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Ratio and Proportion Class 6 Notes CBSE Maths Chapter 12 (Free PDF Download)

Last updated date: 17th Sep 2024
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Revision Notes for CBSE Class 6 Maths Chapter 12 - Free PDF Download

Discover the fascinating world of relationships between quantities in Class 6 Maths Chapter 12 - Ratio and Proportion. This chapter unfolds the essential concepts of ratios and proportions, unveiling the mathematical magic that governs the balanced and proportional nature of various elements. Get ready for a numerical journey that's both enlightening and enjoyable. Free PDF download of Class 6 Maths Chapter 12 - Ratio and Proportion Revision Notes & Short Key-notes prepared by expert Maths teachers from the latest edition of CBSE(NCERT) books. Register for Maths Tuitions on Vedantu.com to clear your doubts.

Access Class 6 Mathematics Chapter 12 - Ratio and Proportion Notes

Comparison by Taking Difference:

1. We often employ the approach of taking differences between quantities when comparing quantities of the same type.

2. In some cases, a comparison by difference is not preferable to a comparison by division.

3. When we examine the two quantities in terms of ‘how many times,' this comparison is called ‘Ratio’.

Comparison by Division:

1. In many cases, division is used to make a more meaningful comparison of amounts, i.e., seeing how many times one quantity is to the other quantity.

Comparison by ratio is the name given to this procedure.

1. The sign $:$ is used to represent a ratio.

2. The two quantities must be in the same unit to be compared via ratio. If they aren't in the same unit, they should be before the ratio is calculated.

3. By multiplying or dividing the numerator and denominator by the same number, we can derive equivalent ratios.

Example:

Isha weighs $\text{10 kg}$ whereas her father weighs $\text{50 kg}$. The weights of Isha's father and Isha are said to be in a $\text{50:10 = 5:1}$ ratio.

1. The same ratio can occur in a variety of circumstances.

2. It's worth noting that the $\text{a : b}$ ratio is not the same as $\text{b : a}$. As a result, the order in which quantities are taken to express their ratio is important.

For example, $\text{5 : 3}$ ratio is not the same as the $\text{3 : 5}$ ratio.

1. A ratio can be expressed as a fraction; for example, the ratio $\text{7 : 9}$ can be expressed as $\dfrac{7}{9}$.

2. In its simplest form, a ratio can be represented.

For example, the ratio $\text{78 : 39}$ is considered as $\dfrac{\text{78}}{39}$ .

In its simplest form, a ratio can be represented as $\dfrac{\text{78}}{39}=\dfrac{2}{1}$.

Hence, the lowest form of the ratio $\text{78 : 39}$ is $\text{2 : 1}$.

1. If the fractions corresponding to two ratios are the same, they are comparable.

Example:

$\text{1 : 2}$ is identical to $\text{5 : 10}$ or $\text{8 : 16}$.

1. We say two ratios are in proportion if they are equal, and we use the symbols ‘$::$’ or ‘$=$' to equate them.

2. We say that two ratios are not in proportion if they are not equal.

The four quantities involved in a statement of proportion are known as respective terms when they are taken in order.

Extreme terms are the first and fourth terms. Whereas, Middle terms are the second and third terms.

Example:

(i) Are $16,48,17$ and $51$ in proportion?

Ans:

$\text{Ratio of }\!\!~\!\!\text{ 16 to 48 = }\dfrac{\text{16}}{\text{48}}$

$\text{ = }\dfrac{\text{1}}{\text{3}}$

$\text{ = 1 : 3}$

$\text{Ratio of }\!\!~\!\!\text{ 17 to 51 = }\dfrac{\text{17}}{51}$

$\text{ = }\dfrac{\text{1}}{\text{3}}$

$\text{ = 1 : 3}$

Since, $16:48=17:51$

Therefore, $16,48,17$ and $51$ are in proportion.

Here, $16$ and $51$ are the extreme terms whereas, $48$ and $17$ are the Middle terms.

(ii) Do the ratios $\text{15 cm}$ to $\text{3 m}$ and $\text{24 seconds}$ to $\text{5 minutes}$ form a proportion?

