In this article of ours, we tried covering everything about the concept of Equality of Rational Numbers using Standard Form. You will find all about how to determine whether two rational numbers are equal or not. However, there are various methods to know whether given rational numbers are equal or not but we will employ the standard form method here.
How to determine the Equality of Rational Numbers using Standard Form?
To check whether the given rational numbers are equal or not you need to find out the standard form of both of them individually. If the standard form of both the rational numbers is equal then the rational numbers are equal or else not equal.
Solved Examples
1. Determine whether the Rational Numbers 4/-9 and -16/36 equal or not using a standard form?
Solution:
Given Rational Numbers are 4/-9, -16/36
Check for the denominators in both the rational numbers if they aren’t positive change them to positive.
4/-9 = 4*(-1)/-9*(-1)
=-4/9
GCD(4,9) = 1, thus -4/9 is the standard form.
-16/36 since it has a positive denominator it remains unchanged
Find the GCD of absolute values of the numerator and denominator for the rational numbers.
GCD(16, 36) = 4
To reduce the rational number to standard form divide both numerator and denominator with GCD obtained.
-16/36 = (-16÷4)/(36÷4)
= -4/9
-4/9 is the standard form of -16/36
Since the standard forms of rational numbers are equal both the given rational numbers 4/-9 and -16/36 are equal.
2. Determine whether the Rational Numbers 2/3 and 5/7 equal or not using a Standard Form?
Solution:
Given Rational Numbers are 2/3 and 5/7
Since both the denominators are positive you need not multiply or divide to make them positive.
Find the GCD of absolute values of numerator and denominator in the given rational numbers.
GCD(2, 3) =1
GCD(5, 7) = 1
Since both the rational numbers have GCD 1 and the numbers are relatively prime. Both the Rational Numbers are in Standard Form.
2/3 is not equal to 5/7
Therefore, Rational Numbers 2/3 and 5/7 are not equal.