Loading [MathJax]/jax/output/HTML-CSS/fonts/TeX/fontdata.js

Subscribe to our YouTube channel for the latest videos, updates, and tips.


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 71058 and 23 in ascending order:

Solution:

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

We have,

58 = 5×(1)(8)×(1) = 58 and 23 = 2×(1)(3)×(1)  = 23

Thus, the given rational numbers with positive denominators are

710, 58, 23

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:

710 = (7)×1210×12 = 84120,

58 = (5)×158×15 = 75120 and

23 = (2)×403×40 = 80120.

Comparing the numerators of these numbers, we get,

- 84 < -80 < -75

Therefore, 84120 < 80120 < 75120710 < 23 < 58710 < 23 < 58

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

710, 23, 58

 

2. Arrange the rational numbers 58, 56, 74 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 56 and 74 are negative.

So, we express 56 and 74 with positive denominator as follows:

56 = 5×(1)(6)×(1) = 56 and 74 = 7×(1)(4)×(1) = 74

Thus, the given rational numbers with positive denominators are

58, 56, 74 and 35

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:

58 = 5×158×15, [Multiplying the numerator and denominator by 120 ÷ 8 = 15]

58 = 75120

56 = (5)×206×20, [Multiplying the numerator and denominator by 120 ÷ 6 = 20]

56 = 100120

74 = (7)×304×30, [Multiplying the numerator and denominator by 120 ÷ 4 = 30]

74 = 210120 and

35 = 3×245×24, [Multiplying the numerator and denominator by 120 ÷ 5 = 24]

35 = 72120

Comparing the numerators of these numbers, we get,

-210 < -100 < 72 < 75

Therefore, 210120 < 100120 < 72120 < 7512074 < 56 < 35 < 5/8 ⇒ 74 < 56 < 35 < 58

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

74, 56, 35, 58.

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. 8 Times Table | Multiplication Table of 8 | Read Eight Times Table

    May 18, 25 04:33 PM

    Printable eight times table
    In 8 times table we will memorize the multiplication table. Printable multiplication table is also available for the homeschoolers. 8 × 0 = 0 8 × 1 = 8 8 × 2 = 16 8 × 3 = 24 8 × 4 = 32 8 × 5 = 40

    Read More

  2. Worksheet on Average | Word Problem on Average | Questions on Average

    May 17, 25 05:37 PM

    In worksheet on average interest we will solve 10 different types of question. Find the average of first 10 prime numbers. The average height of a family of five is 150 cm. If the heights of 4 family

    Read More

  3. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  4. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

  5. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 16, 25 11:13 AM

    Round off to Nearest One
    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    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