Solved Examples on Whole Numbers
Example 1: Identify the whole numbers among the set of numbers { -5, -4.25, 0, 2/5, 8, 19, 68}.
Solution:
The set of all-natural numbers and zero is referred to as whole numbers. In mathematics, the set of whole numbers is given as W = {0, 1, 2, 3, 4,…}.
Hence, the whole numbers among the given numbers are {0, 8, 19, and 68}.
Example 2: Are -135, 51, 112, 169, and 1829 whole numbers?
Solution:
As -135 is a negative integer, all the given numbers except -135 are whole numbers, i.e., 51, 112, 169, and 1829 are whole numbers.
Example 3: Solve 14 × (3 + 7) using the distributive property.
Solution:
The distributive property of multiplication over the addition of whole numbers is:
a × (b + c) = (a × b) + (a × c)
So, 14 × (3 + 7) = (14 × 3) + (14 × 7)
= 42 + 98
= 140
Hence, the value of 14 × (3 + 7) is 140.
Example 4: When is the product of two whole numbers zero?
Solution:
The product of two whole numbers is zero when one of them is zero.
For example, the product of 0 and 6 is 0 (0 × 6 = 0) and the product of 13 and 0 is 0 (13 × 0 = 0).
The product of two whole numbers is zero when both of them are zero, i.e., 0 × 0 = 0.
So, the product of two whole numbers is zero when either of them is zero or both of them are zero.
Example 5: Find the value of 8 × (36 – 6), using the distributive property.
Solution:
The distributive property of multiplication over the subtraction of whole numbers is:
a × (b – c) = (a × b) – (a × c)
So, 8 × (36 – 6) = (8 × 36) – (8 × 6)
= 288 – 48
= 240
Thus, the value of 8 × (36 – 6) is 240.
Properties of Whole Numbers
A number system refers to a system that represents numbers, where a number is defined as the mathematical value that helps to count, measure, or label and perform various mathematical calculations. We have various types of numbers based on their properties, such as natural numbers, whole numbers, integers, rational and irrational numbers, real numbers, etc. In a number system, these numbers are used as digits. A number system also helps us to perform various arithmetic operations such as addition, subtraction, and division. A binary number system, an octal number system, a decimal number system, and a decimal number system are different types of number systems.