What are Whole Numbers?
Whole numbers are a set of numbers that include all natural numbers 1, 2, 3, 4… and 0. As the name suggests, whole numbers only include numbers that can represent a ‘whole’. So, fractional numbers and decimal numbers are not a part of whole numbers. The only difference between the set of natural numbers and the set of whole numbers is the presence of zero in the latter set.
Here is the set of numbers that are included in the set of whole numbers:
- All natural or counting numbers
- All positive integers, including zero
Division of Whole Numbers
The division of whole numbers is performed using the long division method. This operation may result in a whole number or a fraction. The nature of the quotient depends on the value of the dividend and the divisor. If the divisor completely divides the dividend, the result will be a whole number, and the remainder will be zero. If the divisor does not completely divide the dividend, this will result in a remainder. The result of such a division operation will result in a mixed number, which is a fraction.
For example, let us divide 96 by 8.
In this case, the divisor completely divides the dividend and it does not result in a remainder. So, this division operation results in a whole number.
Suppose we replace 96 with 92 in this division operation.
In this case, the divisor does not completely divide the dividend and it results in a remainder. The result of this division operation is 11 R4 or 11\(\frac{4}{8}\), which is a mixed number. Hence, the division operation results in a fraction.
Real-Life Applications
Since division is one of the four basic operations in math and whole numbers are one of the most frequently used sets of numbers, we come across division operations on whole numbers quite frequently. Here are a few instances when the division of whole numbers can be useful:
- Dividing money among people: Division of whole numbers is often used to split bills at restaurants, while traveling with friends, and so on.
- Division of food among people: Division of whole numbers is used while splitting food items like pizza or a pie.
- Finding the speed of a body: Dividing the distance covered by a body by the time taken to cover the distance gives us the speed at which the body is moving.
- Division of study hours: Dividing the hours allocated for studying allows students to prioritize their work efficiently.
These are just a few instances where we use divisions to find solutions to real-life problems.
Solved Examples
Example 1: Divide 245 by 7. Will it result in a whole number?
Solution:
Here, the dividend is 245, and the divisor is 7.
Hence, 245 ÷ 7 = 35.
Since the remainder is zero, the result is a whole number.
Example 2: Evaluate 376 ÷ 16. Determine the nature of the result.
Solution:
We need to find the value of 376 ÷ 16.
Here, 376 is the dividend, and 16 is the divisor.
The result of this division operation is 23 R8. Here, the quotient is 23, and the remainder is 8.
Since this division operation results in a remainder, it gives us a mixed number or a fractional number.
Example 3: A tower in Times Square is retrofitted with a tall LED display. The tower is 48 stories tall, and the height of each story is 3 meters. If the LED display covers the height of a quarter of the total number of stories, find its height. Determine whether the height of the display is a whole number.
Solution:
Total number of stories in the tower = 48
Height of each story = 3 meters
Total height of the tower, H = 48 x 3
H = 144 meters
We need to find the height of the LED display (h).
Height of the LED display (h) = Total height of the tower (H) ÷ 4
h = 144 ÷ 4
Hence, h = 36 R0, which indicates that the height of the LED display is 36 meters. So, the height of the display is a whole number.
The set of whole numbers includes all natural numbers. The only difference between the two sets of numbers is that the number 0 is included only in whole numbers.
Yes, we can divide a whole number by any type of number. But as always, division by zero is not possible.
Division operations on whole numbers may not always result in a whole number. We get a whole number as the result only when the divisor completely divides the dividend. Otherwise, the operation will result in a mixed number or a fraction.