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**12. Ratios and Proportions**

**Ratios:**

Usually, the **comparison of quantities** of the same type can be made by the method of difference between the quantities.

Usually, the **comparison of quantities **of the same type can be made by the method of difference between the quantities. However, a more meaningful comparison between the quantities can be made by using division, i.e. by verifying how many times one quantity is into the other quantity. This method is known as **comparison by ratio.**

For example, Keertana's weight is 20 kg and her father's weight is 80 kg. So we can say that Keertana's father's weight and Keertana's weight are in the ratio 20:80.

To calculate** ratio**, the two quantities have to be measured using the **same unit**. If not, they should be converted to the same unit before ratio is taken. The same ratio can occur in different situations. For example, the ratio 4:5 is different from 5:4.

Thus, the order in which the quantities are taken into consideration to express their ratio is important.

A ratio can be treated as a **fraction. **

For example, 5:6 can be treated as 5/6. Two ratios are said to be** equivalent i**f the fractions corresponding to them are equivalent.

To calculate **equivalent ratio**, convert the ratio into a fraction, and then multiply or divide the numerator and the denominator by the same number. Ex:4:5 is equivalent to 8:10 or 12:15 and so on. A ratio can be expressed in its** lowest form.** For example, the ratio 45:25 in its lowest form can be written as follows:

Thus, the lowest form of 45:25 is 9:5.**Page 53**

**Proportions:**

If the** ratios between Quantity A and Quantity B** is equal to the ratio between Quantity C and Quantity D,

If the** ratios **between Quantity A and Quantity B is equal to the ratio between Quantity C and Quantity D, then the four quantities A, B, C and D, are said to be in **proportion**. Proportion is denoted by the signs **'?' or '='.** Thus, the quantities 4, 16, 5 and 20 can be written as 4:16?5:20 or 4:16=5:20 The order of the terms in a proportion **carries value.** The quantities 4, 16, 5 and 20 are in proportion, whereas 4, 20, 5 and 16 are not in proportion. In the proportion **a:b?c:d,** the quantities **a and d** are the** extreme terms**, and** b and c are the middle terms. **The method of calculating the value of one unit and using this value to calculate the value of the required number of units is called the **unitary method.**

For example, suppose the cost of 8 bags is Rs. 240. Now, to find the cost of 6 bags,

using the unitary method, we first find out the cost of one bag. Cost of one bag =240/8 = Rs. 30

Now, the cost of 6 bags =6 Ã— Rs.30=180 Hence, the cost of 6 bags is Rs. 180.

221 videos|105 docs|43 tests

### Examples: More about Ratios Some

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### What is a Ratio?

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### Test: Ratio And Proportion - 1

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### NCERT Textbook - Ratio and Proportion

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### Test: Ratio And Proportion - 2

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### What is Proportion?

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- NCERT Solutions(Part - 2) - Ratio and Proportion
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