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Addition: First Principles


    what you'll learn...

overview

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

The same is abstracted for addition in number-line. add 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

add two numbers

There are 3 red cars and 4 blue cars in the figure. These cars are combined together and the total number of cars are counted.

add two numbers

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.

add two numbers

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

add two numbers

The two pencils are placed side-by-side. The length measurements is taken from
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.

add two numbers

Addition 3+4 is given in number-line. The count is started from 3. 4 jumps are made to land in 7. The result of the addition is 7.

addend and sum

The English word addition means: combining two quantities and measuring or counting the combined quantity.

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

addend is the number that is added to, and also the number that is being added.

sum is the result of the addition.


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