Relation Between Two Numbers

A number is a mathematical object that is useful for counting, labelling, and measuring the concepts related to mathematics. Moreover, numbers are the most fundamental units in the field of Mathematics. All categories of numbers used in the field of Mathematics are categorised under the segment of a Number system. Furthermore, numerous types of numbers comprise composite numbers, prime numbers, odd numbers, natural numbers, even numbers, whole numbers, decimal numbers, integers, fractions, irrational numbers, rational numbers, real numbers, and imaginary numbers at the same time. On the other hand, all the actual numbers are also called real numbers.

However, all the numbers that don’t exist and are understood to explain some mathematical concepts are known as imaginary numbers. Moreover, real numbers are generally categorised into rational and irrational numbers. We can state the rational numbers in the fraction form where the denominator is not equivalent to zero, i.e. “Denominator ≠ 0”. Notably, irrational numbers are those numbers that can’t be expressed in the fraction form such that the denominator is not equivalent to zero, i.e. “Denominator ≠ 0”.

Proportional Relationships

Let’s just take an example of a close friend, a friend that can affect your mood. When your friend is up, you are up as well. Similarly, when your friend is down, you feel down as well at the same time. In the same way, a proportional relationship among the quantities is way too relatable to this example. Such as a beehive with a lot of bees in it. This has all the bees having six legs each. So, if we take half the number of the bees from the beehive, the number of legs will also become half of the total. 

Therefore, a proportional relationship lies between the number of bees in the beehive. And the number of legs of the bees. Furthermore, a proportional relationship is present between 2 values, ‘x’ and ‘y’, when they are expressible in the general form ‘y = kx’. Here ‘k’ is the proportionality’s constant.

The example of the beehive given above could be expressed by ‘y = 6x’, where ‘x’ is the digit presenting the number of bees in the hive, as well as, ‘y’ is the digit presenting the number of legs of the bees, and ‘k = 6’, as every individual bee has six legs. If we multiply ‘x’ with 2, then, as a result, ‘y’ will also become twice its value, or if we divide ‘y’ with ‘x’, subsequently, ‘y/x’ is always supposed to be six. In other words, if two values are proportional in nature, in that case, dividing them by each other will produce an equal ratio all the time, and this ratio will be the constant ‘k’. This constant can be represented in a fraction or a decimal.

Taste Test for Proportionality

Let’s take an example of preparing lemonade, where we decided to conduct a taste test for knowing the proportion of the needed sugar and the lemon juice for the perpetration of perfect lemonade. The amount of sugar required for the first glass of lemonade is five spoons; however, would we take the same amount of sugar to prepare one extra glass of lemonade? The question is, will the ratio of the lemon juice to sugar be equal at all stages, no matter what amount of lemonade we are preparing?

We can give the proportional relationship of the recipe as ‘s = 5l’, here ‘s’ represents sugar and ‘l’ denotes the lemon juice. Keeping in mind, the proportionality constant is ‘5’. This simply tells that for the preparation of each glass of lemonade. We need five spoons of sugar. For instance, we will be taking 25 spoons of sugar to prepare five lemonade glasses.

Conclusion

In conclusion, the JEE notes that the relation between two numbers contains the following. Various types of numbers include; composite numbers, prime numbers, odd numbers, natural numbers, even numbers, whole numbers, decimal numbers, integers, fractions, irrational numbers, rational numbers, real numbers, and imaginary numbers in mathematics. 

Moreover, the relation between two numbers’ importance exists in very basic mathematics concepts at a huge level.