- Books Name
- CBSE Class 6 Mathematics Book
- Param Publication
- CBSE Class 6
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