Ratios and Proportions

In our daily life, there are many occasions when we compare two quantities.

This topic gives an overview of;

- Ratios and Proportions
- Equivalent Ratios
- Proportion
- Solving Ratio and Proportion

Ratios and Proportions

* Ratios* are used to compare quantities. Ratios help us to

If two quantities cannot be expressed in terms of the** same unit**, there cannot be a ratio between them. Hence to compare two quantities, the units must be the same.

Consider an example to find the ratio of* 3 km to 300 m*.First convert both the distances to the same unit.

So, **3 km = 3 × 1000 m = 3000 m***.*

Thus, the required ratio, **3 km : 300 m is 3000 : 300 = 10 : 1**

Equivalent Ratios

Different ratios can also be compared with each other to know whether they are * equivalent *or not. To do this, we need to write the

To check this, we need to know whether

We have,

We find that which means that

Therefore, the ratio ** 1 :2** is not equivalent to the ratio

Proportion

The ratio of two quantities in the same unit is a fraction that shows how many times one quantity is greater or smaller than the other. **Four quantities** are said to be in * proportion*, if the ratio of first and second quantities is equal to the ratio of third and fourth quantities. If two ratios are equal, then we say that they are in proportion and use the symbol ‘

Ratio and proportion problems can be solved by using two methods, the* unitary method* and

For example,

To check whether 8, 22, 12, and 33 are in proportion or not, we have to find the ratio of 8 to 22 and the ratio of 12 to 33.

Therefore, *8, 22, 12, *and *33* are in proportion as** 8 : 22** and **12 : 33** are equal. When four terms are in proportion, the first and fourth terms are known as * extreme terms* and the second and third terms are known as

The method in which we first find the value of one unit and then the value of the required number of units is known as** unitary method**.

Consider an example to find the cost of 9 bananas if the cost of a dozen bananas is Rs 20.

1 dozen = 12 units

Cost of 12 bananas = Rs 20

∴ Cost of 1 bananas = Rs

∴ Cost of 9 bananas = Rs

This method is known as **unitary method**.

Summary

- We have learnt, Ratios are used to compare quantities.

- Since a ratio is only a comparison or relation between quantities, it is an abstract number.

- Ratios can be written as fractions. They also have all the properties of fractions.

- The ratio of 6 to 3 should be stated as 2 to 1, but common usage has shortened the expression of ratios to be called simply 2.

- If two quantities cannot be expressed in terms of the same unit, there cannot be a ratio between them.

- If any three terms in a proportion are given, the fourth may be found. The product of the means is equal to the product of the extremes.

- It is important to remember that to use the proportion; the ratios must be equal to each other and must remain constant.

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