Whole Numbers

Open your mind to something exciting -- relearn what you know already, the "whole numbers", in a *refreshing new form*.

Learn about

• *grouping* to form place-value

• *regrouping* or carry over

• *de-grouping* or borrowing

• *First principles* of comparison, addition, subtraction, multiplication, and division

• *Procedural Simplifications* by place-value

• numerical expressions and *precedence order*

Numerals 0 to 9

This page quickly reviews the numbers 0 to 9 and introduces

• digits, numerals, numbers

• numbers given in abstraction

The lesson is critical to properly understand the place-value system and whole number arithmetics. These lessons take hardly $20$ mins. Learners are advised to go through them noting *how numbers are represented with units blocks, tens blocks, hundreds blocks, etc. * This helps in understanding explanation of various concepts in numerical arithmetics.

Large Numbers

This page quickly reviews the numbers from $10$ to $1000$ and introduces *grouping* of $10$ units to $1$ ten. The grouping is further explained to understand units, tens, hundreds, etc. This is an important concept to understand numerical arithmetics.

Expanded form of Numbers

This page introduces concept of 2-digit numbers, 3-digit numbers, etc. The expanded forms in hundreds, tens, units and number in words are explained with examples. For large numbers with 5 digits or more, the Indian and International systems of numbers are explained.

Face and Place Values

This page introduces the face value and the place value of a digit in a number.

Approximation and Estimation

This page introduces approximation of a number to a given degree of approximation. The same is also referred as estimation for measurement of an object.

Comparing two Whole Numbers

In this page, comparing two whole numbers to find one as larger, equal or smaller is explained.

The *comparison in first principles* is explained and it is extended to *comparison as ordered sequence*.

A *simplified procedure based on place-value of large numbers* is explained.

Number-line (Whole Numbers)

This page establishes the concept of smaller or larger between two quantities. The comparison is extended to the numbers in abstraction.

The ordered sequence of whole number and the representation of the order using the *number-line* is discussed.

Predecessor and Successor (Whole Numbers)

It was earlier studied that the numbers are in an ordered sequence. In this page, the predecessor and successor of a number is explained.

Largest or Smallest (Whole Numbers)

In this page, finding largest or smallest number among three or more whole numbers is explained.

Ascending and Descending Orders (Whole Numbers)

In this page, arranging three or more whole numbers in ascending or descending order is explained.

Addition: First Principles

This page explains that combining two quantities and counting or measuring the combined quantity is addition in first principles. Addition is also explained using number-line.

Addition: Simplified Procedure for Large Numbers

This page extends the addition in first principles into a simplified procedure for addition of large numbers, which is called as *addition by place value with regrouping*.

Subtraction: First Principles

This page explains that taking away from a quantity, a part of a quantity is subtraction in first principles. Subtraction is also explained using number-line.

Subtraction: Simplified Procedure for Large Numbers

This page extends the subtraction in first principle into a simplified procedure for subtraction of large numbers, which is called as *subtraction by place value with de-grouping*.

Multiplication: First Principles

This page explains the multiplication in first principles as repetition of a quantity, with examples in count or measure of quantities and in the number-line.

Multiplication : Simplified Procedure for Large Numbers

This page extends the multiplication in first principles into a simplified procedure for multiplication of large numbers, which is called *multiplication by place-value with regrouping*.

Division: First Principles

This page explains the division in first principles as splitting of a quantity, with examples in count or measure of quantities and in the number-line.

Division : Simplified Procedure for Large Numbers

This page extends the division in first principles into a simplified procedure for division of large numbers, which is called *division by place-value with de-grouping*.

Numerical Expressions

In this page, numerical expressions are introduced as statement of a number using multiple numbers and arithmetic operations between the multiple numbers.

Precedence of Arithmetic Operations

In this page, the precedence order of arithmetic operations in a numerical expression is explained. That is, multiplication and division has higher precedence to addition and subtraction.

Sequence in Arithmetic Operations of Same Precedence

In this page, the sequence in arithmetic operations of same precedence in a numerical expression is explained. That is, multiple operations of same precedence are evaluation from left to right.

Brackets Or Parenthesis in Precedence Order

In this page, handling of brackets or parenthesis in a numerical expression is explained. That is brackets have the highest precedence order and expressions inside brackets are evaluated first.