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We will learn how to arrange the rational numbers in descending order.
General method to arrange from largest to smallest rational numbers (decreasing):
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 greater numerator is greater.
Solved examples on rational numbers in descending order:
1. Arrange the numbers β35, 7β10 and β58 in descending order.
Solution:
First we write each of the given numbers with positive denominator.
We have;
7β10 = 7Γ(β1)(β10)Γ(β1) = β710.
Thus, the given number are β35, β710 and β58.
L.C.M. of 5, 10, 8 is 40.
Now, β35 = (β3)Γ85Γ8 = β2440;
β710 = (β7)Γ410Γ4 = β2840
and β58 = (β5)Γ58Γ5
= β2540
Clearly, β2440 > β2540 > β2840
Thus, β35 > β58 > β710, i.e., β35 > β58 > 7β10
Hence, the given numbers when arranged in descending order are: β35, β58, 7β10.
2. Arrange the following rational numbers in descending order: 49, β56, β7β12, 11β24.
Solution:
First we express the given rational numbers in the form so that their denominators are positive.
We have,
β7β12 = (β7)Γ(β1)(β12)Γ(β1), [Multiplying the numerator and denominator by -1]
β β7β12 = 712
and 11β24 = 11Γ(β1)(β24)Γ(β1) = β1124
Thus, given rational numbers are:
49, β56, 712, β1124
Now, we find the LCM of 9, 6, 12 and 24.
Required LCM = 2 Γ 2 Γ 2 Γ 3 Γ 3 = 72.
We now write the rational numbers so that they have a common denominator 72.
We have,
49 = 4Γ89Γ8, [Multiplying the numerator and denominator by 72 Γ· 9 = 8]
β 49 = 3272
β56 = β5Γ126Γ12, [Multiplying the numerator and denominator by 72 Γ· 6 = 12]
β β56 = β6072
712 = 7Γ612Γ6, [Multiplying the numerator and denominator by 72 Γ· 12 = 6]
β 712 = 4272
β1124 = β11Γ324Γ3, [Multiplying the numerator and denominator by 72 Γ· 24 = 3]
β β1124 = β3372
Arranging the numerators of these rational numbers in descending order, we have
42 > 32 > -33 > -60
β 4272 > 3272 > β3372 > β6072 β β7β12 > 49 > 11β24 > β56
Hence, the given numbers when arranged in descending order are:
β7β12, 49, 11β24, β56.
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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