There are many situations in daily lives where we need to compare two things to make a decision or better understand the difference in the two quantities under consideration. There are two ways to compare two measurable quantities, calculating the difference between the two or calculating how many times of one quantity is the another quantity. Suppose, if we want to compare the salary of two of our friends A and B. A has a salary of $100 while B has a salary of $400. We can either say that the salary of B is $300 more than the salary of A or the salary of B is 4 times as that of A. The second method of comparing two measurable quantities is expressed in terms of mathematical term ‘Ratio’ written as x:y. For the above example, of the two salaries will be expressed as:
= = 4:1
Now that we have a general idea about the term Ratio and its usage in common life, let us try to find out ‘What is Ration in Math’ and look at its mathematical aspects.
What Is Ratio In Math
The ratio of two numbers is basically a division of one number by another and can be expressed in various forms. Suppose we want to express the ratio of two numbers X and Y, it can be given as:
- The ratio of X to Y
- X is to Y (followed by “as A is to B”, where A and B are numerator and denominator of an equivalents fraction)
When expressed in the form of two numbers separated by a colon as X:Y, the first term before the colon i.e. X is called as antecedent and the term after colon i.e. Y is called as consequent.
Two or more ratios are said to equivalent when antecedent divided by consequent results into a common quotient in each case. For example, 1:2, 2:4, 7:14 and 50:100 are all equivalent ratios as they all results into a common quotient of 0.5 or 1/2. Now that we know ‘What is Ratio in Math’, let us try to learn more about equivalent ratios.
Suppose we have two equivalent ratios as A:B and X:Y, then they can be written as:
A:B = X:Y or A:B::X:Y
The above expressions are read as A is to B is same as X is to Y. Two ratios that are equivalent to each other are also said to be proportional to each other. In the above case, A:B will be said to be in proportion with X:Y and A,B, X and Y are known as terms of the proportion.
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