# Equality of Rational Numbers with Common Denominator

We will learn about the equality of rational numbers with common denominator.

How to determine whether the two given rational numbers are equal or not with the common denominator?

We know there are many methods to determine the equality of two rational numbers but here we will learn the method of equality of two rational numbers with the same denominator.

In this method, denominators of the given rational numbers are made equal by using the following steps:

Step I: Obtain the two numbers.

Step II: Multiply the numerator and denominator of the first number by the denominator of the second number.

Step III: Multiply the numerator and denominator of the second number by the denominator of the first number.

Step IV: Check the numerators of the two numbers obtained in steps II and III.  If their numerators are equal, then the given rational numbers are equal, otherwise they are not equal.

Solved examples:

1. Are the rational numbers $$\frac{-9}{12}$$ and $$\frac{21}{-28}$$ equal?

Solution:

Multiplying the numerator and denominator of $$\frac{-9}{12}$$ by the denominator of $$\frac{21}{-28}$$ i.e. by -28, we get

$$\frac{-9}{12}$$ = $$\frac{(-9) × (-28)}{12 × (-28)}$$ = $$\frac{252}{-336}$$

Multiplying the numerator and denominator of $$\frac{21}{-28}$$ by the denominator of $$\frac{-9}{12}$$ i.e., by 12, we get

$$\frac{21}{-28}$$ = $$\frac{21 × 12}{(-28) × 12}$$ = $$\frac{252}{-336}$$

Clearly, the numerators of the above obtained rational numbers are equal.

Therefore, the given rational numbers $$\frac{-9}{12}$$ and $$\frac{21}{-28}$$ are equal.

2. Show that the rational numbers $$\frac{-6}{8}$$ and $$\frac{10}{-15}$$ are not equal.

Solution:

Multiplying the numerator and denominator of $$\frac{-6}{8}$$ by the denominator of $$\frac{10}{-15}$$ i.e. -15, we get

$$\frac{-6}{8}$$ = $$\frac{(-6) × (-15)}{8 × (-15)}$$ = $$\frac{90}{-120}$$

Multiplying the numerator and denominator of $$\frac{10}{-15}$$ by the denominator of $$\frac{-6}{8}$$ i.e. 8, we get

$$\frac{10}{-15}$$ = $$\frac{10 × 8}{(-15) × 8}$$ = $$\frac{80}{-120}$$

We find that the numerators of rational numbers $$\frac{90}{-120}$$ and $$\frac{80}{-120}$$ are unequal.

Therefore, the given rational numbers $$\frac{-6}{8}$$ and $$\frac{10}{-15}$$ are unequal.

Rational Numbers

What is Rational Numbers?

Is Every Rational Number a Natural Number?

Is Zero a Rational Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

Positive Rational Number

Negative Rational Number

Equivalent Rational Numbers

Equivalent form of Rational Numbers

Rational Number in Different Forms

Properties of Rational Numbers

Lowest form of a Rational Number

Standard form of a Rational Number

Equality of Rational Numbers using Standard Form

Equality of Rational Numbers with Common Denominator

Equality of Rational Numbers using Cross Multiplication

Comparison of Rational Numbers

Rational Numbers in Ascending Order

Representation of Rational Numbers on the Number Line

Addition of Rational Number with Same Denominator

Addition of Rational Number with Different Denominator

Properties of Addition of Rational Numbers

Subtraction of Rational Number with Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

Simplify Rational Expressions Involving the Sum or Difference

Multiplication of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

To Find Rational Numbers

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Method of L.C.M. | Finding L.C.M. | Smallest Common Multiple | Common

Apr 15, 24 01:29 AM

We will discuss here about the method of l.c.m. (least common multiple). Let us consider the numbers 8, 12 and 16. Multiples of 8 are → 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, ......

2. ### Common Multiples | How to Find Common Multiples of Two Numbers?

Apr 15, 24 01:13 AM

Common multiples of two or more given numbers are the numbers which can exactly be divided by each of the given numbers. Consider the following. (i) Multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24…

3. ### Least Common Multiple |Lowest Common Multiple|Smallest Common Multiple

Apr 14, 24 03:06 PM

The least common multiple (L.C.M.) of two or more numbers is the smallest number which can be exactly divided by each of the given number. The lowest common multiple or LCM of two or more numbers is t…

4. ### Worksheet on H.C.F. | Word Problems on H.C.F. | H.C.F. Worksheet | Ans

Apr 14, 24 02:23 PM

Practice the questions given in the worksheet on hcf (highest common factor) by factorization method, prime factorization method and division method. Find the common factors of the following numbers…

5. ### Common Factors | Find the Common Factor | Worksheet | Answer

Apr 14, 24 02:01 PM

Common factors of two or more numbers are a number which divides each of the given numbers exactly. For examples 1. Find the common factor of 6 and 8. Factor of 6 = 1, 2, 3 and 6. Factor

Rational Numbers - Worksheets

Worksheet on Rational Numbers

Worksheet on Lowest form of a Rational Number

Worksheet on Standard form of a Rational Number

Worksheet on Equality of Rational Numbers

Worksheet on Comparison of Rational Numbers

Worksheet on Representation of Rational Number on a Number Line

Worksheet on Properties of Addition of Rational Numbers

Worksheet on Rational Expressions Involving Sum and Difference

Worksheet on Multiplication of Rational Number

Worksheet on Division of Rational Numbers

Worksheet on Finding Rational Numbers between Two Rational Numbers

Worksheet on Word Problems on Rational Numbers

Objective Questions on Rational Numbers