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In Chapter 12, Ratio and Proportion – Class 6, students will be introduced to the concepts of Ratio and Proportion. Students will learn the concepts of ratio to determine the relation among the values of two different values. Ratio and Proportion, Class 6 will teach students to solve complex mathematical problems containing a comparison. The chapter Ratio and Proportion of Class 6 teaches students about Ratio, Proportion, and the Unitary Method. Read through for NCERT Maths Ratio and Proportion Class 6 Chapter 12 Notes and Exercise Solutions.
Table of Contents
Multiplication and Division Word Problems
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NCERT Maths Ratio and Proportion Class 6 Chapter 12 Notes – PDF Available
Check the topic-wise notes for NCERT Maths Ratio and Proportion Class 6 Chapter 12 below. You can also download the PDF of the notes and take a printout to study later when you need quick revision before going to the exam hall.
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Topic 1: Ratio
When we compare two quantities in terms of ‘how many times’. This comparison is known as the Ratio. We denote the ratio using the symbol ‘:’.
However, it must be noted that two quantities can be compared only if they are in the same units of measurement.
- Equivalent Ratio: Equivalent ratios can be obtained by multiplying or dividing the numerator and denominator by the same number
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In a simpler manner, Ratios can be explained as – “We often make the comparisons between two quantities by taking their difference. However, in certain situations, a more meaningful comparison between quantities is required and that comparison is made by using division, i.e. by seeing how many times one quantity is to the other quantity. This method is known as comparison by ratio.”.
For example, Isha’s weight is 25 kg and her father’s weight is 75 kg. We say that Isha’s father’s weight and Isha’s weight are in the ratio 3 : 1.
Topic 2: Proportions
If two ratios are equal, we say that they are in proportion and use the symbol ‘::’ or ‘=’ to equate the two ratios. If two ratios are not equal, then we say that they are not in proportion.
- Respective Terms: In a statement of proportion, the four quantities involved when taken in order are known as respective terms. The first and fourth terms are known as extreme terms. The second and third terms are known as middle terms.
For example, in the proportion a:b::c:d, a, b and c, d are the respective terms. And a and d are the extreme terms and c and b are the middle terms.
Topic 3: Unitary Method
The method in which first we find the value of one unit and then the value of the required number of units is known as the Unitary Method.
NCERT Maths Solutions for Ratio and Proportion Class 6 Chapter 12 – Free PDF Download
Below we have provided solutions for NCERT Maths Ratio and Proportion Class 6 Chapter 12. Go through for answers to some important questions.
Exercise 12.1 Solutions
Q 1. There are 20 girls and 15 boys in a class.
- What is the ratio of number of girls to the number of boys?
- What is the ratio of number of girls to the total number of students in the class?
Solutions. The answers are given below.
- The ratio of the number of girls to the number of boys can be calculated by dividing both numbers. So, the ratio is given by:
Hence, the ratio of the number of girls to the number of boys is 4:3.
- Total number of students in the class = number of boys + number of girls = 20 + 15 = 35
Now, the ratio of number of girls to the total number of students in the class can be calculated by dividing both numbers. So, the ratio is given by:
Hence, the ratio of number of girls to the total number of students is 4:7.
Q 2. Out of 30 students in a class, 6 like football, 12 like cricket and remaining like tennis. Find the ratio of
- The number of students liking football to the number of students liking tennis.
- Number of students liking cricket to the total number of students.
Solutions. The solutions for each are given below.
- Number of students liking tennis = 30 – (number of students liking football and cricket)
So, number of students who like playing tennis = 30 – (6 + 12) = 12
The ratio of the number of students liking football to the number of students liking tennis can be calculated by:
So, the ratio is 1:2.
- The ratio of students liking cricket to the total number of students can be calculated by:
So, the ratio is 2:5.
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Q 3. Distances travelled by Hamid and Akhtar in an hour are 9 km and 12 km. Find the ratio of the speed of Hamid to the speed of Akhtar.
Solutions. We know, speed is calculated by the distance travelled per unit time. Since Hamid and Akhtar both have travelled for an hour, their speeds can be calculated as follows:
Now that we have calculated Hamid’s and Akhtar’s speeds, we can easily determine their ratio as:
∴ The ratio of the speed of Hamid to the speed of Akhtar is 3:4.
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Q 4. Fill in the following blanks:
[Are these equivalent ratios?]
Solutions. The solutions to each of the given blanks are given below.
Now, again:
Finally,
∴ the value of each ◻ is 5, 12 and 25. Yes, the given ratios are equivalent ratios.
Q 5. Find the ratio of 30 minutes to 1.5 hours.
