Rational Numbers in Ascending Order

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 \(\frac{-7}{10}\), \(\frac{5}{-8}\) and \(\frac{2}{-3}\) in ascending order:

Solution:

We first write the given rational numbers so that their denominators are positive.

We have,

\(\frac{5}{-8}\) = \(\frac{5  ×  (-1)}{(-8)  ×  (-1)}\) = \(\frac{-5}{8}\) and \(\frac{2}{-3}\) = \(\frac{2  ×  (-1)}{(-3)  ×  (-1)}\)  = \(\frac{-2}{3}\)

Thus, the given rational numbers with positive denominators are

\(\frac{-7}{10}\), \(\frac{-5}{8}\), \(\frac{-2}{3}\)

Now, LCM of the denominators 10, 8 and 3 is 2 × 2 × 2 × 3 × 5 = 120

We now write the numerators so that they have a common denominator 120 as follows:

\(\frac{-7}{10}\) = \(\frac{(-7)  ×  12}{10  ×  12}\) = \(\frac{-84}{120}\),

\(\frac{-5}{8}\) = \(\frac{(-5)  ×  15}{8  ×  15}\) = \(\frac{-75}{120}\) and

\(\frac{-2}{3}\) = \(\frac{(-2)  ×  40}{3  ×  40}\) = \(\frac{-80}{120}\).

Comparing the numerators of these numbers, we get,

- 84 < -80 < -75

Therefore, \(\frac{-84}{120}\) < \(\frac{-80}{120}\) < \(\frac{-75}{120}\) ⇒ \(\frac{-7}{10}\) < \(\frac{-2}{3}\) < \(\frac{-5}{8}\) ⇒ \(\frac{-7}{10}\) < \(\frac{2}{-3}\) < \(\frac{5}{-8}\)

Hence, the given numbers when arranged in ascending order are:

\(\frac{-7}{10}\), \(\frac{2}{-3}\), \(\frac{5}{-8}\)

 

2. Arrange the rational numbers \(\frac{5}{8}\), \(\frac{5}{-6}\), \(\frac{7}{-4}\) and \(\frac{3}{5}\) in ascending order.

Solution:

First we write each one of the given rational numbers with positive denominator.

Clearly, denominators of \(\frac{5}{8}\) and \(\frac{3}{5}\) are positive.

The denominators of \(\frac{5}{-6}\) and \(\frac{7}{-4}\) are negative.

So, we express \(\frac{5}{-6}\) and \(\frac{7}{-4}\) with positive denominator as follows:

\(\frac{5}{-6}\) = \(\frac{5  ×  (-1)}{(-6)  ×  (-1)}\) = \(\frac{-5}{6}\) and \(\frac{7}{-4}\) = \(\frac{7  ×  (-1)}{(-4)  ×  (-1)}\) = \(\frac{-7}{4}\)

Thus, the given rational numbers with positive denominators are

\(\frac{5}{8}\), \(\frac{-5}{6}\), \(\frac{-7}{4}\) and \(\frac{3}{5}\)

Now, LCM of the denominators 8, 6, 4 and 5 is 2 × 2 × 2 × 3 × 5 = 120

Now we convert each of the rational numbers to their equivalent rational number with common denominator 120 as follows:

\(\frac{5}{8}\) = \(\frac{5  ×  15}{8  ×  15}\), [Multiplying the numerator and denominator by 120 ÷ 8 = 15]

\(\frac{5}{8}\) = \(\frac{75}{120}\)

\(\frac{-5}{6}\) = \(\frac{(-5)  ×  20}{6  ×  20}\), [Multiplying the numerator and denominator by 120 ÷ 6 = 20]

\(\frac{-5}{6}\) = \(\frac{-100}{120}\)

\(\frac{-7}{4}\) = \(\frac{(-7)  ×  30}{4  ×  30}\), [Multiplying the numerator and denominator by 120 ÷ 4 = 30]

\(\frac{-7}{4}\) = \(\frac{-210}{120}\) and

\(\frac{3}{5}\) = \(\frac{3  ×  24}{5  ×  24}\), [Multiplying the numerator and denominator by 120 ÷ 5 = 24]

\(\frac{3}{5}\) = \(\frac{72}{120}\)

Comparing the numerators of these numbers, we get,

-210 < -100 < 72 < 75

Therefore, \(\frac{-210}{120}\) < \(\frac{-100}{120}\) < \(\frac{72}{120}\) < \(\frac{75}{120}\) ⇒ \(\frac{-7}{4}\) < \(\frac{-5}{6}\) < \(\frac{3}{5}\) < 5/8 ⇒ \(\frac{7}{-4}\) < \(\frac{5}{-6}\) < \(\frac{3}{5}\) < \(\frac{5}{8}\)

Hence, the given numbers when arranged in ascending order are:

\(\frac{7}{-4}\), \(\frac{5}{-6}\), \(\frac{3}{5}\), \(\frac{5}{8}\).

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 Rational Numbers in Ascending Order to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Expanded form of Decimal Fractions |How to Write a Decimal in Expanded

    Jul 22, 24 03:27 PM

    Expanded form of Decimal
    Decimal numbers can be expressed in expanded form using the place-value chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is mi…

    Read More

  2. Worksheet on Decimal Numbers | Decimals Number Concepts | Answers

    Jul 22, 24 02:41 PM

    Worksheet on Decimal Numbers
    Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts.

    Read More

  3. Decimal Place Value Chart |Tenths Place |Hundredths Place |Thousandths

    Jul 21, 24 02:14 PM

    Decimal place value chart
    Decimal place value chart are discussed here: The first place after the decimal is got by dividing the number by 10; it is called the tenths place.

    Read More

  4. Thousandths Place in Decimals | Decimal Place Value | Decimal Numbers

    Jul 20, 24 03:45 PM

    Thousandths Place in Decimals
    When we write a decimal number with three places, we are representing the thousandths place. Each part in the given figure represents one-thousandth of the whole. It is written as 1/1000. In the decim…

    Read More

  5. Hundredths Place in Decimals | Decimal Place Value | Decimal Number

    Jul 20, 24 02:30 PM

    Hundredths Place in Decimals
    When we write a decimal number with two places, we are representing the hundredths place. Let us take plane sheet which represents one whole. Now, we divide the sheet into 100 equal parts. Each part r…

    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