
arithmetic reciprocals

Exponent of −1
A number with an exponent of −1 is equal to 1 divided by the number.
arithmetic exponent_-1

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reciprocals
an exponent of −1

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This page was written by Stephen Clarke.