Problems on Comparison Between Rational Numbers

Rational numbers are in the form of fractions. In this topic we will solve the problems based on the comparison between the fractions. Methods of comparing the fraction is based upon the types of fractions we have to compare. Here we have to compare between two types of fractions: like fractions and unlike fractions.

Like Fractions: These fractions are those which have same denominator. Since they have the same denominator we only need to compare their numerators. The one having larger numerator will be the greater of two fractions.

Unlike Fractions: These fractions are those which have different denominators and their comparison method differs with like fractions by one step only. First we have to make their denominators equal and rest of the process will be same as that to the like fraction.


Notes:

(i) Always remember that the denominators of the fractions should be positive.

(ii) Always remember that a positive integer is greater that the negative integer.


Let us solve some examples to have better understanding of the the topic:

1. Compare 35 and 75.

Solution:

The given fractions are like fractions as their denominators are equal. So, the one having larger numerator will be greater of the two. Since, 3 < 7 so, 35 is less than 75.


2. Compare 59and 73.

Solution: 

The given fractions are unlike fractions as their denominators are unequal. To have a comparison between them first we need to convert them to like fractions by making their denominators equal. So, the L.C.M. of 9 and 3 is 9.

So, we have two fractions as:

     59 and 7×39 

 59 and 219

Since they have become like fractions and the one having larger denominator will be greater of the two. Since, 21 > 5.

Hence, 219 > 59.


3. Compare and arrange the following fractions into ascending order.

117, 517, 3217, 417, 1917

Solution: 

Since the given fractions are like fractions. So, we just need to compare their numerators. Since, 

            1 < 4 < 5 < 19 < 32

So, the ascending order arrangement is:

117 < 417 < 517 < 1917 < 3217.


4. Compare and arrange the following in descending order:

25, 415, 56, 720

Solution:

The given fractions are unlike fractions. So, first we need to convert them to like fractions and then carry out the comparison process. So, the L.C.M. of 5, 15, 6 and 20 is 60.

Now the fractions become: 

2×1260, 4×460, 5×1060, 7×360

i.e., 2460, 1660, 5060 and 2160.

Now, we need to compare the like fractions.

Since, 50 > 24 > 21 > 16. So, the required descending order of the fractions is as:

5060 > 2460 > 2160 > 1660

i.e., 56 > 25 > 720 > 415


Rational Numbers

Rational Numbers

Decimal Representation of Rational Numbers

Rational Numbers in Terminating and Non-Terminating Decimals

Recurring Decimals as Rational Numbers

Laws of Algebra for Rational Numbers

Comparison between Two Rational Numbers

Rational Numbers Between Two Unequal Rational Numbers

Representation of Rational Numbers on Number Line

Problems on Rational numbers as Decimal Numbers

Problems Based On Recurring Decimals as Rational Numbers

Problems on Comparison Between Rational Numbers

Problems on Representation of Rational Numbers on Number Line

Worksheet on Comparison between Rational Numbers

Worksheet on Representation of Rational Numbers on the Number Line







9th Grade Math

From Problems on Comparison Between Rational Numbers 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. Worksheet on Area, Perimeter and Volume | Square, Rectangle, Cube,Cubo

    Jul 25, 25 12:21 PM

    In this worksheet on area perimeter and volume you will get different types of questions on find the perimeter of a rectangle, find the perimeter of a square, find the area of a rectangle, find the ar…

    Read More

  2. Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox

    Jul 25, 25 03:15 AM

    Volume of a Cube and Cuboid
    We will practice the questions given in the worksheet on volume of a cube and cuboid. We know the volume of an object is the amount of space occupied by the object.1. Fill in the blanks:

    Read More

  3. Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume

    Jul 24, 25 03:46 PM

    Volume of Cuboid
    Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measur…

    Read More

  4. Volume of a Cube | How to Calculate the Volume of a Cube? | Examples

    Jul 23, 25 11:37 AM

    Volume of a Cube
    A cube is a solid box whose every surface is a square of same area. Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure i…

    Read More

  5. 5th Grade Volume | Units of Volume | Measurement of Volume|Cubic Units

    Jul 20, 25 10:22 AM

    Cubes in Cuboid
    Volume is the amount of space enclosed by an object or shape, how much 3-dimensional space (length, height, and width) it occupies. A flat shape like triangle, square and rectangle occupies surface on…

    Read More