CBSE Class 6 Mathematics Ratio And Proportion Chapter Notes

CBSE Class 6 Ratio and Proportion Chapter Concepts. Learning the important concepts is very important for every student to get better marks in examinations. The concepts should be clear which will help in faster learning. The attached concepts made as per NCERT and CBSE pattern will help the student to understand the chapter and score better marks in the examinations.

Ratio and Proportion

12.1 Ratio

A ratio is a pair of numbers used to describe a relationship or make a comparison between two quantities. A ratio can be written three ways. Like fractions, ratios should be reduced. Notice that each form has been reduced.

1. Using the word “to” 48 to 8 = 6 to 1

2. Using a “colon” 48:8 = 6:1

3. Expressed in “fraction form” 48/8 = 6/1

Note: Given ratio a: b. Here a is called the “Antecedent” of the ratio and b is called “Consequent” of the ratio.

12.2 Proportion

A part considered in relation to the whole. The relationship between things or parts of things with respect to the total magnitude or quantity. Or it can be defined as “A statement that two ratios are the same.” Sign of Proportion: The Sign of Proportion is denoted as “:” For example, the ratios 1:4 and 4:16 are equal which means both the ratios are in proportion. It can be written as 1:4::4:16.

In a proportion 1st term and 4th term are known as extremes while 2nd and 3rd terms are known as means.

Note: If a:b=c:d then ad=bc i.e., Product of extremes = Product of means

Continued Proportions: If three quantities of the same kind are said to be in continued proportion, then the ratio of the first and second is equal to the ratio of the second and the third.

For example, If a:b=b:c, then a, b, c are in continue proportion and b2 = ac.  

Here b is called the mean proportional and the mean proportional

Note:

1. Suppose it is given that A:B, B:C, C:D then A:D can be easily find out using the following relation:

2. If a and b are two quantities then

Example 1: What do we mean by the ratio of two natural numbers?

Solution: It is their relationship with respect to relative size that we can express verbally in a sentence. Specifically, one number is a multiple of the other (so many times it), a part of it, or parts of it.

Example 2: What ratio has 15 to 5?

Solution:. 15 is three times 5. That is the ratio -- the relationship -- of 15 to 5.

Example 3. What ratio has 5 to 15?

Solution: 5 is the third part of 15. That is called the inverse ratio of 15 to 5

Example 4: What ratio has 10 to 15?

Solution: 10 is two thirds of 15.

Example 5: Let’s suppose you earn Rs.200 a week. Your house rent is Rs.40 weekly. What is the ratio of your rent to your income?

Solution: Make a ratio with the rent on top (numerator) and the weekly income on the bottom (denominator). Then reduce.

Example 6: Simplify the ratio 1/3:1/2.

Solution: Ratio is a comparison of numbers by division. Rewrite the above example as a division problem and solve.1/3:1/2 = 1/3 ¸ 1/2 = 1/3 ´ 2/1 = 2/3 or 2:3

Example7: On a workplace mathematics test of 20 questions, you missed 2 questions. What is the ratio of the number you answered correctly to the number you missed?

Step 1: Subtract the number of questions you missed from the total number of questions.

Total questions - 20

Number missed - 2

Number correct - 18

Step 2: Make a ratio with the number you answered correctly on top (numerator) and the number you missed on the bottom (denominator). Then reduce if necessary.

N u m b e r c o r r e c t =  18  =  9  = 1
N u m b e r m i s s e d        2      1

Example 8: In a ratio which is equal to 8:9 if the antecedent is 64, What is the consequent?

Solution: If the antecedent is 8 then consequent is 9. If the antecedent is 64, then consequent is Proportions

Example 1: 5 is to 15 as 8 is to 24. Is this a proportion?

This is a proportion because

5 : 15 = 5/15 = 1/3

8:24 =1/3

Example 2: Why is this a proportion? 16 is to 2 as 80 is to 10.

Solution: This is a proportion because 16: 2 =16/2= 8

80:10 = 80/10 =8

Example 3: Why is this a proportion? 10 is to 15 as 2 is to 3.

Solution: This is a proportion because 10 : 15 = 10/15= 2/3

Example 4: Complete this proportion: 8 is to 32 as 9 is to ?

Solution: Let the missing number be x 8:32:: 9:x

USE: Product of extremes = Product of means

⇒ 8  x = 3 2 x 9

x = 32 x 9 / 8

288/8 = 36

Example 5: Complete this proportion: 27 is to 3 as ? is to 5

Solution: Let the missing number be x 27:3:: x :5

USE: Product of extremes = Product of means

⇒  27 x 5 = 3 x x

x = 27 x 5 / 3

= 135/3 45

Example 6: In each item below, what ratio has a to b?

Solution: a) Since 1 is the sixth part of 6, then a is the sixth part of b.

b) Since 10 is ten times 1, then a is ten times b.

(a simply means the first term; b means the second.)

a) a is to b as 1 is to 6.

b) a is to b as 10 is to 1.

Example 7: Read this proportion, and complete it:

8/2 = 20/?

Solution: Let the missing number be x

8/2 = 20/ x

⇒ 8 * x = 20 * 2

x = 20*2/8 = 40/8 = 5

Example 8: Complete this proportion

7/21 = 4/? :

Solution: Let the missing number be x

7/21 = 4/x

⇒ 7 * x = 21 * 4

x = 21*4/7 = 84/7 = 12

Example 9: Complete this proportion:

2/3 = ?/12

Solution: Let the missing number be x

2/3 = x/12

⇒ 2 * 12 = x * 3

x = 2*12/3 = 24/3 = 8

Please click on below link to download pdf file for CBSE Class 6 Ratio and Proportion Chapter Concepts.