RS Aggarwal Class 8 Chapter 1 Rational Numbers Solutions- Free PDF Download
FAQs on RS Aggarwal Class 8 Mathematics Solutions for Chapter-1 Rational Numbers
1. How do you find the additive inverse of a rational number in RS Aggarwal Class 8 Maths, Chapter 1?
To find the additive inverse of any rational number, you simply change its sign. If the number is positive (like 5/9), its additive inverse is negative (-5/9). If the number is negative (like -3/8), its additive inverse is positive (3/8). The core principle is that a number and its additive inverse must add up to zero.
2. What is the step-by-step method to represent a rational number like 4/7 on the number line as per the solutions?
To represent 4/7 on a number line, follow these steps:
- Draw a straight line and mark the integer points, especially 0 and 1, since 4/7 is between them.
- Divide the segment between 0 and 1 into 7 equal parts (because the denominator is 7).
- Starting from 0, count 4 of these parts to the right.
- The fourth mark represents the position of the rational number 4/7.
3. How is the distributive property used to simplify problems in RS Aggarwal Class 8 solutions for Rational Numbers?
The distributive property of multiplication over addition, a × (b + c) = (a × b) + (a × c), is used to simplify complex expressions. For example, to solve 2/5 × (-3/7 + 1/4), you can multiply 2/5 by -3/7 and 2/5 by 1/4 separately and then add the results. This method often helps break down a difficult problem into simpler calculations.
4. What is the correct method for comparing two negative rational numbers, like -3/4 and -5/6, using the techniques in this chapter?
To compare two negative rational numbers, you should first make their denominators equal.
- Find the Least Common Multiple (LCM) of the denominators. The LCM of 4 and 6 is 12.
- Convert each number to an equivalent fraction with a denominator of 12. -3/4 becomes -9/12, and -5/6 becomes -10/12.
- Now, compare the numerators. For negative numbers, the one with the smaller absolute value is greater. Since -9 is greater than -10, it means -9/12 > -10/12.
- Therefore, -3/4 > -5/6.
5. Why is it necessary to find a common denominator when adding or subtracting rational numbers, but not when multiplying them?
Finding a common denominator is essential for addition and subtraction because these operations require combining or taking away parts of a whole. The denominator represents the size of these parts. To combine them accurately, the parts must be of the same size. Multiplication, however, is a process of scaling or finding a 'fraction of a fraction,' so you can directly multiply the numerators and denominators without needing same-sized parts.
6. How do you find five rational numbers between -1 and 0, and is there only one correct set of answers?
To find rational numbers between -1 and 0, you can express them with a larger common denominator. For instance, write -1 as -6/6 and 0 as 0/6. Now, you can easily pick the numbers between them: -5/6, -4/6, -3/6, -2/6, and -1/6. Importantly, this is not the only correct answer. There are infinite rational numbers between any two rational numbers; using a larger denominator like 10 (-10/10) would give you a different set of numbers.
7. What is a common mistake students make when finding the multiplicative inverse (reciprocal) of a mixed fraction in RS Aggarwal exercises?
A frequent error is to find the reciprocal of the whole number and the fraction part separately. The correct method is to first convert the mixed fraction into an improper fraction. For example, to find the reciprocal of 3 1/2, you must first convert it to 7/2. Only then can you find its reciprocal, which is 2/7.
8. What is the role of '1' in the properties of rational numbers, as explained in Chapter 1?
In the context of rational numbers, the number '1' is known as the multiplicative identity. This is because multiplying any rational number (p/q) by 1 results in the same rational number (p/q). This property is fundamental to many simplification and verification steps shown in the RS Aggarwal solutions.











