Comparison of Ratios

In comparison of ratios, we first need to convert them into like fractions by using the following steps and then compare them.

Step I: Obtain the given ratios.

Step II: Now we express each of the given ratios as a fraction in the simplest form.

Step III: Find the L.C.M (least common multiple) of the denominators of the fractions obtained in the above step (Step II).

Step IV: Obtain the first fraction and its denominator. Divide the L.C.M (least common multiple) obtained in the above step (Step III) by the denominator to get a number z (say).

Now, multiply the numerator and denominator of the fraction by the z (L.C.M). Similarly apply the same procedure to the all other fraction.

In other words convert each fraction to its equivalent fractions with denominator equal to the L.C.M (least common multiple).

Thus, the denominators of all the fractions are be same.

Step V: Compare the numerators of the equivalent fractions whose denominators are same.

Compare the numerators of the fractions obtained in the above step (Step IV). The fraction having larger numerator will be larger than the other fraction.

Two or more ratios can be compared by writing their equivalent fractions with common denominators.


Solved examples of comparison of ratios:

1. Compare the ratios 4 : 5 and 2 : 3.

Solution:

Express the given ratios as fraction

4 : 5 = 4/5  and 2 : 3 =2/3

Now find the L.C.M (least common multiple) of 5 and 3

The L.C.M (least common multiple) of 5 and 3 is 15.

Making the denominator of each fraction equal to 15, we have

4/5 = (4 ×3)/(5 ×3) = 12/15 and 2/3 = (2 ×5)/(3 ×5) = 10/15

Clearly, 12 > 10

 Now, 12/15 > 10/15

Therefore, 4 : 5 > 2 : 3.


2. Compare the ratios 5 : 6 and 7 : 9.

Solution:

Express the given ratios as fraction

5 : 6 = 5/6  and 7 : 9 =7/9

Now find the L.C.M (least common multiple) of 6 and 9

The L.C.M (least common multiple) of 6 and 9 is 18.

Making the denominator of each fraction equal to 18, we have

5/6  = (5 ×3)/(6 ×3) = 15/18 and 7/9  = (7 ×2)/(9 ×2) = 14/18

Clearly, 15 > 14

 Now, 15/18 > 14/18

Therefore, 5 : 6 > 7 : 9.


3. Compare the ratios 1.2 : 2.5 and 3.5 : 7.

Solution:

1.2 : 2.5 = 1.2/2.5 and 3.5 : 7 =3.5/7

1.2/2.5 = (1.2 ×10)/(2.5 ×10 ) = 12/25 and 3.5/7 = (3.5 ×10)/(7 ×10) = 35/70 = 1/2

[We removed the decimal point from the ratios now, we will compare the ratio]

Now find the L.C.M (least common multiple) of 25 and 2

The L.C.M (least common multiple) of 25 and 2 is 50.

Making the denominator of each fraction equal to 50, we have

= 12/25 = (12 ×2)/(25 ×2)  = 24/50 and 1/2 = (1 ×25)/(2 ×25)  = 25/50

Now, 25/50 >  24/50

Therefore,  3.5 : 7 > 1.2 : 2.5.










6th Grade Page

From Comparison of Ratios 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.



Share this page: What’s this?

Recent Articles

  1. Fundamental Geometrical Concepts | Point | Line | Properties of Lines

    Apr 18, 24 02:58 AM

    Point P
    The fundamental geometrical concepts depend on three basic concepts — point, line and plane. The terms cannot be precisely defined. However, the meanings of these terms are explained through examples.

    Read More

  2. What is a Polygon? | Simple Closed Curve | Triangle | Quadrilateral

    Apr 18, 24 02:15 AM

    What is a polygon? A simple closed curve made of three or more line-segments is called a polygon. A polygon has at least three line-segments.

    Read More

  3. Simple Closed Curves | Types of Closed Curves | Collection of Curves

    Apr 18, 24 01:36 AM

    Closed Curves Examples
    In simple closed curves the shapes are closed by line-segments or by a curved line. Triangle, quadrilateral, circle, etc., are examples of closed curves.

    Read More

  4. Tangrams Math | Traditional Chinese Geometrical Puzzle | Triangles

    Apr 18, 24 12:31 AM

    Tangrams
    Tangram is a traditional Chinese geometrical puzzle with 7 pieces (1 parallelogram, 1 square and 5 triangles) that can be arranged to match any particular design. In the given figure, it consists of o…

    Read More

  5. Time Duration |How to Calculate the Time Duration (in Hours & Minutes)

    Apr 17, 24 01:32 PM

    Duration of Time
    We will learn how to calculate the time duration in minutes and in hours. Time Duration (in minutes) Ron and Clara play badminton every evening. Yesterday, their game started at 5 : 15 p.m.

    Read More