# Whole Numbers: Basic Concepts, Properties, and Applications

## Definition

Whole Numbers is the union set of zero and set of natural numbers (counting numbers/positive integers). It is conventionally denoted with * W*. It can be written as

*{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14...}.*

**W:**## Properties of Whole Numbers

**1. Commutative Property of Addition and Multiplication.** The sum and product of two whole numbers will be the same regardless the order of adding or multiplying them.

Examples:

a. 9 + 3 = 12 ; 3+9=12

b. 5 × 3 = 15 ; 3 × 5 = 15

**2. Closure Property**. The sum or product of two whole numbers is always a whole number.

Examples:

a. 11 + 3 =14

b. 5 × 3 = 15

**3. Additive Property.** Any whole number added to zero (0) remains unchanged. Zero is called the additive identity of whole numbers.

Examples:

a. 19 + 0 = 19

b. 0 + 6 = 6

**4. Multiplicative Identity**. Any whole number multiplied by one (1) remains unchanged. One (1) is a multiplicative identity of whole numbers.

Examples:

a. 13 × 1 = 13

b. 1 × 109 = 109

**5. Multiplication by Zero.** When a number is multiplied by zero (0), the product is always zero.

Examples:

a. 13 × 1 = 13

b. 1 × 109 = 109

**6. Division by Zero.** Division of a whole number by zero is NOT DEFINED.

**7. Associative Property (under addition and multiplication)**. Adding or multiplying whole numbers as a set, regardless of grouping, the sum or product will be the same.

Examples:

a. 13 + (3 + 20) = 36 ; ( 13 + 3 ) + 20 = 36

b. 10 × (9 × 11) = 990 ; (10 × 9) × 11 = 990

**8. Distributive Property of Multiplication .** When multipliying a whole number by the sum or difference of two whole numbers, the result is equal to the sum or difference of each addend multiplied by the third number.

Examples:

a. 10 × (3 + 20) = 230 ; (10 × 3) + (10 × 20) = 230

b. 21 × (33 - 20) = 227 ; (21 × 33) - (21 × 20) = 227

## Place Values

In a whole number, ones place is always the farthest digit to the right. The next farthest to the right is tens digit; followed by hundreds, thousands, and so on. The illustration below shows the place values of digits in a given whole number.

*Example*: Identify the place value of digits in 987 452 139.

9 - hundred millions

8 - ten millions

7 - millions

4 - hundred thousands

5 - ten thousands

2 - thousands

1 - hundreds

3 - tens

9 - ones

## Rounding Off Whole Numbers

Rounding off can be defined as estimating the numbers in the rounded off form instead the exact values. Few steps are followed when rounding whole numbers; you can round up or round down.

1. Find the place value to be rounded off

2. Look the digit at the right of place value to be rounded off

3. i. The digit in the place value to be rounded off remains unchanged if the digit to its right is less than 5; and all digits to its right are changed to zero; digits at the left remain unchanged.

ii. The digit in theplace value to be rounded off is added by one if the digit to its right is 5 or greater; and all digits to its right are changed to zero; digits athe left remain unchanged.

## Comparing Whole Numbers

When comparing whole numbers we use the comparison symbols to show whether a number is greater than, less than, or equal to the another number. Below are the commonly used comparison symbols for intermediate mathematics.

a. Greater than symbol is >.

b. Less than symbol is <.

c. Equal to symbol is =.

Examples:

a. 10 001 > 990

b. 23 < 40,000

c. 45 120 = 45 120

## Ordering Whole Numbers

Ordering whole numbers is simply arranging the whole numbers in ascending or descending order.

Ascending order means the whole numbers are arranged from smallest to largest whole numbers.

Descending order means the whole numbers are arranged from largest to smallest whole numbers.

*Example*: We order/arrange the set of the given whole numbers in ascending and descending order.

*Given*: 2 ; 15; 89; 190 ; 6; 14

**Ascending Order:** 2; 6; 14; 15; 89; 190

**Descending Order**: 190; 89; 15; 14; 6; 2

## Basic Operations on Whole Numbers

**A . Addition on Whole Numbers**

In adding whole numbers, the numbers you are adding up are called addends; the result is called sum.

**B. Subtraction on Whole Numbers **

Terms to subtraction on whole numbers are subtrahend, minuend, and difference.Subtrahend is the number which is to be subtacted from a number. Minuend is the number where a number (subtrahend) is to be subtracted from. Difference is the result of subtracting whole numbers.

**C. Multiplication on Whole Numbers**

Terms related to multiplication on whole numbers are factors and product. Factors are the numbers which are multiplied. Factors are multiplicand and multiplier. Multiplicand is the number which is to be

multiplied by another number (multiplier). The result is called product.

**D. Division on Whole Numbers**

Terms related to division on whole numbers are dividend, divisor, and quotient. Dividend is the number to be divided by another number (divisor). Divisor is the number that divides the dividend. Quotient is the result after dividing the two numbers.

*This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.*

**© 2022 Ryan Bernido**