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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 14β35 and β2665 equal?
Solution:
First we express the given rational numbers in the standard form.
14β35
The denominator of 14β35 is negative. So, we first make it positive.
Multiplying the numerator and denominator of 14β35 by -1, we get
= 14Γ(β1)(β35)Γ(β1)
β 14β35 = β1435 β 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
β 14β35 = (β14)Γ·735Γ·7
β 14β35 = β23
and, β2665 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
β β2665 = (β26)Γ·1365Γ·13
β β2665 = β23
Clearly, the given rational numbers have the same standard form.
Hence, 14β35 = β2665
Therefore, the given rational numbers 14β35 and β2665 are equal.
2. Are the
rational numbers β1240 and 24β54 equal?
Solution:
In order to test the equality of the given rational numbers, we first express them in the standard form.
β1240 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
β1240 = (β12)Γ·440Γ·4
β β1240 = β310
and 24β54 is not in standard from so, we first express them in the standard form.
The denominator of 24β54 is negative. So, we first make it positive.
Multiplying the numerator and denominator of 24β54 by -1, we get
β 24β54 = 24Γ(β1)(β54)Γ(β1)
β 24β54 = β2454 β 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
β β2454 = (β24)Γ·654Γ·6
β β2454 = β49
Clearly, the standard forms of two rational numbers are not same.
Therefore, the given rational numbers β1240 and 24β54 are not equal.
β 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
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β 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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