Ans:

$\text{Ratio of }\!\!~\!\!\text{ 15 cm to 3 m = 15 : 3}\times 100$

Since, $\left( \text{1 m = 100 cm} \right)$,

Therefore, we get,

$\text{Ratio of }\!\!~\!\!\text{ 15 cm to 3 m = 15 : }300$

$\text{Ratio of }\!\!~\!\!\text{ 15 cm to 3 m = 1 : }20$

$\text{Ratio of }\!\!~\!\!\text{ 24 sec to 5 minutes = 24 : 8}\times 60$

Since, $\left( \text{1 minute = 60 seconds} \right)$,

Therefore, we get,

$\text{Ratio of }\!\!~\!\!\text{ 24 sec to 5 minutes = 24 : }300$

$\text{Ratio of }\!\!~\!\!\text{ 24 sec to 5 minutes = 1 : }12.5$

Since, $1:20\ne 1:12.5$

Therefore, the given ratios $\text{5 cm}$ to $\text{3 m}$ and $\text{24 seconds}$ to $\text{5 minutes}$ do not form a proportion.

1. The unitary method is a method that involves first determining the value of one unit and then determining the value of the required number of units.

Example:

If the cost of a dozen soaps is $\text{Rs}\text{. 250}$ , what will be the cost of $\text{23}$ such soaps?

Ans:

We have, a

Cost of a dozen soaps is $\text{Rs}\text{. 250}$.

Since, $\text{1 dozen = 12}$

Therefore,

$\text{Cost of }\!\!~\!\!\text{ 1 soap = }\dfrac{\text{250}}{\text{12}}$

$\text{ = Rs}\text{. 20}\text{.83}$

Therefore,

$\text{Cost of }\!\!~\!\!\text{ 23 soaps = 20}\text{.83}\times 23$

$\text{ = Rs}\text{. 479}\text{.09}$

Hence, the cost of $\text{23}$ soaps is $\text{Rs}\text{. 479}\text{.09}$.

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Embark on an enriching mathematical journey with Vedantu's Revision Notes for Class 6 Maths Chapter 12 - Ratio and Proportion. These notes act as invaluable companions, unlocking the secrets of proportional relationships in a simplified manner. Let's delve into the benefits:

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Conclusion

Unlock the mysteries of Ratio and Proportion with Vedantu's meticulously crafted guide to NCERT - Class 6 Maths Chapter 12. Expertly designed by seasoned educators, these notes serve as your indispensable companion. Breaking down complexities into digestible sections, they facilitate seamless understanding, empowering you to master formulas, navigate questions effortlessly, and swiftly tackle last-minute revisions. Immerse yourself in these notes for efficient study preparation, fostering not only exam readiness but also a profound comprehension of the subject matter.

FAQs on Ratio and Proportion Class 6 Notes CBSE Maths Chapter 12 (Free PDF Download)

Q1. Where can I download the latest 2024 Chapter 12 Ratio and Proportion of Class 6 Maths notes?

Class 6 Maths Chapter 12 Ratio and proportion are the basic fundamentals and should be learnt in an accurate and precise manner. This can be downloaded by visiting the Vedantu website from NCERT solutions. These solutions are very well-formatted in a systematic way making an easy preparation for students. The exercises solutions are given according to the chapter and can be understood easily. The extra questions at the end of the chapter will give an additional practice of the chapter.

Q2. What is a unitary method?

When we want to determine the cost of any material, say for example the cost of 12 pens. First, we see the cost of a pen. For example, if the cost of 1 pen is Rs 5 then it is easy to find the cost of 12 pens.

12x5=60 Rs.

The cost of 12 pens has been determined by the unitary method. So a unitary method can be defined as determining the value of one unit then the value of the required units can be determined easily.

Q3. Explain comparison by division method?

When we compare the quantities in terms of ratio then this comparison is known as the division method. The symbol used is(:). The two quantities should be in the same unit to be compared by the method of ratio. If the quantities are not of the same unit then it has to be converted to similar units and then the quantities can be compared by this method. The equivalent ratio can be derived when we multiply the numerator and the denominator by the same number.

Q4. Explain comparison by taking the difference?

Comparison by the difference is where we take and compare the difference between the two quantities.  But sometimes it is not preferred.  When we want to compare the two quantities and we consider just by calculating a difference can be termed as comparison by difference. Certain terms are very important to know from the lower classes. Further explanation of this chapter in higher classes will be explained and the basics will not be taught again. This is the right time to focus and learn in an appropriate manner.

These solutions are available on Vedantu's official website(vedantu.com) and mobile app free of cost.

Q5. What do you understand by ratio according to the chapter?

Ratio is the comparison of the quantities. For example when we have two quantities and the comparison between the two where we see which is more than each other. Such comparisons are termed ratios. This chapter is an important chapter for class 6 Maths. The students learn the ratio and the comparisons of the quantities in different methods. The chapter is interesting and can be learnt easily if the proper practice of numericals is done on a regular basis.

For the details of the chapter, you can refer to Vedantu to make the learning easier and enjoyable.