Solutions. From the rule of determining the ratios, we know that both quantities must be in the same unit of measurement.
We know, 1 hour = 60 minutes
∴ 1.5 hours = 60 + (60 × ½) = 90 minutes
Now, the ratio of 30 minutes to 90 minutes is 30/90 = 1:3
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Q 6. Mother wants to divide ₹ 36 between her daughters Shreya and Bhoomika in the ratio of their ages. If the age of Shreya is 15 years and the age of Bhoomika is 12 years, find how much Shreya and Bhoomika will get.
Solutions. Let us calculate the ratio between Shreya’s and Bhoomika’s ages:
To divide the money between two sisters by the ratio of their ages, we must calculate the sum of the ratio as:
Ratio = 5:4, Sum of 5 and 4 = 5 + 4 = 9
Hence. Shreya must get 5/9 of the total money and Bhoomika must get 4/9 of the total money.
∴ money that Shreya must get –
And the money that Bhoomika must get –
So, Shreya must get ₹ 20 and Bhoomika must get ₹ 16.
Exercise 12.2 Solutions
Q 1. Determine if the following are in proportion.
- 15, 45, 40, 120
- 33, 121, 9,96
Solutions. We know that two ratios are in proportion if they are equal.
- We must simplify the ratio of each of the given respective terms in order to compare their ratios.
15/45 = ⅓ and 40/120 = ⅓
Hence, 15/45 = 40/120, they are in proportion.
- Now, 33/121 = 3/11 and 9/96 = 3/32
∴ 33/121 ≠ 9/96, they are not in proportion.
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Q 2. Are the following statements true?
- 40 persons : 200 persons = ₹ 15 : ₹ 75
- 7.5 litres : 15 litres = 5 kg : 10 kg
- 99 kg : 45 kg = ₹ 44 : ₹ 20
Solutions. Let us see the solution to each of the questions below.
- 40/200 = 1:5 and 15/75 = 1:5
So, 40/200 = 15/75
∴ The given proportionality statement is true.
- 7.5/15 = 75/150 = 1:2 and 5/10 = 1:2
So, 7.5/15 = 5/10
∴ The given proportionality statement is true.
- 99/45 = 11/5 and 44/20 = 11/5
So, 99/45 = 11/5
∴ The given proportionality statement is true.
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Exercise 12.3 Solutions
Q 1. If the cost of 7 m of cloth is ₹ 1470, find the cost of 5 m of cloth.
Solutions. Given, the cost of 7 m of cloth is ₹ 1470.
Cost of 1 m of cloth = ₹1470/7
Now, the cost of 5 m of cloth = 1470/7 × 5 = ₹ 1050
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Q 2. If it has rained 276 mm in the last 3 days, how many cm of rain will fall in one full week (7 days)? Assume that the rain continues to fall at the same rate.
Solutions. Given that it has rained 276 mm in 3 days. If the rain continues to fall at the same rate then –
Amount of rain in 3 days = 276 mm
Amount of rain in 1 day = 276/3 mm
Now, the amount of rain in 7 days = 276/3 × 7 = 644 mm
Now, we know 1 mm = 0.1 cm
∴ 644 mm = 64.4 cm
So, 64.4 cm of rain will fall in 7 days.
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Q 3. Shaina pays ₹ 15000 as rent for 3 months. How much does she have to pay for a whole year, if the rent per month remains the same?
Solutions. Given, rent for 3 months = ₹ 15,000
Rent for 1 month = ₹ 15000/3
Rent for 12 months = ₹ 15000/3 × 12 = ₹ 60,000
So, Shaina will have to pay ₹ 60,000 as rent for 12 months.
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Check out Maths Class 6 Notes and Exercise Solutions for other chapters below.
FAQs
Ans: When we compare two quantities in terms of ‘how many times’. This comparison is known as the Ratio. We denote the ratio using the symbol ‘:’.
Ans: If two ratios are equal, we say that they are in proportion and use the symbol ‘::’ or ‘=’ to equate the two ratios. If two ratios are not equal, then we say that they are not in proportion.
Ans: The method in which first we find the value of one unit and then the value of the required number of units is known as the Unitary Method.
This was all about NCERT Maths Ratio and Proportion Class 6, Chapter 12 in which we studied the use of variables to make certain rules and that mathematical operations can be operated on variables when we need to determine an unknown value for a given quantity. Download the NCERT Maths Ratio and Proportion Class 6 Notes and Exercise Solutions to ace your exam preparations. Follow the CBSE Class 6 Maths Notes for more such chapter notes and important questions and answers for preparation for CBSE Class 6 Maths.