What is ratio and proportion? We all come across various kinds of comparisons in each and every field. We do the comparison by how many times or by how much? Here we will learn more about the above questions.

In mathematics, we define a ratio as a relationship between two numbers indicating how many times the first number contains the second number.

In simple words we can say that a ratio is a comparison between two numbers which tells us that first number is how many times the second number.

For example the cost of an apple is Rs 30 whereas the cost of an orange is Rs 15 .Hence the cost of an apple is twice the cost of an orange. Hence the ratio is two and it is represented as

Here an important is to be remembered that only those quantities can be compared which has the same unit or they are in the same unit.

For example the price of a pencil and pen can be compared but the price of the pencil cannot be compared to the weight of the pen.

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**Example 1**: The length of a park is 120m the breadth is 45m. Find the ratio of length to breadth and also find the ratio of length to the area.

**Solution**: The ratio of length to breadth will be

**Proportion**

A proportion is a name which we give to any statement that two ratios are equal. It can be written in two ways, two equal fractions, or, using a colon, a: b = c: d or a: b::c:d.

- It is obvious that if the two ratios are not equal then they are definitely not in proportion.
- In any proportion the first and fourth term are called as extreme terms and the second and third as middle terms.

**Example 3**: Are the terms 20, 30, 40, 60 in proportion?

**Solution**: The ratio of first two terms is 20:30 = 2:3.

The ratio of the next two terms is 40:30 = 4:6= 2:3.

Since both the ratios are equal and hence the terms are in proportion.

**Unitary Method**

The method in which we first find out the value of one unit and then the value of required number of units is called as Unitary method.

**Example 4**: If the cost of 6 notebooks is Rs 72. Then what will be the cost of 4 notebooks?

**Solution**: Cost of 6 notebooks = Rs 72

**Practice Questions**

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**Q1)** Ramesh made 63 runs in 7 overs and Raju made 72 runs in 8 overs. Who made more run per over?

**Q2)** The cost of 4kg wheat is Rs 48. Find the cost of 10 kg of wheat.

**Q3)** State True or False

- a) Rs 40: Rs 200 = 80kg : 400kg
- b) 23 litre : 69 litre = 12g:36g

**Q4) **Determine the proportion

- 30, 40, 90, 360.
- 1,2,4,8
- 4,6,8,12

**Q5**) The cost of 5 dozen bananas is Rs 60.Find how much dozens of bananas one will get for Rs 40.

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**Recap**

- For comparison by ratio, the two quantities must be in the same unit. If they are not, they should be expressed in the same unit before the ratio is taken.

- The order in which quantities are taken to express their ratio is important.

- Two ratios are equivalent, if the fractions corresponding to them are equivalent. Thus, 3 : 2 is equivalent to 6 : 4 or 12:8.

- 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 the unitary method.

- In ratio and proportion the order is very important because as the order changes the ratio also changes.