Whole Numbers: Whole number is collection of positive numbers and zero. Whole number also called as integer. The whole number is represented as {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ….}.

The opposite of whole numbers are negative numbers. The representation of negative number is {-1, -2, -3, -4, -5, -6, -7, -8, -9..}

## What is a Whole Number?

Let us learn what are whole numbers, whole numbers are a group of zero and positive integers. Integer is the another name of whole number. Negative numbers are opposites of whole numbers. The positive integer use ‘+’ symbol to represent the term positive. Addition, subtraction, multiplication and division operations are activities of whole number.

**Brief history of Whole numbers**

Here we could see brief history of whats a whole number. Through out the history of recorded history people have used various symbols and numerals to represent numbers.

- The Aztecs from Central and South America have used fir trees, dots and flags to represent numbers.
- The Egyptians used pointed fingers, polliwogs and lotus flowers, while the Indian continent came out with the numbers that we know today 1, 2, 3 …which were brought to Europe by the Arabs.
- The Romans used symbols like I, II, III and Iv to represent 1, 2, 3, 4….which are still in vogue.

**How to read large numbers?**

- We need to begin at the right and make as many groups of three digits as we can by placing commas in between.
- To read the number, we need to read the number farthest left and then say the name of the group first. eg 4, 352,221; we would begin saying 4 millions.
- Now we have to read the number in the next group, three hundred fifty-two thousands.
- When we reach the last group, we just need to read the number in that group without saying the name of that group, two hundred twenty two.

We can do following activities between the whole numbers:

- Addition
- Subtraction
- Multiplication
- Division

## Table of Contents

## Whole Number Definition

Let W be the set of whole number as W = { 0, 1, 2, 3,…..}. The set of whole numbers may be finite or infinite. The finite defines the numbers in the set are countable. Infinite set means the numbers are uncountable.

The whole numbers are well-ordered contains only positive integers. The whole numbers can be represented as small alphabetic letters.

Example let a, c, m be three whole numbers. The whole numbers can be used for counting and ordering.

## Is 0 a Whole Number?

Is zero a whole number? Yes, if we are referring to the non-negative integers or all integers. Zero is neither a fraction nor a decimal, so zero is an whole number.

Below you could see one of the following sense:

- Positive Integers ( 1, 2, 3,…..)
- All Integers ( ….,-3, -2, -1, 0, 1, 2, 3,…)
- The not quite Whole integer (0.999…)

## Adding Whole Numbers

Addition is what we do with some objects, put them together and come up with a sum or total. The total or sum tells us how many things were there in all and to get the total we need to count the objects.

### Procedure for Adding Whole Numbers

- Step 1: Add the one’s place number and take the carry to the next step.
- Step 2: Add the ten’s place number and also add the carry and over the new carry to the next step. Continue this process for every place in the given number.

Below you could see handy rules for addition and column of number

**Handy rules for Addition:**

- Add the rightmost column. If this column contains only one digit, we just write that digit under the column we are adding.
- We need to go on to the next column and repeat the same procedure.

**Handy rules for column of numbers:**

- Look at the column of numbers.
- Break them up into several small parts.
- Add each part separately.
- Check each total and add the sub-total.

**Adding Whole Numbers Practice Problems**

**Question 1: **A garden pipe of length 13 meters is added to another pipe of length 29 meters. What is the new length of the pipe?

**Question 2: **A music concert group went to Kansas city and the first day there were 2,139 people who attended the program. The next day 3,309 people attended the programmer. The last day the crowd swelled to 9,219. What is the total number of people who attended the concert in all together?

**Question 3: **Nancy and Carole wanted to buy a gift for their mother for her birthday. Each of them saved $ 24 and pooled it together to buy the gift. How much is the amount they could make use of to buy the gift?

## Subtracting Whole Numbers

Subtraction is the process of finding the difference, or remainder between two numbers or quantities. The subtraction operation is used to subtract two numbers and its symbol is represented as “-“.

### Procedure for Subtracting Whole Numbers:

- Step 1: Subtract the one’s place numbers. If minuend number is greater than subtrahend number we follow the process or else borrow from the next place number.
- Step 2: Subtract the ten’s place numbers. If minuend number is greater than subtrahend number we follow the process or else borrow from the next place number. Continue this process for every place in the given number.

Below you could see handy rules for subtraction of whole numbers

Handy rules for Subtraction Whole Numbers :

- The number to be subtracted (subtrahend) is placed under the number to be subtracted from (minuend) with both numbers aligned on the right side column.
- The subtraction is started from right by subtracting the bottom number from the top number.
- If the number being subtracted is larger than the number it is subtracted from then we need to borrow 1 from the digit to the left and add ten to the number that is too small.
- We need to subtract 1 from the digit used for borrowing before using it to subtract the number below it.

**Subtracting Whole Numbers Practice Problems**

**Question 1: **Clarence went for weight loss programme. Before the programme began she weighed 244 pounds. After one month of the programme she weighed around 165 pounds. What is the weight lost in that month?

