CLASS-7
CONVERSION OF RATIO TO PERCENTAGE

CONVERSION OF RATIO TO PERCENTAGE -

Converting a ratio to a percentage involves expressing the relationship between the two parts of the ratio as a percentage. Here's how you can do it:

Steps to Convert a Ratio to a Percentage:-

    1. Express the Ratio as a Fraction:- 

                                                          a

  A ratio a : b can be expressed as the fraction -------- .

                                                        a + b

    This fraction represents the part a of the total a + b.

   2. Convert the Fraction to a Percentage:-

    Multiply the fraction by 100 to convert it into a percentage.

Example 1: Convert the Ratio 3:5 to a Percentage

Step 1:-  Express the ratio as a fraction:-

                      3             3 

                 --------- = -------

                    3 + 5​          8

Step 2:-  Convert the fraction to a percentage by multiplying by 100:-

                 3

             -------- x 100 = 37.5%

                 8

So, in the ratio 3:5, the first part (3) represents 37.5% of the total.   (Ans.)

Example 2: Convert the Ratio 2:3 to a Percentage

Step 1:-  Express the ratio as a fraction:-

              2             2

         --------- = --------​ 

            2 + 3           5

Step 2:- Convert the fraction to a percentage by multiplying by 100:-

                 2

             -------- x 100 = 40%

                 5

So, in the ratio 2:3, the first part (2) represents 40% of the total.   (Ans.)

Converting Each Part of the Ratio:-

If you want to express each part of the ratio as a percentage of the whole:-

   1. First Part:-

    Percentage of first part = (First part/Total) × 100 

   2. Second Part:- 

      Percentage of second part = (Second part/Total) × 100

For the ratio 2:3:-

                            2                   2

• First part (2):-  -------- x 100 = ------- x 100 = 40%

                         (2 + 3)                5

                               3                   3

• Second part (3):-  --------- x 100 = ------ x 100 = 60%      

                            (2 + 3)                5                 

So, the ratio 2:3 can be expressed as 40% and 60%.      (Ans.)

ANOTHER WAY OF UNDERSTANDING -

To convert a ratio to a percentage, follow these steps:-

   1. Express the Ratio as a Fraction:-

      If the ratio is given in the form a:b, rewrite it as a fraction a/b.

  2. Divide the Numerator by the Denominator:-

      Perform the division a/b to get a decimal.

  3. Multiply by 100:-

     Multiply the result from the previous step by 100 to convert it into a percentage.

   4. Add the Percentage Symbol (%):-

    Add the "%" symbol to indicate that the number is a percentage.

Let's say we want to convert the ratio 3:4 to a percentage.

1. Express as a fraction:-  3/4​.
2. Divide:-  3 ÷ 4 = 0.75.
3. Multiply by 100:-  0.75 × 100 = 75.
4. Add the percentage symbol:-  75%.

So, the ratio 3:4 is equivalent to 75%.    (Ans.)

Summary:-

To convert a ratio to a percentage, express one part of the ratio as a fraction of the total (sum of the parts), then multiply by 100. This process allows you to understand the relationship between the parts of the ratio in percentage terms, which is often useful for comparisons and analysis.