NCERT Book Class 6 Maths Ratio and Proportion

Ratio and Proportion

12.1 Introduction

In our daily life, many a times we compare two quantities of the same type. For example, Avnee and Shari collected flowers for scrap notebook. Avnee collected 30 flowers and Shari collected 45 flowers. So, we may say that Shari collected 45 – 30 = 15 flowers more than Avnee.

Also, if height of Rahim is 150 cm and that of Avnee is 140 cm then, we may say that the height of Rahim is 150 cm – 140 cm = 10 cm more than Avnee. This is one way of comparison by taking difference. 

If we wish to compare the lengths of an ant and a grasshopper, taking the difference does not express the comparison. The grasshopper’s length, typically 4 cm to 5 cm is too long as compared to the ant’s length which is a few mm. Comparison will be better if we try to find that how many ants can be placed one behind the other to match the length of grasshopper. So, we can say that 20 to 30 ants have the same length as a grasshopper.

Consider another example.

Cost of a car is Rs 2,50,000 and that of a motorbike is Rs 50,000. If we calculate the difference between the costs, it is Rs 2,00,000 and if we compare by division; i.e. 2,50,000/50,000 =5/1

We can say that the cost of the car is five times the cost of the motorbike. Thus, in certain situations, comparison by division makes better sense than comparison by taking the difference. The comparison by division is the Ratio. In the next section, we shall learn more about ‘Ratios’.

12.2 Ratio

Consider the following:

Isha’s weight is 25 kg and her father’s weight is 75 kg. How many times Father’s weight is of Isha’s weight? It is three times. Cost of a pen is Rs 10 and cost of a pencil is Rs 2. How many times the cost of a pencil is the cost of a pen? Obviously it is five times. 

In the above examples, we compared the two quantities in terms of ‘how many times’. This comparison is known as the Ratio. We denote ratio using symbol ‘:’

Consider the earlier examples again. We can say,

The ratio of father’s weight to Isha’s weight = 75/25 = 3/1 = 3:1

The ratio of the cost of a pen to the cost of a pencil = 10/2 = 5/1 = 5:1

Let us look at this problem.

In a class, there are 20 boys and 40 girls. What is the ratio of

(a) Number of girls to the total number of students.

(b) Number of boys to the total number of students.

First we need to find the total number of students, which is, Number of girls + Number of boys = 20 + 40 = 60.

Then, the ratio of number of girls to the total

number of students is 40/60 = 2/3

Please refer to attached file for NCERT Class 6 Maths Ratio and Proportion