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Ratio and Proportion

There are situations, when we need to compare two quantities.

For example, Swaminathan and Rohan both are in the same class. Their respective marks in mathematics are 96 and 48.

Marks scored by Swaminathan and Rohan can be compared by two methods.

1. Subtraction method

In this method, we subtract one quantity from other to find that one is how much more than the other.

Now,

Marks scored by Swaminathan –  Marks scored by Rohan = 96 – 48 = 48

So, it can be said that Swaminathan scored 48 marks more than Rohan in mathematics.

2. Division method

In this method, we divide one quantity by other to find that one is how many times the other.

Now,

So, it can be said that the marks scored by Swaminathan are twice the marks scored by Rohan.

When two quantities are compared using division method, the quotient obtained is called "ratio".

To understand the concept of ratios, look at the following video.

First term of a ratio is called "antecedent" and the second term is called "consequent".

For example, in the ratio x : y, x is antecedent and y is consequent.

Remember

• Comparison is made between the quantities carrying the same units.
• Comparison cannot be made between the quantities which are not similar.
• Ratio does not have any unit.

If x and y are two quantities in a particular ratio, one should not be confused between x : y and y : x.

The ratio x : y means and y : x means .

Conversion of a Fractional Ratio into a Whole Number Ratio

Example: Convert $\frac{1}{5}:\frac{1}{3}$ into ratio in simple form

There are two methods of converting a fractional ratio into a whole number ratio. They are:

Method I: Dividing the first quantity by the second

Solution: We are given the ratio as $\frac{1}{5}:\frac{1}{3}$.
We simply divide the first quantity by the second.

$\frac{\frac{1}{5}}{\frac{1}{3}}=\frac{1}{5}×\frac{3}{1}=\frac{3}{5}=3:5$

Method II:

(i) Find the LCM of the denominators.
So, LCM of 5 and 3 will be 15

(ii) Multiply the terms of the given ratio with the LCM and simplify.

$\frac{1}{5}×15:\frac{1}{3}×15=3:5$

Let us now look at an example to understand this concept better.

Example:

Identify the cases out of the following in which a comparison can be

1. The ratio between the price of a book and the price of a shirt
2. The ratio between the age of a person and the amount of money he has
3. The ratio of the length of a park to its breadth

Solution:

1. The price of a book and the price of a shirt are of the same typ…

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