**Question 2:** Rebecca was getting $2314 as her monthly salary. After her salary hike she is getting $4125. What is the difference in hike?

## Multiplying Whole Numbers

Multiplying whole numbers means scaling a number by another. Multiplication is a simple way of repeated addition. Multiplication method is defined as multiplying more than one number.

### Procedure for Multiplying whole numbers:

- Step 1: Multiply the multiplicand by one’s place value of multiplier.
- Step 2: Multiply the multiplicand by ten’s place value of multiplier. Continue this process for every place elements of multiplier.
- Step 3: Finally add the results.

Below you could see a handy rules for multiplication of whole numbers

**Handy rules for Multiplication of Whole Numbers:**

- To multiply numbers, write the numbers to be multiplied or multiplicand first.
- We need to take the bigger of the two numbers as the multiplicand.
- Write the multiplier under the multiplicand aligning both the numbers on the right side.
- If the product is greater than 9, we need to carry the digit above 9 to the next column to the left and added to the product of that column.
- After all the multipliers are used the product obtained is aligned under that multiplier and added together.

**Multiplying Whole Numbers Practice Problems**

**Question 1:** A car travels 65 miles in one hour. How many miles will it travel in 9 hours?

**Question 2:** A fisherman on an average catches 1500 pounds of sardines every day. What will be the total catch after the end of 5 days?

## Dividing Whole Numbers

Division is nothing but a simple way of repeated subtraction of numbers. It can be also stated as a specialized form of subtraction where a smaller number is subtracted from the larger one a specific number of times.

### Procedure for Dividing Whole Numbers:

- Step 1: Divide the last place value of dividend by divisor. If dividend does not go to the divisor means take the next element of dividend.
- Step 2: Now multiply the quotient and divisor.
- Step 3: Now do the subtraction process
- Step 4: Continue (if necessary)

Below you could see a handy rules for division of whole numbers

**Handy rules for Division of Whole Numbers:**

- Any number divided by itself equals 1.
- Any number divided by 1 equals itself.
- Zero divided by any non-zero number equals zero.
- Any number divided by zero gives us undefined or infinite answer and so is difficult.

**Dividing Whole Numbers Practice Problems**

**Question 1:** A school bus covers 355 miles in 5 days. How much distance will it cover in one day?

**Question 2:** A college canteen consumes 850 bottles of coke in one week (7 days). How many bottles are consumed per day?

## Whole Numbers Examples

Below you could see some whole numbers examples

**Question 1: Add 71 with 46**

Solution:

Given 71 + 46

Write the given number as follows

7 1

4 6

———–

Add the one’s place number and take the carry to the next step. Here one’s place numbers are 1 and 6 (1 + 6 = 7). Carry is not available in this step.

Add the ten’s place number and also add the carry and over the new carry to the next step. Here ten’s place number is 7 and 4 (7 + 4= 11)

Correct answer is 71 + 46 = 117

**Question 2: Subtract 52 from 85**

Solution:

Given 85 – 52

Write the given number as follows

8 5

(-) 5 2

———–

———–

Subtract the one’s place numbers. If minuend number greater than subtrahend number do the process else get borrow from the next place number. Here minuend is greater than subtrahend so do the subtraction.

Subtract the ten’s place numbers. If minuend number greater than subtrahend number do the process else get borrow from the next place number. Here minuend is greater than subtrahend so do the subtraction.

Correct answer is 33

**Question 3: Multiply 4 by 2**

Solution:

Given, 4 × 2

Correct answer is 8

**Question 4: Divide 10 by 5**

Solution:

Given, 10 ÷ 5

Correct answer is 2

## Rounding Whole Numbers

Rounding to nearest whole number is easy and simple. If the one’s digit of the given number is greater than 5, then it is rounded to the nearest 10th value. The third rule is that more or less half of the number will be rounded up and the other half of the time it means below 5 will be rounded down. This is known as the rounding of the numbers.

Round nearest values means is replacing by another accurate values but that values should be equal to the given values.

For example : Round 5620 to nearest hundred is 5600.

Round 5626 to nearest tens is 5630. This called rounding whole numbers.

Rounding whole numbers Solved Examples

**Question 1: Rounding whole numbers 66,543 to the nearest hundred**

Solution:

Given 66,543, round to the nearest whole number

- Step 1: As we are rounding up a number that is nearest to hundred, we just underline the digit in the hundreds place is 5
- Step 2: The underline digit is 4, we keep 5 as it is and replace all digits to the right with zeros
- Step 3: So answer is 66,500

**Question 2: Rounding whole numbers 78,623 to the nearest ten**

Solution:

Given 78,623 , round to the nearest whole number

- Step 1: As we are rounding up a number that is nearest to ten, we just underline the digit in tenth place is 2
- Step 2: The underline digit is 3, we keep 2 as it is and replace all digits to the right with zeros
- Step 3: So answer is 78,620