Mathematics is a language of numbers that helps us in counting, weighing, and labeling things. The numbers obtained from the ten digits of arithmetic have been divided into a variety of groups. Hence, arithmetic presents us with many different kinds of numbers based on their purpose and properties, such as integers, real numbers, natural numbers, whole numbers, fractional numbers, prime numbers, composite numbers, and so on.
Let us talk about real numbers. These can be rational or irrational. A number can be defined as rational if it can be expressed as x/y, where x and y are integers and y is not zero. While an irrational number cannot be expressed as the ratio of two numbers. Coming to the prime numbers, these are those natural numbers that can only be divided by one and themselves. To put it in another way, their factors would be one and the number itself. A composite number is one that can be generated by multiplying two or more numbers together. As a result, composite numbers have more than two factors, or at the very least three. One thing to keep in mind is that 1 is neither prime nor composite.
Elaborating further on the rational numbers, which form a category of real numbers, numbers that can be expressed as a fraction and have the integers in the numerator and denominator are known as rational numbers. And two distinct fractions may correspond to the same rational number, such as 7/4 = 14/8.
0.50 = 1/2 is a rational number.
Since they can be written as a number divided by one, all whole numbers are also known as rational numbers. Like 2, which can be written as 2/1, is a rational number. In basic terms, it’s a number that can be generated by dividing two integers. In addition, the term rational comes from the word ratio.
Negative rational numbers, such as -1/2 and -3/5, are also possible.
When it comes to irrational numbers, those numbers that can’t be represented as a ratio of two integers, such as the square root of 2. The square root of 2 is an interesting number. We would never be able to determine the precise square root of 2 in decimals. Consider another famous irrational number, “pi,” which is incredible since it is the only number that relates the length of a circle’s radius to its circumference.
This number pi can be expressed as a fraction, 22/7, but when translated to decimal, the digits after the decimal point become interminable, such as 22/7= 3.1415926535897932……
Remember that pi multiplied by pi produces an irrational number, but the square root of two produces a rational number, when multiplied by itself. As a consequence, multiplying irrational numbers can give both rational and irrational results.
Speaking of prime numbers, its examples would be 2, 3, 5, 7, 11, etc., as these have only two factors, 1 and the number itself. To find out if a number is a prime or a composite, we can do a divisibility test using the numbers 2, 3, 5, 7, 11, and 13.
Prime factorization of any given number can be done by breaking the number into its factors till all of its factors are prime numbers. For this, proceed by dividing the given number from the smallest prime number and continue until all its factors are prime. The smallest prime number that we know is 2.Interestingly, there is no largest prime number.
To strengthen these number concepts, students should be encouraged to practice math worksheets that have a variety of problems to solve. And these worksheets are easily available on the internet these days. One such website is Cuemath which offers a variety of math worksheets to be downloaded for free and are easy to follow by the students.