# RD Sharma Solutions for Class 7 Maths Chapter 5: Operations on Rational Numbers

The RD Sharma Solutions for Class 7 Maths Chapter 5 operations on rational numbers explain how one can add, subtract, multiply and divide the rational numbers, following how these operations can be done on fractions and integers. In the addition concept, if there are two rational numbers with the same denominators, the addition operation is done by adding the two numerators while keeping the same denominator. For example, the following steps needed to be followed to add two numbers with different denominators.

• If the denominator of the rational number is negative, then the numbers need to be adjusted to have positive denominators.
• Next, find the LCM of the given numbers.
• After taking the LCM, the numbers need to be converted to have the same denominator. In simple terms, this is done by multiplying both the numerator and the denominator with the common multiple.
• Finally, add the two numbers (if the denominator or numerator contains a negative sign, then this addition will convert to subtraction). Finally, it leads to the final answer.

Next, in subtraction, one can learn how to subtract rational numbers. For example, if there are two rational numbers, m/n and x/y, and one subtracts x/y from m/n, this equals adding the additive inverse of x/y to m/n. Thus, when x/y needs to be subtracted from m/n, it can be written as (m/n) + (-x/y). After writing in this form, the same method of addition discussed above needs to be applied here.

In Class 7 Maths Chapter 5 operations on rational numbers, multiplication explains multiplying two rational numbers. For this, take m/n and x/y, multiplication of two rational numbers can simply be done by multiplying the numerator to the numerator and denominator to the denominator like this (m/n) * (x/y). Lastly, the division is merely the inversion of the multiplication process, and the same concept applies here as well. Consider two rational numbers a/b and c/d and c/d does not equal to zero, (a/b) / (c/d) = (a/b) * (d/c).