Addition: First Principles

overview

This page introduces addition of whole numbers as combining two quantities and counting or measuring the combined quantity.
Counts of 33 and 44 are combined together and the counting is done from 11 to 77. The resulting count is 77
Measures of 33 and 4 are combined together. The measure of combined quantity is 7

The same is abstracted for addition in number-line.
The definition of addition in first principles forms the basis to understanding the simplified procedure for addition of large numbers.

combine them

There are 3 red cars and 4 blue cars in the figure. These cars are

Considering the figure with 3 red cars and 4 blue cars. 3 and 4 are combined together and the counting is done from 1 to 7. The resulting count is 7.

A red pencil is 3 centimeters in length. A green pencil is 4 centimeters in length.

The two pencils are

0 and the measure at the end is 7.

The count or measure of quantities can be combined or *added*.

The *addition* results in count or measure of the combined quantity.

Addition 3+4 is given in

addend and sum

The English word

**Addition - First Principles** : Two numbers are considered, each of which represents a count or measurement. The quantities represented by the numbers are combined to form a result representing a combined count or measurement. The combined count or measurement is the result of addition.

eg: 20 and 13 are combined together 20+13=33.

20 is an addend

13 is also an addend

33 is the sum

What is the sum of 4 and 2?

The answer is '6'.

summary

**Addition - First Principles** : Two numbers are considered, each of which represents a count or measurement. The quantities represented by the numbers are combined to form a result representing a combined count or measurement. The combined count or measurement is the result of addition.

eg: 20 and 13 are combined together 20+13=33.

20 is an *addend*

13 is also an *addend*

33 is the *sum*

Outline

The outline of material to learn whole numbers is as follows

Note: * click here for detailed outline of Whole numbers *

• Introduction

→ __Numbers__

→ __Large Numbers__

→ __Expanded form__

→ __Face and place values__

→ __Approximation and Estimation__

• Comparison

→ __Comparing two numbers__

→ __Number line__

→ __Predecessor & Successor__

→ __Largest & Smallest__

→ __Ascending & Descending__

• Addition Subtraction

→ __Addtion: First Principles__

→ __Addition: Simplified Procedure__

→ __Subtraction: First Principles__

→ __Subtraction: Simplified Procedure__

• Multiplication Division

→ __Multiplication: First Principles__

→ __Multiplication: Simplified Procedure__

→ __Division: First Principles__

→ __Division: Simplified Procedure__

• Numerical Expression

→ __Introducing Numerical Expressions__

→ __Precedence__

→ __Sequence__

→ __Brackets__