# 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. ### Worksheet on Word Problems on Fractions | Fraction Word Problems | Ans

Jul 16, 24 02:20 AM

In worksheet on word problems on fractions we will solve different types of word problems on multiplication of fractions, word problems on division of fractions etc... 1. How many one-fifths

2. ### Word Problems on Fraction | Math Fraction Word Problems |Fraction Math

Jul 16, 24 01:36 AM

In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

3. ### Worksheet on Add and Subtract Fractions | Word Problems | Fractions

Jul 16, 24 12:17 AM

Recall the topic carefully and practice the questions given in the math worksheet on add and subtract fractions. The question mainly covers addition with the help of a fraction number line, subtractio…

4. ### Comparison of Like Fractions | Comparing Fractions | Like Fractions

Jul 15, 24 03:22 PM

Any two like fractions can be compared by comparing their numerators. The fraction with larger numerator is greater than the fraction with smaller numerator, for example $$\frac{7}{13}$$ > \(\frac{2…

5. ### Worksheet on Reducing Fraction | Simplifying Fractions | Lowest Form

Jul 15, 24 03:17 PM

Practice the questions given in the math worksheet on reducing fraction to the lowest terms by using division. Fractional numbers are given in the questions to reduce to its lowest term.

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