RS Aggarwal Solutions Class 7 Chapter - 4 Rational Numbers (Exercise 4B) Exercise 4.2: Download Free PDF

Q: 2. What is the step-by-step method to determine if a rational number is positive or negative before representing it on a number line?

A rational number is positive if both its numerator and denominator have the same sign (e.g., 5/7 or -5/-7). It is negative if they have opposite signs (e.g., -5/7 or 5/-7). Before plotting on a number line as in Exercise 4B, simplify it to its standard form. A positive number will be on the right of zero, and a negative number will be on the left.

Q: 3. What are the precise steps to represent a rational number like 5/3 on a number line?

To represent a rational number like 5/3 on a number line, follow these steps:Check if it's positive or negative. Since 5/3 is positive, it lies to the right of 0.Identify the two integers it lies between. 5/3 is equal to 1 and 2/3, so it lies between 1 and 2.Divide the segment between 1 and 2 into three equal parts (as the denominator is 3).The second mark after 1 represents the point 5/3.This method is essential for solving the problems in Exercise 4B.

Q: 4. Why is converting a rational number to its standard form a crucial first step before comparing or plotting it?

Converting a rational number to its standard form is crucial because it provides a unique and simplified representation. For instance, 2/3, 4/6, and 8/12 all represent the same value, but 2/3 is the standard form. Using this form prevents confusion and errors when comparing magnitudes (e.g., which is greater?) or locating the precise point on a number line. It ensures consistency in your solutions.

Q: 5. How does finding a common denominator help in comparing two different rational numbers like 3/4 and 5/6?

Finding a common denominator transforms fractions into equivalent ones that can be compared directly by their numerators. For 3/4 and 5/6, the least common multiple of 4 and 6 is 12.3/4 becomes (3×3)/(4×3) = 9/12.5/6 becomes (5×2)/(6×2) = 10/12.Now, you only need to compare the numerators. Since 10 > 9, we can conclude that 10/12 > 9/12, which means 5/6 > 3/4. This systematic approach is the foundation for ordering rational numbers.

Download RS Aggarwal Solutions Class 7 Chapter-4 Rational Numbers (Exercise 4B) Exercise 4.2 - Free PDF

Free PDF download of RS Aggarwal Solutions Class 7 Chapter-4 Rational Numbers (Ex 4B) Exercise 4.2 solved by Expert Mathematics Teachers of Vedantu. All Exercise 4.2 Questions with Solutions for Class 7 RS Aggarwal will help you to revise and complete the syllabus and to score more marks.

RS Aggarwal has been recommended by experts, teachers and toppers to students preparing for the CBSE math exam. This chapter has around 50 questions about rational numbers. Students are supposed to answer them by themselves and cross-check them with the solutions provided. RS Aggarwal can be bought from a nearby bookstore or online. But for students who are looking for online solutions for this chapter, Vedantu provides free PDFs to download and read offline. Below is the PDF for RS Aggarwal Class 7 chapter 4 solutions and problems.

RS Aggarwal Class 7 Chapter 4 Rational Numbers: Topics

This chapter deals with rational numbers. Some of the subtopics of the chapter are:

Need For Rational Numbers.
What Are Rational Numbers?
Positive And Negative Rational Numbers.
Rationals Numbers represented on a Number Line.
Representing the rational numbers in Standard Form.
Comparison of Rational Numbers.
Rational Numbers Between Two Rational Numbers.
Operations On Rational Numbers.
Addition, Subtraction, Multiplication, and Division of Rational Numbers.

Find the ideal solutions for all these sections and the exercises included in the books. Get to know how the experts have framed the answers in simple ways and learn how to score more in the exams. Refer to this solution provided by Vedantu for clarifying your doubts to become better at solving mathematical problems.

FAQs on RS Aggarwal Solutions Class 7 Chapter - 4 Rational Numbers (Exercise 4B) Exercise 4.2: Download Free PDF

1. How do you correctly identify and express a rational number in its standard form as required in RS Aggarwal Class 7, Exercise 4B?

To solve problems in Exercise 4B, first ensure the number can be written as p/q where q is not zero. For its standard form, the denominator 'q' must be positive, and the only common factor between the numerator 'p' and the denominator 'q' should be 1. For example, to express 33/-44 in standard form, first make the denominator positive: -33/44. Then, divide both by their greatest common divisor (11) to get -3/4.

2. What is the step-by-step method to determine if a rational number is positive or negative before representing it on a number line?

A rational number is positive if both its numerator and denominator have the same sign (e.g., 5/7 or -5/-7). It is negative if they have opposite signs (e.g., -5/7 or 5/-7). Before plotting on a number line as in Exercise 4B, simplify it to its standard form. A positive number will be on the right of zero, and a negative number will be on the left.

3. What are the precise steps to represent a rational number like 5/3 on a number line?

To represent a rational number like 5/3 on a number line, follow these steps:

Check if it's positive or negative. Since 5/3 is positive, it lies to the right of 0.
Identify the two integers it lies between. 5/3 is equal to 1 and 2/3, so it lies between 1 and 2.
Divide the segment between 1 and 2 into three equal parts (as the denominator is 3).
The second mark after 1 represents the point 5/3.

This method is essential for solving the problems in Exercise 4B.

4. Why is converting a rational number to its standard form a crucial first step before comparing or plotting it?

Converting a rational number to its standard form is crucial because it provides a unique and simplified representation. For instance, 2/3, 4/6, and 8/12 all represent the same value, but 2/3 is the standard form. Using this form prevents confusion and errors when comparing magnitudes (e.g., which is greater?) or locating the precise point on a number line. It ensures consistency in your solutions.

5. How does finding a common denominator help in comparing two different rational numbers like 3/4 and 5/6?

Finding a common denominator transforms fractions into equivalent ones that can be compared directly by their numerators. For 3/4 and 5/6, the least common multiple of 4 and 6 is 12.

3/4 becomes (3×3)/(4×3) = 9/12.
5/6 becomes (5×2)/(6×2) = 10/12.

Now, you only need to compare the numerators. Since 10 > 9, we can conclude that 10/12 > 9/12, which means 5/6 > 3/4. This systematic approach is the foundation for ordering rational numbers.

6. What is a common mistake when comparing two negative rational numbers, for example, -2/3 and -4/5?

A common mistake is to assume the number with the larger-looking numerator is greater, which is incorrect for negative numbers. The correct method is to first find a common denominator (15):

-2/3 becomes -10/15.
-4/5 becomes -12/15.

When comparing negative integers, the one closer to zero is greater. Since -10 is greater than -12, it follows that -10/15 > -12/15. Therefore, -2/3 > -4/5. Always remember that on the number line, the number to the right is always greater.