According to NCERT Solutions for Class 6, this is one of the most essential chapters in Maths. This will be crucial in shaping your foundation. 

This chapter will define the term ratio. There are various types of ratios. NCERT Solutions for Class 6 teaches students about all types of ratios and how to apply them. This lesson will also introduce the concept of 'Proportion.' Proportion, like ratio, is divided into several forms. To excel in the topic, you must master them all.

NCERT Solutions for Class 6 Maths Chapter 12 covers the ratio segment in this part and discusses the meaning of ratio. Ratio is one of the most important components of the mathematics syllabus. 

According to Chapter 12 Ratio and Proportion, you can calculate a ratio only if the quantities under comparison are:

• • Similar in nature.
  • In the same metric system.

The symbol ":" signifies a ratio (colon).

The notes, animated movies, and visualisations provided by the MSVGo app help you to skillfully solve ratio problems.

The properties of Ratio are as follows:

1. If both the antecedent and the consequent are multiplied or divided by the same non-zero value, the ratio stays the same

x/y = px/py = qx/qy , p, q ≠0

x/y = (x/p)  /  (y/p) = (x/q)  / (y/q) , p, q ≠0

2. Two ratios in fraction notation can be compared in the same way as actual numbers can.

x/y = p/q ⟺ xq = yp

x/y> p/q ⟺ xq > yp

x/y < p/q ⟺ xq < yp

3. If the ratios x/y and c/d are the same, then

x/y = c/d ⟹ y/x = d/c (Invertendo)

x/y = c/d ⟹ x/c = y/d (Alternendo)

x/y = c/d ⟹ (x+y)/y = (c+d)/d (Componendo)

x/y = c/d ⟹ (x-y)/y = (c-d)/d (Dividendo)

After learning about ratio in the previous section, the NCERT Solutions for Class 6 Maths then teaches students about proportion. This concept is another very essential part of the chapter. Chapter 12 Ratio and proportion discusses the meaning of proportion and also provides examples to understand the topic better. 

Proportion is usually denoted using the symbols “::” (two colons) and “=” (equal to).

The primary goal of the MSVGo app in Chapter 12 of Class 6 Maths is to promote smart learning by building a solid base. Once you understand the ideas, you will be able to answer all the questions quickly. The app handles all the exercise problems step-by-step to help you learn everything.

Students learn about the various properties of proportion in the NCERT Solutions for Class 6 mathematics.

The properties of proportion describe its magic. For example, if A:B = C:D, then:

A+B = C+D

A-C = B-D

B:A = D:C

A-B:B = C-D:D

A+B:B = C+D:D

MSVGo app also mentions numerous other such properties which you can learn about, at your own pace. For example, the app covers the unitary approach in detail. The unitary method is a problem-solving procedure that involves determining the outcome of a single unit and calculating the result of many units related to it.

The formula of a ratio is given as A:B (assuming A and B are two quantities of a similar kind).

The formula of proportion is given as A:B = C:D (assuming A:B and C:D are ratios of two similar quantities).

• What is the concept of ratios?

Ans. A ratio is a mathematical tool used to compare or find the relationship between two different quantities. It helps you compare two quantities in its own unit and format.

 

• How do you solve a ratio?

Ans. You can solve a ratio by dividing the two numbers or quantities with each other.

 

• How do you solve ratio and proportion word problems?

Ans. You can solve ratio and proportion word problems by first assigning the quantities to the formulae. Read the word problems carefully and extract the numbers as A, B, C, and D (individual quantities). Then, calculate the ratios separately and compare them to check if they are in proportion or not.

 

• What is a proportion (with an example)?

Ans. A proportion is a comparison between two ratios. For example, consider 1:2 and 1:3 as two ratios. When comparing these ratios, you can deduce that they are not equal. It means that the ratios are not in proportion, i.e., they are not equal.

 

• Divide Rs. 60 amongst Tina and Meena in a 1:2 ratio.

Ans.  Let Tina’s part be x.

Then Meena’s part is 2x.

Thus, x+2x = 60

=> 3x = 60

=> x = (60/3)

=> x = 20.

Therefore, Tina’s share = x = Rs. 20

Meena’s share = 3x = Rs. (2*20) = Rs. 40

 

• Find the ratio of the following:

(a) 40 to 60

(b) 68 to 52

(c) 44 m to 121 m

(d) 60 seconds to 45 seconds

Ans:

(a) 40 / 60 = (2 x 2 x 2 x 5) / (2 × 2 × 3 × 5)

= 2 / 3

(b) 68 / 52 = (2 x 2 x 17) / (2 x 2 x 13)

= 17 / 13

(c) 44 / 121 = (4 × 11) / (11 × 11)

= 4 / 11

(d) 60 / 45 = (2 × 2 x 3 × 5) / (3 × 3 × 5)

= 4 / 3

 

• Find the ratio of the following:

(a) 50 minutes to 2.4 hours

(b) 60 seconds to 150 seconds

(c) 90 paise to ₹ 1

(d) 600 ml to 4 litres

Ans:

(a) 50 minutes to 2.4 hours

50 min = 50 / 60

= 0.8 hours

Required ratio = (0.2 x 0.2 x 0.2) / (2 x 2 x 0.2 x 0.3)

= 1 / 3

(b) 60 seconds to 150 seconds

= 60( 2 x 2 x 3 x 5)

=150(2 x 3 x 5 x 5)

Ratio= 4 / 5

(c) 90 paise to ₹ 1

₹ 1 = 100 paise

Required ratio = 90 / 100 = (10 x 9) / (10 x 10)

= 9 / 10

(d) 600 ml to 4 litres

1 litre = 1000 ml

4 litre = 4000 ml

Required ratio = 600 / 4000 = 6 / 40 

= 3 / 20

 

• There are 102 teachers in a school of 3300 students. Find the ratio of the number of teachers to the number of students.

Ans:

Given

Number of teachers in a school = 102

Number of students in a school = 3300

Ratios of number of teachers to the number of students = 102 / 3300

= (2 × 3 × 17) / (2 × 3 × 550)

= 17 / 550

 

• Divide 20 pens in a 3:2 ratio between Raj and Veer.

Ans:

Terms of 3: 2 = 3 and 2

Sum of these terms = 3 + 2

= 5

Now Raj will get 3 / 5 of total pens and Veer will get 2 / 5 of total pens

Number of pens having with Raj = 3 / 5 × 20

= 3 × 4

= 12

Number of pens having with Veer = 2 / 5 × 20

= 2 × 4

= 8

On the MSVGo app, we studied Ratio and Proportion- their definitions, properties, and formulas, for the class 6 Maths Chapter 12. NCERT solutions provided in this section will help the students clear the concepts by practising them. 

We can now deduce that these two concepts of comparison and relationship between numbers are known as ratio and proportion. They are an integral part of mathematics and lay a foundation for advanced concepts, such as probability and statistics.