Natural Numbers

In mathematics numbers play an important role.There are various types of numbers with various properties. Natural numbers are the non-negative numbers which starts from 0 and ends at infinity. {0, 1, 2 ……} is a set of natural numbers. In this article, we shall discuss the natural numbers and its fascinating properties. Also we shall see some sample examples for natural numbers.

Laws of natural numbers:

Addition law of associative:

(a + b) + c = a + (b + c)

Addition law of commutative:

a + b = b + a

Addition law of cancellation:

If a + c = b + c, then a = b

Law of  distributive with multiplication on the left:

a * (b + c) = a * b + a * c

Law of  distributive with multiplication on the right:

(a + b) * c = a * c + b * c

Multiplication law of associative:

(a * b) * c = a * (b * c)

Multiplication law of commutative:

a * b = b * a

Multiplication law of cancellation:

If a * c = b * c, then a = b.

Example problems to set of natural numbers:

Set of natural number - Example problem: 1

Find (3 + 5) + 7 = 3 + (5 + 7)

Solution:

Using the addition associative property,

(3 + 5) + 7 = 3 + (5 + 7)

(8) + 7 = 3 + (12)

15      =     15

Set of natural number - Example problem: 2

Find 23 + 5 = 5 + 23

Solution:

Using the addition commutative property,

23 + 5 = 5 + 23

28      =    28

Set of natural number - Example problem: 3

Find a + 7 = b + 7

Solution:

Using the addition cancellation property,

a + 7 = b + 7

Subtract 7 on both sides of the equation,

a + 7 – 7 = b + 7 – 7

a    =      b

Set of natural number - Example problem: 4

Find (5 * 8) * 2 = 5 * (8 * 2)

Solution:

Using the multiplication associative property,

(5 * 8) * 2 = 5 * (8 * 2)

(40) * 2 = 5 + (16)

80      =     80

Set of natural number - Example problem: 5

Find 200 * 3 = 3 * 200

Solution:

Using the multiplication commutative property,

200 * 3 = 3 * 200

600      =    600

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Set of natural number - Example problem: 6

Find a * 7 = b * 7

Solution:

Using the multiplication cancellation property,

a * 7 = b *  7

Divide 7 on both sides of the equation,

a * 7 / 7  = b * 7 / 7

a    =      b