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Addition: Whole Numbers

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Addition: Whole Numbers

Study Guide

Key Definition

Addition of whole numbers is simply combining two or more numbers or objects to find a total. The numbers (or objects) are called 'terms' or 'addends', and the total is called the 'sum'.

Important Notes

Addition is a fundamental operation in mathematics
Addition is commutative, meaning the order of the numbers does not change the result
Addition is associative, meaning the way the numbers are grouped does not change the result
The identity element for addition is zero, because adding zero to any number does not change the number
In the broader set of integers (which includes negative numbers), each number has an additive inverse (its negation), because adding a number and its inverse results in zero

Mathematical Notation

The '+' symbol represents addition

The '=' symbol represents equality

The '∑' (sigma) symbol represents the sum of a series of numbers

Remember to use proper notation when solving problems

Why It Works

When you add two whole numbers, you can think of placing them on a number line: start at the first number and move right one step for each unit in the second number. This counting process shows why the result is the total of both quantities.

Remember

The order of numbers does not matter in addition (commutative property), and adding zero to any number leaves the number unchanged (identity property).

Quick Reference

Commutative Property:$a + b = b + a$

Associative Property:$(a + b) + c = a + (b + c)$

Identity Property:$a + 0 = a$

Understanding Addition: Whole Numbers

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Addition means putting two groups together and counting all items. For example, if you have 2 apples and get 3 more, you count 2, 3, 4, 5, so the total is 5.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the sum of $5$ and $7$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have $5$ apples and your friend gives you $3$ more. How many apples do you have now?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If you add a number to its negative, what do you get?

Challenge Quiz

Single Choice Quiz

Advanced

What is the sum of all the numbers from $1$ to $100$?

Recap

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Review key concepts and takeaways