In Maths, arithmetic operations are the basic operations we perform on integers. Let us discuss here how we can perform these operations on rational numbers, say p/q and s/t.
Addition: When we add p/q and s/t, we need to make the denominator the same. Hence, we get (pt+qs)/qt.
Example: 1/2 + 3/4 = (2+3)/4 = 5/4
Subtraction: Similarly, if we subtract p/q and s/t, then also, we need to make the denominator same, first, and then do the subtraction.
Example: 1/2 – 3/4 = (2-3)/4 = -1/4
Multiplication: In case of multiplication, while multiplying two rational numbers, the numerator and denominators of the rational numbers are multiplied, respectively. If p/q is multiplied by s/t, then we get (p×s)/(q×t).
Example: 1/2 × 3/4 = (1×3)/(2×4) = 3/8
Division: If p/q is divided by s/t, then it is represented as:
(p/q)÷(s/t) = pt/qs
Example: 1/2 ÷ 3/4 = (1×4)/(2×3) = 4/6 = 2/3
Multiplicative Inverse of Rational Numbers
As the rational number is represented in the form p/q, which is a fraction, then the multiplicative inverse of the rational number is the reciprocal of the given fraction.
For example, 4/7 is a rational number, then the multiplicative inverse of the rational number 4/7 is 7/4, such that (4/7)x(7/4) = 1
Rational Numbers Properties
Since a rational number is a subset of the real number, the rational number will obey all the properties of the real number system. Some of the important properties of the rational numbers are as follows:
- The results are always a rational number if we multiply, add, or subtract any two rational numbers.
- A rational number remains the same if we divide or multiply both the numerator and denominator with the same factor.
- If we add zero to a rational number then we will get the same number itself.
- Rational numbers are closed under addition, subtraction, and multiplication.
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