Class 7 RS Aggarwal Chapter-4 Rational Numbers Solutions - Free PDF Download
FAQs on RS Aggarwal Class 7 Solutions Chapter-4 Rational Numbers
1. What defines a rational number in its standard form as per the solutions for RS Aggarwal Class 7 Chapter 4?
A rational number is considered to be in its standard form when its denominator is a positive integer, and the numerator and denominator share no common factor other than 1. For instance, the rational number 3/5 is in standard form, whereas 6/10 is not because it can be simplified further to 3/5.
2. What is the correct method for adding two rational numbers with different denominators, as explained in Chapter 4?
To add rational numbers with different denominators, follow these steps: First, find the Least Common Multiple (LCM) of the denominators. Next, convert each rational number into an equivalent fraction that has the LCM as its denominator. Finally, add the numerators of these new, like-fractions, keeping the common denominator. For example, to add 1/4 and 2/3, the LCM is 12. The equivalent fractions are 3/12 and 8/12, and their sum is (3+8)/12 = 11/12.
3. How do the RS Aggarwal solutions for Class 7 explain the subtraction of one rational number from another?
Subtracting a rational number is explained as the process of adding its additive inverse. To subtract c/d from a/b, you calculate a/b + (-c/d). The additive inverse of any rational number p/q is simply -p/q. If the denominators are not the same, you must first find their LCM to create like-fractions before performing the addition.
4. What is the step-by-step process for representing a rational number like -7/4 on a number line?
To represent -7/4 on a number line, you should first convert it to a mixed fraction, which is -1 3/4. This tells you the number lies between the integers -1 and -2. Next, divide the segment on the number line between -1 and -2 into four equal parts. The third mark to the left of -1 represents the position of -7/4.
5. Is every integer also a rational number? Explain how this is addressed in Class 7 Maths Chapter 4.
Yes, every integer is a rational number. A rational number is defined as any number that can be written in the form p/q, where p and q are integers and q is not zero. Any integer, such as 8, can be expressed as 8/1. In this case, p=8 and q=1, fulfilling the definition. Similarly, a negative integer like -5 can be written as -5/1, confirming it is also a rational number.
6. Why is finding the LCM a necessary first step when adding or subtracting rational numbers with unlike denominators?
Finding the Least Common Multiple (LCM) is essential because it allows us to convert the rational numbers into 'like' fractions—fractions that share a common denominator. We can only add or subtract parts of a whole accurately when the parts are of the same size. The LCM provides this common sizing, ensuring that the numerators we add or subtract represent portions of the same-sized unit.
7. What is the fundamental difference between the additive inverse and the multiplicative inverse of a rational number?
The primary difference is the mathematical operation and the identity element they relate to.
- The additive inverse of a number p/q is -p/q. When added together, they result in 0 (the additive identity). Example: 3/7 + (-3/7) = 0.
- The multiplicative inverse (or reciprocal) of a non-zero number p/q is q/p. When multiplied, they result in 1 (the multiplicative identity). Example: (3/7) × (7/3) = 1.
8. How does the 'density property' of rational numbers explain what lies between any two rational numbers on a number line?
The density property states that between any two distinct rational numbers, you can always find another rational number. In fact, you can find infinitely many. For example, to find a number between 1/2 and 3/4, you can find their average: [(1/2) + (3/4)] / 2 = (5/4) / 2 = 5/8. This process can be repeated endlessly, proving that the rational numbers are densely packed along the number line.
9. What is a common mistake students make when solving division problems with rational numbers?
A common mistake is to divide the numerators and denominators directly, similar to multiplication. The correct method for dividing a rational number a/b by c/d is to multiply a/b by the reciprocal (multiplicative inverse) of c/d. The correct calculation is (a/b) ÷ (c/d) = (a/b) × (d/c). Forgetting to flip the second fraction before multiplying is a frequent error.
10. How do you correctly compare a negative rational number with a positive one, for example, -5/2 and 1/8?
When comparing a negative and a positive rational number, the rule is absolute: any positive rational number is always greater than any negative rational number. Therefore, without needing to find a common denominator or compare the numerical values, we know that 1/8 is greater than -5/2 simply because 1/8 is positive and -5/2 is negative.





