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Definition of Rational Number

The ratio of two integers called as Rational number but the ratio of two intergers should not be infinite (∞).

Let us consider a and b are two integers which may be either positive or negative. The ratio of these two integers called as Rational number.

In other words

» a/b

The ration of two integer values always called as rational number. However, the ration should not be infinite as per definition.

a/b ≠ ∞

So, the value of b should not be zero. However, the value of a could be zero.

For example:

5/8, 4/2, 6/7, 0, 2, 7, 4 and etc

All above stated examples called as Rational numbers but below examples never call as rational numbers.

5/0, 2/0, 1.24/4.67 and etc.

I think, you understood the concept of Rational numbers perfectly.

Definition of Integer

Integer is a numberical number which does not have fractions. Integer can be either negative or postive value.

According to the Interger definition.

Numerical numbers 1, 2, 3, 4, 5, 6, 7, 8 …… ∞

These are called as positive integers.

Similarly,

Numerical numbers – 1, – 2, – 3, – 4, – 5, – 6, – 7, – 8 …… – ∞

These are called as negative integers.

I think, you understood the concept of Integer. So, integers could have either negative or postive value. Similarly, Zero (0) is also an interger because the value zero does not have fraction.

So, we can consider values from – ∞ to ∞ including zero as interger.

Remember in your mind

Numbers like 3.28, 1.246, 2.3534, 8.293737 and etc can not be called as Integer beause the numerical numbers should not have fractions.

I think, most of people consider Surd is only one type but it is not correct. Surds can be classified into eight categories by considering their properties. These are the list of Surds as per Mathematical basics. Every student has to learn each surd to improve knowledge on Surds concepts.

1. Mixed Surd
2. Entire or Pure Surd
3. Simple Surd
4. Compound Surd
5. Binomial Surd
6. Trinomial Surd
7. Like Surd
8. Unlike Surd

Componendo and Dividendo Rule is a fundamental concept of Mathematics.  Componendo and Dividendo Rule simplifies complicated mathematical functions. Everyone should learn this basic mathematical concept to solve some problems easily.

Now, i am going to explain this concept by deriving mathematically. Let us consider a, b, c and d are four mathematical elements. The ratio of first two mathematical elements are equal to the ration of remaining two elements. In other words, we can express the relationship between these four mathematical elements as stated below.

a/b = c/d

Now, add 1 both sides

(a/b) + 1 = (c/d) + 1

We get a function like this and named as equation (1) for our convenience.

» (a + b)/b = (c + d)/d → (1)

Similarly, add – 1 both sides

(a/b) – 1 = (c/d) – 1

We get a function like this and named as equation (2) for our convenience.

» (a – b)/b = (c – d)/d → (2)

Now, we can write resultant solution from equation (1) and (2) by dividing first equation with second equation.

» [(a + b)/b]/[(a - b)/b] = [(c + d)/d]/[(c - d)/d]

» (a + b)/(a – b) = (c + d)/(c – d)

Therefore, we have proved that

a/b = c/d ↔ (a + b)/(a – b) = (c + d)/(c – d)

This relation called as Componendo and Dividendo Rule. a, b, c and d could be numerical numbers, trigonmetry functions or anything.

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