# Math Tutorial 1.3 - Operations with Numbers and Properties of Operations

Please provide a rating, it takes seconds and helps us to keep this resource free for all to use

[ 13 Votes ]

There are 5 lessons in this math tutorial covering Operations with Numbers and Properties of Operations. The tutorial starts with an introduction to Operations with Numbers and Properties of Operations and is then followed with a list of the separate lessons, the tutorial is designed to be read in order but you can skip to a specific lesson or return to recover a specific math lesson as required to build your math knowledge of Operations with Numbers and Properties of Operations. You can access all the lessons from this tutorial below.

In this Math tutorial, you will learn:

• What is a mathematical operation? What are the four basic operations used in math?
• What is addition? What are the properties of addition?
• Why we sometimes split an addend in two parts.
• How to add two numbers in a column and in a number line.
• What is subtraction? What is/are the property (ies) of subtraction?
• How is subtraction related to addition?
• How to subtract two numbers in a column and in a number line.
• What is multiplication? What does it have in common with addition?
• What are the properties of multiplication?
• How to do a multiplication in a column?
• What is division? How is it related to multiplication?
• What is/are the property (ies) of division?
• How to make a division operation easier?
• What is the remainder of a division?
• What is "power of numbers"? How is it expressed in exercises?

## Introduction

Items we count by using numbers are changeable. Their number may increase (when we buy extra items at the store), or decrease (when we lose or remove some of them from a collection). On the other hand, from a single item we may obtain a number of identical items (we say the items multiply, (such as the case of fruits when we plant a single fruit seed) or we may obtain a number of pieces when we cut an item into equal pieces like an apple into slices.

All the above situations involve the four basic mathematical operations we use to calculate the new number of items after a process. All these operation and their corresponding properties are explained in this guide.

## Definition of Basic Mathematical Operations

A mathematical operation is a process in which a number or quantity is changed in order to create another number or quantity. For example, if we want to increase the number of participants in an event, we use the addition operation, i.e. we add the number of the new participants to that of the actual ones. On the other hand, if we want to remove some items from a set, we use the subtraction operation for this. Likewise, if we want to make a number of replies (copies) of an item, we multiply them. Finally, if we want to divide an item into equal pieces, we use the division operation.

Put simply, there are four basic mathematical operations: addition, subtraction, multiplication and division. In this tutorial we will discover that this number can be further reduced to only 2 basic operations: addition and multiplication. But first, let's start with the four operations mentioned above.

Please select a specific "Operations with Numbers and Properties of Operations" lesson from the table below, review the video tutorial, print the revision notes or use the practice question to improve your knowledge of this math topic.

Arithmetic Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
1.3Operations with Numbers and Properties of Operations
Lesson IDMath Lesson TitleLessonVideo
Lesson
1.3.1Addition
1.3.2Subtraction
1.3.3Multiplication
1.3.4Division
1.3.5Power of a number

## Whats next?

Enjoy the "Operations with Numbers and Properties of Operations" math tutorial? People who liked the "Operations with Numbers and Properties of Operations" tutorial found the following resources useful:

1. Math tutorial Feedback. Helps other - Leave a rating for this tutorial (see below)
2. Arithmetic Video tutorial: Operations with Numbers and Properties of Operations. Watch or listen to the Operations with Numbers and Properties of Operations video tutorial, a useful way to help you revise when travelling to and from school/college
3. Arithmetic Revision Notes: Operations with Numbers and Properties of Operations. Print the notes so you can revise the key points covered in the math tutorial for Operations with Numbers and Properties of Operations
4. Arithmetic Practice Questions: Operations with Numbers and Properties of Operations. Test and improve your knowledge of Operations with Numbers and Properties of Operations with example questins and answers
5. Check your calculations for Arithmetic questions with our excellent Arithmetic calculators which contain full equations and calculations clearly displayed line by line. See the Arithmetic Calculators by iCalculator™ below.
6. Continuing learning arithmetic - read our next math tutorial: Order of Operation and the PEMDAS Rule

## Help others Learning Math just like you

Please provide a rating, it takes seconds and helps us to keep this resource free for all to use

[ 13 Votes ]

We hope you found this Math math tutorial "Operations with Numbers and Properties of Operations" useful. If you did it would be great if you could spare the time to rate this math tutorial (simply click on the number of stars that match your assessment of this math learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of math and other disciplines.

## Math Calculators

You may also find the following Math calculators useful.