You will learn about the Equality of Rational Numbers with Common Denominator from this article. Check out how to determine whether given Rational Numbers are equal or not using the Common Denominator. Apart from the procedure, we have even listed a few examples for better understanding.

## How to determine Equality of Rational Numbers with Common Denominator?

There are many methods to check the equality of rational numbers but here in this article, we are going to discuss the method of the same denominator. We have listed the procedure on how to make denominators equal for the given rational numbers and they are in the following fashion.

**Step 1: **Check the given Rational Numbers.

**Step 2: **Multiply the numerator and denominator of the first number with the denominator of the second number.

**Step 3: **On the other hand, multiply the numerator and denominator of the second number with the denominator of the first number.

**Step 4: **Later check the numerators of the numbers obtained in steps 2, 3. If the numerators are equal then the given rational numbers are equal or else they are not equal.

### Solved Examples

1. Are the Rational Numbers -7/5 and -5/3 equal?

**Solution:**

Given Rational Numbers are -7/5, -5/3

Multiply the second number numerator and denominator with the denominator of the first number i.e.

-5*5/3*5

= -25/15

Multiply the first number numerator and denominator with the denominator of the second number i.e.

-7*3/5*3

= -21/15

Check the numerators obtained in the earlier steps and see whether they are equal or not.

Since 21, 25 aren’t equal both the given rational numbers aren’t equal.

Therefore, -7/5 and -5/3 are not equal.

2. Show that the Rational Numbers -6/8 and -9/12 are equal?

**Solution:**

Given Rational Numbers are -6/8, -9/12

Multiply both numerator and denominator of the second number with the denominator of the first number.

= (-9/12)*8

= -72/96

Multiply both numerator and denominator of the first number with the denominator of the second number.

= (-6/8)*12

= -72/96

Therefore, Rational Numbers -6/8 and -9/12 are equal.