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RS Aggarwal Solutions

RS Aggarwal Solutions Class 6 Chapter-10 Ratio, Proportion and Unitary Method (Ex 10A) Exercise 10.1

RS Aggarwal Solutions Class 6 Chapter-10 Ratio, Proportion and Unitary Method (Ex 10A) Exercise 10.1

Q: 5. How does understanding ratios as fractions in Exercise 10A prepare me for solving proportion problems later in the chapter?

Understanding a ratio like a:b as a fraction a/b is the foundational skill for proportions. A proportion is simply a statement that two ratios are equal (e.g., a:b = c:d), which is written as an equation of two fractions: a/b = c/d. By mastering how to express and simplify ratios in fractional form in Ex 10A, you learn the language needed to set up and solve these proportion equations correctly.

Q: 6. What is a common mistake when simplifying ratios in Chapter 10, and how can the RS Aggarwal solutions help prevent it?

A common mistake is incomplete simplification. For instance, a student might simplify the ratio 12:18 to 6:9 by dividing by 2, but forget to simplify it further to 2:3 by dividing by 3. The RS Aggarwal solutions consistently show the process of reducing a ratio to its simplest form by finding the Highest Common Factor (HCF). Following these solved examples helps reinforce the habit of always checking for complete simplification.

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RS Aggarwal Solutions Class 6 Chapter-10 Ratio, Proportion and Unitary Method (Ex 10A) Exercise 10.1 - Free PDF

The chapter on Ratio, Proportion and Unitary Method is an important topic for Class 6 students. It is important to have the basics clear from the very beginning as the advanced topics in higher classes are based on these rudimentary concepts. It is in this aspect that the RS Aggarwal class 6 maths exercise 10A solution enables students to get started with this chapter. While it is important to have a copious amount of practice to be able to score well in Mathematics, it can be done only when students understand the topic fully. To that end, one can download the RS Aggarwal class 6 chapter 10A PDF from Vedantu’s website without any charge.

Vedantu also provides NCERT Solutions free PDFs for all the students. You can download NCERT Solution for Class 6 Science to score more marks in the examinations.

Sneak Peek of Chapter 10 of Class 6 - Ratio, Proportion and Unitary Method

The RS Aggarwal’s class 6 mathematics covers Ratios and Proportions, as its chapter 10, includes the following major topics: Ratio and proportion is the most important topic in class 6 math. This is because it helps to learn basic numerical concepts of addition, subtraction, multiplication, division, ratios, and proportions in mathematical language. The ratio of two numbers that are divided by each other is expressed by a fraction or decimal number. The two types of ratio are verbal ratio and visual ratio.

A verbal ratio shows how many of one thing there are to an amount of another thing, whereas a visual ratio represents how much of one thing there is for every unit of another. The ratio is not considered as a separate subject like other classes; rather, it can be included in any of these subjects such as arithmetic, algebra, geometry, etc.

List of Sections in Chapter-10 Ratio, Proportion, and Unitary Method

Here is the list of sections that you will learn subsequently;

10.1 Introduction

10.2 Ratio

10.3 Proportion

10.4 Unitary Method

List of Exercises in Chapter - 10: Ratio, Proportion, and Unitary Method

Please practice the exercises diligently to score better in your exams;

Exercise 10.1 - 16 questions

Exercise 10.2 - 4 questions

Exercise 10.3 - 11 questions

FAQs on RS Aggarwal Solutions Class 6 Chapter-10 Ratio, Proportion and Unitary Method (Ex 10A) Exercise 10.1

1. What is the correct step-by-step method to find the ratio of two quantities as per the solutions for RS Aggarwal Class 6, Ex 10A?

To find the ratio between two quantities according to the methods in the solutions for Exercise 10A, you should follow these steps:

First, ensure both quantities are in the same unit. For example, convert both to centimetres or both to metres.
Write the two quantities as a fraction, with the first quantity as the numerator and the second as the denominator.
Simplify this fraction to its lowest terms by dividing both the numerator and the denominator by their Highest Common Factor (HCF).
Finally, write the simplified fraction in the ratio form, using a colon (e.g., a:b).

2. How do the RS Aggarwal solutions for Class 6 Maths Chapter 10 explain the comparison of two different ratios?

The solutions demonstrate a clear method for comparing two ratios. The process is as follows:

Convert both ratios into their fractional forms (e.g., a:b becomes a/b).
To compare the fractions, find the Least Common Multiple (LCM) of their denominators.
Convert each fraction into an equivalent fraction with the LCM as the new denominator.
The fraction with the larger numerator represents the greater ratio.

This method ensures an accurate and systematic comparison.

3. What is the standard procedure shown in Ex 10A solutions for dividing a certain amount in a given ratio?

To divide a quantity in a given ratio (for example, a:b), the solutions outline this reliable method:

Find the sum of the terms in the ratio (i.e., a + b). This sum represents the total number of equal parts the quantity is divided into.
To find the first share, multiply the total quantity by the fraction corresponding to the first term (a / (a+b)).
To find the second share, multiply the total quantity by the fraction for the second term (b / (a+b)).

This ensures the quantity is distributed precisely according to the specified ratio.

4. Why is it crucial to convert quantities to the same unit before finding a ratio, a principle strictly followed in Ex 10A solutions?

It is crucial to convert quantities to the same unit because a ratio is a comparison of like quantities. Comparing '5 metres' to '50 centimetres' directly is meaningless. By converting both to centimetres (500 cm and 50 cm), you create a valid mathematical relationship. The ratio 500:50 (or 10:1) correctly shows that the first length is ten times the second. Without this step, the comparison is fundamentally flawed.

5. How does understanding ratios as fractions in Exercise 10A prepare me for solving proportion problems later in the chapter?

Understanding a ratio like a:b as a fraction a/b is the foundational skill for proportions. A proportion is simply a statement that two ratios are equal (e.g., a:b = c:d), which is written as an equation of two fractions: a/b = c/d. By mastering how to express and simplify ratios in fractional form in Ex 10A, you learn the language needed to set up and solve these proportion equations correctly.

6. What is a common mistake when simplifying ratios in Chapter 10, and how can the RS Aggarwal solutions help prevent it?

A common mistake is incomplete simplification. For instance, a student might simplify the ratio 12:18 to 6:9 by dividing by 2, but forget to simplify it further to 2:3 by dividing by 3. The RS Aggarwal solutions consistently show the process of reducing a ratio to its simplest form by finding the Highest Common Factor (HCF). Following these solved examples helps reinforce the habit of always checking for complete simplification.

7. When dividing an amount in a ratio like 3:5, why do the solutions guide us to use a total of 8 parts (3+5)?

The ratio 3:5 means the whole quantity is conceptually split into two groups of parts. One group contains 3 equal parts and the other contains 5 of the same equal parts. Therefore, the entire quantity consists of a total of 3 + 5 = 8 of these equal parts. To find the value of one part, you must divide the total amount by 8. This logic is the basis of the method for distributing any quantity in a given ratio.