What is a Whole Number?
Whole numbers are an important part of the number system which are integers ranging from 0 to an infinite number of positive integers. A set of whole numbers in mathematics can be represented as,
W = {0, 1, 2, 3, 4 …}
Are natural numbers a subset of whole numbers?
A set A is a subset of set B when all the elements of set A are also elements of set B.
Every whole number other than 0 is a natural number. So, every natural number is a whole number. Hence, in simpler terms, natural numbers are a subset of whole numbers.
What are the properties of whole numbers?
The properties of whole numbers are dependent on arithmetic operations. Here are the following properties of whole numbers:
Closure Property
This property is ideal for addition and multiplication. If two whole numbers are added or multiplied together, then the result will be a whole number.
Commutative Property of Addition and Multiplication
In this property, the sum and product of any two whole numbers will always be the same in whatever order they are added or multiplied. For example, 4 + 7 = 7 + 4 = 11 and 5 * 8 = 8 * 5 = 40
Associative Property
If whole numbers are added or multiplied, the order of grouping does not change the sum or the product. For example,
2 + (6 + 4) = (2 + 6) + 4 = 12 and 3 * (5 * 6) = (3 * 5) * 6 = 90
Distributive Property
If there are three whole numbers, a, b and c, then the distributive property of multiplication over addition will be,
a * (b + c) = (a * b) + (a * c), this value will also be a whole number.
Along with these properties, there are additive and multiplicative identities:
According to additive identity, if a whole number is added to 0, the number remains the same.
For example, 8 + 0 = 8.
In terms of the multiplicative identity, if a whole number is multiplied by 1, the number remains the same.
For example, 3 x 1 = 3.
Solved Whole Numbers Examples
1. Can you identify the whole numbers from the following numbers: 34, -359, \(\frac{5}{8}\), 8999, 21.5, 0.5, \(\frac{45}{78}\), 200.
Answer: As we have learned, a set of whole numbers is denoted by the symbol W as W = {0, 1, 2, 3, 4,……} and whole numbers don’t include fractions, decimals and negative numbers.
Thus from the above list of numbers, whole numbers are: 34, 8999, 200.
2. Solve 20 x (10 + 7) using the distributive property.
Answer: The distributive property of multiplication over addition for whole numbers is given by, a * (b + c) = (a * b) + (a * c).
So, by that, 20 x (10 + 7) = (20 x 10) + (20 x 7)
= 200 + 140
= 340
Thus, 20 x (10 + 7) = 340
3. Marissa donated $100 to a charity on Monday whereas Leonard donated $20 to the same charity for 5 days each. What is the total amount received by the charity?
Answer: As per the problem, Marissa donated $100 to the charity. Leonard donated ($20 x 5) to the charity for 5 days, which is $100. As you can see, both the numbers are whole numbers, thus by finding the total through the addition operation, we will get a whole number as well as a result.
Total amount received by the charity = $100 + $100
= $200
The charity received $200 in total from Marissa and Leonard.
Here are some differences between whole numbers and natural numbers:
Here are some interesting facts about whole numbers:
- All natural numbers are whole numbers.
- All counting numbers are whole numbers.
- All positive integers along with 0 are whole numbers.
- All whole numbers are real numbers.
