Equality of Rational Numbers using Standard Form

We will learn about the equality of rational numbers using standard form.

How to determine whether the two given rational numbers are equal or not using standard form?

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 using standard form.

In order to determine the equality of two rational numbers, we express both the rational numbers in the standard form. If they have the same standard form they are equal, otherwise they are not equal. 

Solved examples on equality of rational numbers using standard form:

1. Are the rational numbers $\frac{14}{-35}$ and  $\frac{-26}{65}$ equal?

Solution:  

First we express the given rational numbers in the standard form.

$\frac{14}{-35}$

The denominator of $\frac{14}{-35}$ is negative. So, we first make it positive.

Multiplying the numerator and denominator of $\frac{14}{-35}$ by -1, we get

= $\frac{14  ×  (-1)}{(-35)  ×  (-1)}$

⇒ $\frac{14}{-35}$ = $\frac{-14}{35}$ ← Standard form

The greatest common divisor of 14 and 35 is 7.

Dividing the numerator and denominator by the greatest common divisor of 14 and 35 i.e. 7, we get

⇒ $\frac{14}{-35}$ = $\frac{(-14)  ÷  7}{35  ÷  7}$

⇒ $\frac{14}{-35}$ = $\frac{-2}{3}$

and, $\frac{-26}{65}$ is already in the standard from.

The greatest common divisor of 26 and 65 is 13.

Dividing the numerator and denominator by the greatest common divisor of 26 and 65 i.e., 13

⇒ $\frac{-26}{65}$ = $\frac{(-26)  ÷  13}{65  ÷  13}$

⇒ $\frac{-26}{65}$ = $\frac{-2}{3}$

Clearly, the given rational numbers have the same standard form.

Hence, $\frac{14}{-35}$ = $\frac{-26}{65}$

Therefore, the given rational numbers $\frac{14}{-35}$ and $\frac{-26}{65}$ are equal.

2. Are the rational numbers $\frac{-12}{40}$ and $\frac{24}{-54}$ equal?

Solution:

In order to test the equality of the given rational numbers, we first express them in the standard form.

$\frac{-12}{40}$ is already in the standard from.

The greatest common divisor of 12 and 40 is 4.

Dividing the numerator and denominator by the greatest common divisor of 12 and 40 i.e. 4, we get

$\frac{-12}{40}$ = $\frac{(-12)  ÷  4}{40  ÷  4}$            

⇒ $\frac{-12}{40}$ = $\frac{-3}{10}$

and $\frac{24}{-54}$ is not in standard from so, we first express them in the standard form.

The denominator of $\frac{24}{-54}$ is negative. So, we first make it positive.

Multiplying the numerator and denominator of $\frac{24}{-54}$ by -1, we get

⇒ $\frac{24}{-54}$ = $\frac{24  ×  (-1)}{(-54)  ×  (-1)}$

⇒ $\frac{24}{-54}$ = $\frac{-24}{54}$ ← Standard form

The greatest common divisor of 24 and 54 is 6.

Dividing the numerator and denominator by the greatest common divisor of 24 and 54 i.e. 6, we get

⇒ $\frac{-24}{54}$ = $\frac{(-24)  ÷  6}{54  ÷  6}$

⇒ $\frac{-24}{54}$ = $\frac{-4}{9}$

Clearly, the standard forms of two rational numbers are not same.

Therefore, the given rational numbers $\frac{-12}{40}$ and $\frac{24}{-54}$ are not equal.

● Rational Numbers

Introduction of 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

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

Addition of Rational Numbers

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

Product of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Reciprocal of a Rational  Number

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

Rational Numbers between Two Rational Numbers

To Find Rational Numbers

8th Grade Math Practice 

From Equality of Rational Numbers using Standard Form to HOME PAGE

Recent Articles

• 

1. Worksheet on Area, Perimeter and Volume | Square, Rectangle, Cube,Cubo

   Jul 25, 25 12:21 PM

   In this worksheet on area perimeter and volume you will get different types of questions on find the perimeter of a rectangle, find the perimeter of a square, find the area of a rectangle, find the ar…

   Read More

2. Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox

   Jul 25, 25 03:15 AM

   
   We will practice the questions given in the worksheet on volume of a cube and cuboid. We know the volume of an object is the amount of space occupied by the object.1. Fill in the blanks:

   Read More

3. Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume

   Jul 24, 25 03:46 PM

   
   Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measur…

   Read More

4. Volume of a Cube | How to Calculate the Volume of a Cube? | Examples

   Jul 23, 25 11:37 AM

   
   A cube is a solid box whose every surface is a square of same area. Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure i…

   Read More

5. 5th Grade Volume | Units of Volume | Measurement of Volume|Cubic Units

   Jul 20, 25 10:22 AM

   
   Volume is the amount of space enclosed by an object or shape, how much 3-dimensional space (length, height, and width) it occupies. A flat shape like triangle, square and rectangle occupies surface on…

   Read More

● Rational Numbers - Worksheets

Worksheet on Rational Numbers

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

Worksheet on Operations on Rational Expressions

Objective Questions on Rational Numbers