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**

Introduction of Rational Numbers

Is Every Rational Number a Natural Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

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

Rational Numbers in Descending Order

Representation of Rational Numbers on the Number Line

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 Same Denominator

Subtraction of Rational Number with Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

Rational Expressions Involving Addition and Subtraction

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

Reciprocal of a Rational Number

Rational Expressions Involving Division

Properties of Division of Rational Numbers

Rational Numbers between Two Rational Numbers

**8th Grade Math Practice****From Equality of Rational Numbers with Common Denominator to HOME PAGE**

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● **Rational Numbers - Worksheets**

Worksheet on Equivalent 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 Adding Rational Numbers

Worksheet on Properties of Addition of Rational Numbers

Worksheet on Subtracting Rational Numbers

Worksheet on Addition and
Subtraction of Rational Number

Worksheet on Rational Expressions Involving Sum and Difference

Worksheet on Multiplication of Rational Number

Worksheet on Properties of Multiplication of Rational Numbers

Worksheet on Division of Rational Numbers

Worksheet on Properties of Division of Rational Numbers

Worksheet on Finding Rational Numbers between Two Rational Numbers

Worksheet on Word Problems on Rational Numbers

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