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# Whole Numbers, Properties, Operations, Example, Application

## Whole Numbers

Whole Numbers: Under mathematics, Whole Numbers have different importance of their own. It becomes easier to understand arithmetic, algebra, and number theory in the field of mathematics through integers because Whole Numbers are used the most in the fields.

Generally, the standard books written by CBSE and other educational boards provide information about Whole Numbers in very difficult language, which makes it difficult for the students to understand.

But in today’s article, we have provided you with all the information about Whole Numbers in the simplest language below. If you want to understand all the information about Whole Numbers in simple terms, then stay with us till the end of today’s article.

## Whole Numbers: What are Whole Numbers?

Generally, Whole Numbers are a set of numbers that include all the natural numbers (positive integers) and zero. Whole Numbers do not include any negative numbers or fractions. They are represented by the set of numbers {0, 1, 2, 3, 4, 5, …}. Whole Numbers are used in many areas of mathematics, including arithmetic, algebra, and number theory. They are also used in everyday life situations, such as counting objects or measuring quantities.

All Prime Numbers from 1 to 100 List Trick, Chart

## Whole Numbers: Properties of Whole Numbers

The properties of Whole Numbers include:

• Closure: Whole Numbers are closed under addition, subtraction, and multiplication. This means that if you add, subtract, or multiply any two Whole Numbers, the result is always a whole number.
• Commutative property: The order in which you add or multiply Whole Numbers does not affect the result. For example, 3 + 4 = 4 + 3 and 3 × 4 = 4 × 3.
• Associative property: The way you group the numbers when adding or multiplying does not affect the result. For example, (2 + 3) + 4 = 2 + (3 + 4) and (2 × 3) × 4 = 2 × (3 × 4).
• Identity property: The sum of any whole number and zero is that whole number itself. For example, 7 + 0 = 7
• Distributive property: Multiplication distributes over addition. For example, 3 × (4 + 2) = (3 × 4) + (3 × 2).
• Divisibility: Whole Numbers can be divided by other Whole Numbers evenly. For example, 12 can be fully divide by 3, so 12 ÷ 3 = 4 with no remaining.
• Order: Whole Numbers can be ordered from least to greatest or greatest to least. For example, 2 < 5 and 7 > 4.

Rational Numbers- Definition Symbol, and Examples

## Whole Numbers: Place value and positional notation in Whole Numbers

Place value and positional notation are important concepts in understanding how Whole Numbers are written and represented.

Place value Indicates the value of a digit-based position in a number. In Whole Numbers, the value of each digit is determined by its place in the number, starting from the rightmost digit. The first digit from the right represents ones, the second digit represents tens, the third digit represents hundreds, and so on. For example, in the number 347, the digit 7 represents 7 ones, the digit 4 represents 4 tens, and the digit 3 represents 3 hundred.

Positional notation, also known as the decimal system, is the way in which Whole Numbers are written using place value. This is a system where each digit can take on 10 different values (0-9), and the value of each digit is determined by its position in the number

For example, the number 1234.56 is written using positional notation, where the digit 1 is in the thousands place, the digit 2 is in the hundreds place, the digit 3 is in the tens place, the digit 4 is in the ones place, the digit 5 is in the tenths place, and the digit 6 is in the hundredths place. The value of the number is the sum of the products of each digit and its corresponding place value. In this case, the value is 1 x 1000 + 2 x 100 + 3 x 10 + 4 x 1 + 5 x 0.1 + 6 x 0.01, which equals 1234.56.

