NCERT Solutions for Class 6 Maths Chapter 12 Exercise 12.2

NCERT Solutions for Class 6 Maths Chapter 12 Exercise 12.2 (Ex. 12.2) Ratio and Proportion in Hindi and English Medium updated for academic session 2021-22. All the contents are given in videos and PDF file format free to access online or download.

In class 6 math exercise 12.2 questions are based on proportion and its properties. It also tell how to use proportion in daily life situations. Most of the questions in ex. 12.2 of 6th math are interesting to solve.

Class 6 Maths Chapter 12 Exercise 12.2 Solution




Class: 6Mathematics
Chapter: 12Ratio and Proportion
Exercise: 12.2NCERT Book’s Solution

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Class 6 Maths Chapter 12 Exercise 12.2 Solution in Videos




Proportion

We know that ¼ and 2/8 are equivalent fractions.
So, 1 : 4 = 2 : 8
Similarly, 6 : 18 = 12 : 36
And 25 : 10 = 100 : 40
Each of the above statements expresses the equality of two given ratios.

An equality of two ratios is called proportion.
In general, four numbers a, b, c, d are said to be in proportion, if the ratio of the first two is equal to the ratio of the last two, i.e., a : b = c : d. This is equivalent to a/b = c/d, i.e., ad = bc.
The equality “3 :5 = 6 :10” forms a proportion. We sometimes write “3 : 5 = 6 : 10” as “3 : 5 :: 6 : 10”, which is read as “3 is to 5 as 6 is to 10” or “3 to 5 as 6 to 10”.

A proportion consists of four terms. The first and the fourth terms of the proportion are called extreme terms or extremes. The second and the third terms are called middle terms or means.

ProportionProduct of the extremesProduct of means
1 : 2 = 2 : 41 × 4 = 42 × 2 = 4
5 : 12 = 15 : 365 × 36 = 18012 × 15 = 180
27 : 45 = 18 : 3027 × 30 = 81045 × 18 = 810
128 : 16 = 48 : 6128 × 6 = 76816 × 48 = 768

What do we conclude? We conclude that in a proportion, the product of the extremes is equal to the product of the means. In other words, a : b = c : d if and only if ad = bc.

Note: If in an arrangement of four numbers, the product of their extremes is not equal to the product of their means, we say that the four numbers in that order are not in proportion.

Class 6 Maths Exercise 12.2 Important Questions

Check whether the given ratios are equal, i.e., they are in proportion: (i) 3 : 7 and 12 : 21, (ii) 14 : 8 and 42 : 24, (iii) 31 : 5 and 15 : 2

(i) Product of extremes = 3 × 21 = 63
Product of means = 7 × 12 = 84
Since, the product of extremes ≠ product of means,
Therefore 3 : 7 and 12 : 21 are not in proportion.

(ii) Product of extremes = 14 × 24 = 336
Product of means = 8 × 42 = 336
Since, the product of extremes = product of means,
Therefore, the two ratios are in proportion.

(iii) Product of extremes = 31 × 2 = 62
Product of means = 5 × 15 = 75
Since, the two product are not equal,
Therefore, the two ratios are not in proportion.

How are proportions used in real life?

The business can use proportions to figure out how much money they will earn if they sell more products. If the company sells ten products, for example, the proportional ratio is Rs. 25.00:10, which shows that for every ten products, the business will earn Rs. 25.

What are the different types of proportion?

There are two types of proportions.
(i) Direct Proportion.
(ii) Inverse Proportion.

The second, third and fourth terms in a proportion are 15, 8, 12 respectively. Find the first term.

Let the first term be x.
Then x, 15, 8 and 12 are in proportion.
So, x × 12 = 15 × 8
Or, x = 120/12 = 10.
Thus, the first term is 10.

NCERT Solutions for Class 6 Maths Chapter 12 Exercise 12.2
NCERT Solutions for Class 6 Maths Chapter 12 Exercise 12.2 in free pdf form
NCERT Solutions for Class 6 Maths Chapter 12 Exercise 12.2 in english medium
NCERT Solutions for Class 6 Maths Chapter 12 Exercise 12.2 download in free file
Class 6 Maths Chapter 12 Exercise 12.2
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