Concept of Ratio

In concept of ratio we will learn how a ratio is compared with two or more quantities of the same kind. It can be represented as a fraction.

A ratio is a comparison of two or more quantities of the same kind. It can be represented as a fraction.

Most of time, we compare things, number, etc. (say, m and n) by saying:

(i) m greater than n

(ii) m less than n

When we want to see how much more (m greater than n) or less (m less than n) one quantities is than the other, we find the difference of their magnitudes and such a comparison is known as the comparison by division.

(iii) m is double of n

(iv) m is one-fourth of n

If we want to see how many times more (m is double of n) or less (m is one-fourth of n) one quantities is than the other, we find the ratio or division of their magnitudes and such a comparison is known as the comparison by difference.


(v) \(\frac{m}{n}\) = \(\frac{2}{3}\)

(vi) \(\frac{n}{m}\) = \(\frac{5}{7}\), etc.

The method of comparing two quantities (numbers, things, etc.) by dividing one quantity by the other is called a ratio.

Thus:  (v) \(\frac{m}{n}\) = \(\frac{2}{3}\) represents the ratio between m and n.

         (vi) \(\frac{n}{m}\) = \(\frac{5}{7}\) represents the ratio between n and m.

When we compare two quantities of the same kind of division, we say that we form a ratio of the two quantities.


Therefore, it is evident from the basic concept of ratio is that a ratio is a fraction that shows how many times a quantity is of another quantity of the same kind.


Definition of Ratio:

The relation between two quantities (both of them are same kind and in the same unit) obtain on dividing one quantity by the other, is called the ratio.

The symbol used for this purpose " " and is put between the two quantities compared.

Therefore, the ratio between two quantities m and n (n ≠ 0), both of them same kind and in the same unit, is \(\frac{m}{n}\) and often written as m : n (read as m to n or m is to n)

In the ratio m : n, the quantities (numbers) m and n are called the terms of the ratio. The first term (i.e. m) is called antecedent and the second term (i.e. is n) is called consequent.

Note: From the concept of ratio and its definition we come to know that when numerator and denominator of a fraction are divided or multiplied by the same non-zero numbers, the value of the fraction does not change. In this reason, the value of a ratio does not alter, if its antecedent and consequent are divided or multiplied by the same non-zero numbers.

For example, the ratio of 15 and 25 = 15 : 25 = \(\frac{15}{25}\)

Now, multiply numerator (antecedent) and denominator (consequent) by 5

\(\frac{15}{25}\) = \(\frac{15 × 5}{25 × 5}\) = \(\frac{75}{125}\)

Therefore, \(\frac{15}{25}\) = \(\frac{75}{125}\)

Again, divide numerator (antecedent) and denominator (consequent) by 5

\(\frac{15}{25}\) = \(\frac{15 ÷ 5}{25 ÷ 5}\) = \(\frac{3}{5}\)

Therefore, \(\frac{15}{25}\) = \(\frac{3}{5}\)


Examples on ratio:

(i) The ratio of $ 2 to $ 3 = \(\frac{$ 2}{$ 3}\) = \(\frac{2}{3}\) = 2 : 3.

(ii) The ratio of 7 metres to 4 metres = \(\frac{\textrm{7 metres}}{\textrm{4 metres}}\) = \(\frac{7}{4}\) = 7 : 4.

(iii) The ratio of 9 kg to 17 kg = \(\frac{\textrm{9 kg}}{\textrm{17 kg}}\) = \(\frac{9}{17}\) = 9 : 17.

(iv) The ratio of 13 litres to 5 litres = \(\frac{\textrm{13 litres}}{\textrm{5 litres}}\) = \(\frac{13}{5}\) = 13 : 5.





6th Grade Page

From Concept of Ratio to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Converting Fractions to Decimals | Solved Examples | Free Worksheet

    Apr 28, 25 01:43 AM

    Converting Fractions to Decimals
    In converting fractions to decimals, we know that decimals are fractions with denominators 10, 100, 1000 etc. In order to convert other fractions into decimals, we follow the following steps:

    Read More

  2. Expanded Form of a Number | Writing Numbers in Expanded Form | Values

    Apr 27, 25 10:13 AM

    Expanded Form of a Number
    We know that the number written as sum of the place-values of its digits is called the expanded form of a number. In expanded form of a number, the number is shown according to the place values of its…

    Read More

  3. Converting Decimals to Fractions | Solved Examples | Free Worksheet

    Apr 26, 25 04:56 PM

    Converting Decimals to Fractions
    In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps: Step I: Obtain the decimal. Step II: Remove the decimal points from th…

    Read More

  4. Worksheet on Decimal Numbers | Decimals Number Concepts | Answers

    Apr 26, 25 03:48 PM

    Worksheet on Decimal Numbers
    Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts.

    Read More

  5. Multiplication Table of 4 |Read and Write the Table of 4|4 Times Table

    Apr 26, 25 01:00 PM

    Multiplication Table of Four
    Repeated addition by 4’s means the multiplication table of 4. (i) When 5 candle-stands having four candles each. By repeated addition we can show 4 + 4 + 4 + 4 + 4 = 20 Then, four 5 times

    Read More