Co Prime Numbers- Definition, Properties, List, and Examples

## Whole Numbers: Operations on Whole Numbers

Operations on Whole Numbers include

2. Subtraction
3. Multiplication
4. Division
• Addition: Whole Numbers can be added together by aligning them according to place value and adding each column. The result is a sum that can be written as a whole number. For example, to add 42 and 73, you would align the one’s place and the tens place and add 2+3=5 in the one’s place and 4+7=11 in the tens place. So, the answer is 115.
• Subtraction: Whole Numbers can be subtracted by aligning them according to place value and subtracting each column. If the number in the column being subtracted from is smaller than the number being subtracted, then borrow from the next column to the left. For example, to subtract 36 from 79, you would start at the one’s place and subtract 6 from 9. Since 6 is smaller than 9, you need to borrow from the tens place. The 7 in the tens place becomes 6, and the 9 in the one’s place becomes 19. Then, you subtract 6 from 16 and get 10. So the answer is 43.
• Multiplication: Whole Numbers can be multiplied by using the distributive property and the multiplication table. The distributive property states that a x (b+c) = a x b + a x c. For example, to multiply 23 by 4, you can use the distributive property: 23 x 4 = 20 x 4 + 3 x 4 = 80 + 12 = 92.
• Division: Whole Numbers can be divided by long division or by using repeated subtraction. For example, to divide 75 by 5 using long division, you would divide 7 by 5 and get 1 with a remainder of 2. Then, you bring down the 5 and divide 25 by 5 and get 5. So, the answer is 15.

Composite Number- Definition, Example, 1 to 100 List

## Whole Numbers: Solving real-life problems with Whole Numbers

Problem: A farmer has 30 cows, and he wants to divide them equally into 6 different man. How many cows will be in each man?

Solution: To solve this problem, we need to divide the total number of cows (30) by the number of man (6):

30 ÷ 6 = 5

Therefore, there will be 5 cows in each man.

Problem: Sarah is planning to bake cookies and she needs to buy some ingredients. She needs 2 cups of sugar for each set of cookies, and she wants to make 8 sets. How many cups of sugar does she need in total?

Solution: To solve this problem, we need to multiply the amount of sugar needed for each batch (2 cups) by the number of batches (8):

2 x 8 = 16

Therefore, Sarah needs 16 cups of sugar in total.

Problem: A construction worker needs to lay bricks to build a wall that is 20 feet long. Each brick is 1 foot long. How many bricks does he need?

Solution: To solve this problem, we need to divide the length of the wall (20 feet) by the length of each brick (1 foot):

20 ÷ 1 = 20

Therefore, the construction worker needs 20 bricks.

## Whole Numbers: Applications of Whole Numbers

Here are five applications of Whole Numbers:

• Counting: Whole Numbers are used for counting objects and quantities.
• Measurement: Whole Numbers are used to measuring distances, weights, and volumes.
• Money: Whole Numbers are used in financial transactions, such as counting rupees and coins or calculating the tax.
• Time: Whole Numbers are used to measuring time in hours, minutes, and seconds, and to perform calculations involving time.
• Sports: Whole Numbers are used in sports to keep score and record statistics..

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## FAQs

### How are Whole Numbers different from natural numbers?

Whole Numbers are a set of numbers that include all the natural numbers (positive integers) along with zero. On the other hand, natural numbers start at 1 and go up, Whole Numbers include 0 as well as all the natural numbers.

### Can zero be considered a whole number?

Yes, zero is considered a whole number.

### What are the properties of Whole Numbers?

The properties of Whole Numbers include closure, commutativity, associativity, distributivity, identity, and inverse.

### How do I add, subtract, multiply, and divide Whole Numbers?

To add or subtract Whole Numbers, line up the digits according to their place value and then add or subtract each column from right to left. To multiply Whole Numbers, use the distributive property and then add the products. To divide Whole Numbers, use long division, which involves dividing the largest possible multiple of the divisor into the dividend, and then repeating the process.

### How do I round Whole Numbers to a given place value?

To round a whole number to a given place value, look at the digit to the right of the place value you want to round to. If it is 5 or greater, round up, and if it is less than 5, round down. If the digit is exactly 5, round up if the digit to the left of it is odd, and round down if the digit to the left of it is even.

### What is the least common multiple (LCM) of two or more Whole Numbers?

The least common multiple (LCM) of two or more Whole Numbers is the smallest whole number that is a multiple of all the given numbers.

### What is the greatest common factor (GCF) of two or more Whole Numbers?

The greatest common factor (GCF) of two or more Whole Numbers is the largest whole number that divides evenly into all of the given numbers.

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