NCERT Book Class 7 Maths Comparing Quantities

Comparing Quantities

8.1 INTRODUCTION

In our daily life, there are many occasions when we compare two quantities. Suppose we are comparing heights of Heena and Amir. We find that

1. Heena is two times taller than Amir.

       Or

2. Amir’s height is1/2 of Heena’s height.

Consider another example, where 20 marbles are divided between Rita and Amit such that Rita has 12 marbles and Amit has 8 marbles. We say,

1. Rita has 3/2 times the marbles that Amit has.

     Or

2. Amit has2/3 part of what Rita has.

Yet another example is where we compare speeds of a Cheetah and a Man.

The speed of a Cheetah is 6 times the speed of a Man.

     Or

The speed of a Man is1/6 of the speed of the Cheetah. Do you remember comparisons like this? In Class VI, we have learnt to make comparisons by saying how many times one quantity is of the other. Here, we see that it can also be inverted and written as what part one quantity is of the other.

In the given cases, we write the ratio of the heights as :

Heena’s height : Amir’s height is 150 : 75 or 2 : 1.

Can you now write the ratios for the other comparisons?

These are relative comparisons and could be same for two different situations.

If Heena’s height was 150 cm and Amir’s was 100 cm, then the ratio of their heights would be,

Heena’s height : Amir’s height = 150 : 100 =150/100 = 3/2 or 3 : 2.

This is same as the ratio for Rita’s to Amit’s share of marbles.

Thus, we see that the ratio for two different comparisons may be the same. Remember that to compare two quantities, the units must be the same.

EXAMPLE 1 Find the ratio of 3 km to 300 m.

SOLUTION First convert both the distances to the same unit.

So, 3 km = 3 × 1000 m = 3000 m.

Thus, the required ratio, 3 km : 300 m is 3000 : 300 = 10 : 1.

8.2 EQUIVALENT RATIOS

Different ratios can also be compared with each other to know whether they are equivalent or not. To do this, we need to write the ratios in the form of fractions and then compare them by converting them to like fractions. If these like fractions are equal, we say the given ratios are equivalent.

EXAMPLE 2 Are the ratios 1:2 and 2:3 equivalent?

SOLUTION To check this, we need to know whether 1/2 = 2/3.

We have,1/2 = 1×3/2×3 = 3/6 = 2×2/3×2 = 4/6

We find that  3/6 < 4/6, which means that 1/2 < 2/3

Therefore, the ratio 1:2 is not equivalent to the ratio 2:3.

Use of such comparisons can be seen by the following example.

EXERCISE 8.1

1. Find the ratio of:

(a) Rs 5 to 50 paise    (b) 15 kg to 210 g

(c) 9 m to 27 cm     (d) 30 days to 36 hours

2. In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?

3. Population of Rajasthan = 570 lakhs and population of UP = 1660 lakhs.

Area of Rajasthan = 3 lakh km2 and area of UP = 2 lakh km2.

(i) How many people are there per km2 in both these States?

(ii) Which State is less populated?

Please refer to attached file for NCERT Class 7 Maths Comparing Quantities