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We will learn how to arrange the rational numbers in ascending order.
General method to arrange from smallest to largest rational numbers (increasing):
Step 1: Express the given rational numbers with positive denominator.
Step 2: Take the least common multiple (L.C.M.) of these positive denominator.
Step 3: Express each rational number (obtained in step 1) with this least common multiple (LCM) as the common denominator.
Step 4: The number having the smaller numerator is smaller.
Solved examples on rational numbers in ascending order:
1. Arrange the rational numbers β710, 5β8 and 2β3 in ascending order:
Solution:
We first write the given rational numbers so that their denominators are positive.
We have,
5β8 = 5Γ(β1)(β8)Γ(β1) = β58 and 2β3 = 2Γ(β1)(β3)Γ(β1) = β23
Thus, the given rational numbers with positive denominators are
β710, β58, β23
Now, LCM of the denominators 10, 8 and 3 is 2 Γ 2 Γ 2 Γ 3 Γ 5 = 120
We now write the numerators so that they have a common denominator 120 as follows:
β710 = (β7)Γ1210Γ12 = β84120,
β58 = (β5)Γ158Γ15 = β75120 and
β23 = (β2)Γ403Γ40 = β80120.
Comparing the numerators of these numbers, we get,
- 84 < -80 < -75
Therefore, β84120 < β80120 < β75120 β β710 < β23 < β58 β β710 < 2β3 < 5β8
Hence, the given numbers when arranged in ascending order are:
β710, 2β3, 5β8
2. Arrange the rational numbers 58, 5β6, 7β4 and 35 in ascending order.
Solution:
First we write each one of the given rational numbers with positive denominator.
Clearly, denominators of 58 and 35 are positive.
The denominators of 5β6 and 7β4 are negative.
So, we express 5β6 and 7β4 with positive denominator as follows:
5β6 = 5Γ(β1)(β6)Γ(β1) = β56 and 7β4 = 7Γ(β1)(β4)Γ(β1) = β74
Thus, the given rational numbers with positive denominators are
58, β56, β74 and 35
Now, LCM of the denominators 8, 6, 4 and 5 is 2 Γ 2 Γ 2 Γ 3 Γ 5 = 120
Now we convert each of the rational numbers to their equivalent rational number with common denominator 120 as follows:
58 = 5Γ158Γ15, [Multiplying the numerator and denominator by 120 Γ· 8 = 15]
β 58 = 75120
β56 = (β5)Γ206Γ20, [Multiplying the numerator and denominator by 120 Γ· 6 = 20]
β β56 = β100120
β74 = (β7)Γ304Γ30, [Multiplying the numerator and denominator by 120 Γ· 4 = 30]
β β74 = β210120 and
35 = 3Γ245Γ24, [Multiplying the numerator and denominator by 120 Γ· 5 = 24]
β 35 = 72120
Comparing the numerators of these numbers, we get,
-210 < -100 < 72 < 75
Therefore, β210120 < β100120 < 72120 < 75120 β β74 < β56 < 35 < 5/8 β 7β4 < 5β6 < 35 < 58
Hence, the given numbers when arranged in ascending order are:
7β4, 5β6, 35, 58.
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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