- Books Name
- CBSE Class 6 Mathematics Book

- Publication
- Param Publication

- Course
- CBSE Class 6

- Subject
- Mathmatics

**Ratio**

A ratio is a comparison of two numbers (quantities) by division. A ratio is usually denoted by the symbol (:). The ratio of a to b (b *≠* 0) is written as a : b or

In the ratio a : b, a and b are called terms of the ratio. 'a' is the antecedent and 'b' is the consequent.

A ratio is a number, so to find the ratio of two quantities they must be expressed in the same units.

**Properties of Ratios**

(a) In a ratio, two quantities are compared. So, the quantities must be of the same kind. i.e., they must be expressed in the same units.

(b) The value of a ratio remains unaltered if the given ratio is multiplied or divided by the same non-zero quantity.

(c) The order of the terms in a ratio a : b is very important. The ratio 3 : 2 is different from the ratio 2 : 3.

**Ratio in the simplest or lowest form :**

**Ex.1 **Find the ratio of the following :

(a) 36 minutes to 2 hours.

(b) 32 g to 1 kg

(c) 3 days to 1 years.

**Sol. ** (a) Change both 36 minutes and 2 hours to the same unit.

Now, 36 minutes = 36 minutes

2 hours = 2 × 60 minutes = 120 minutes

*∴* Ratio of 36 minutes to 2 hours

(b) First convert both into numbers with the same unit.

32 g = 32 g

3kg = 3000 g

(c) First , convert both into numbers with the same unit.

3 days = 3 days

1 year = 365 days

Ratio = 3 : 365

**Ex.2** Find the (i) ratio of M20 to M80 (ii) ratio of 3 km to 600m

**Sol. ** (i) 20 : 80 or 1 : 4

(ii) 3000m : 600m or 3000 : 600 or 5 : 1

**Comparison of Ratios :**

1. Write the given ratios as fractions in the simplest form.

2. Find the LCM of the denominators of the fractions.

3. Convert them into like fractions with same denominators .

4. Compare the numerators and arrange the fractions.

5. Then respective ratios are also in the same order.

**Ex.2** Two numbers are in the ratio 4 : 5. If the sum of the number is 63, then find the numbers.

**Sol. ** Here 63 is to be divided in the ratio 4 : 5.

**Ex.3** Mr. Harry divided Rs. 84,630 between Shinchan and Nimavari in the ratio 3 : 4. How much did each of them get ?

**Sol.** Ratio of money between Shinchan and Nimavari = 3 : 4

Sum of the terms of the ratio = 3 + 4 = 7