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

Comparing Ratios

In comparing ratios we will learn how to arrange the ratios.  


How to Compare Ratios?

To compare two ratios, follow these steps:

Step I: Make the second term of both the ratios equal.

For this, determine the LCM of the second terms of the ratios. Divide the LCM by the second term of each ratio. Multiply the numerator and the denominator of each ratio by the quotient.

Step II: Compare the first terms (numerators) of the new ratios.

Solved Examples on Comparing Ratios:

1. Which of the following ratios is grater?

Compare the ratios 3 : 4 and 1 : 2. 

LCM of the second terms, i.e., 4 and 2 = 4

Now, dividing the LCM by the second term of each ratio, we get 4 ÷ 4 = 1, and 4 ÷ 2 = 2

Therefore, 34 = 3141 = 34

12 = 1222 = 24

As 3 > 2, 34 > 24, i.e., 3 : 4 > 1 : 2

Therefore the ratio 3:4 is greater than the ratio 1:2 according to the ratio comparison rules.



2. Which of the following ratios is grater?

Compare the ratios 3 : 5 and 2 : 11.

LCM of the second terms, i.e., 5 and 11 = 55

Now, dividing the LCM by the second term of each ratio, we get 55 ÷ 5 = 11, and 55 ÷ 11 = 5

Therefore, 35 = 311511 = 3355

211 = 25115 = 1055

As 33 > 10, 35 > 211, i.e., 3 : 5 > 2 : 11.

Therefore the ratio 3 : 5 is greater than the ratio 2 : 11 according to the ratio comparison rules.


Working Rules for Comparison of Ratios:

To compare two or more given ratios, follow the steps given below:

Step I: Write each one of the given ratios in the form of a fraction in the simplest form.

Step II: Convert these fractions into like fractions and then compare.


3. Compare the ratios 4 : 7 and 5 : 8.

Solution:

4 : 7 = 47 and 5 : 8 = 58

LCM of 7 and 8 is 56.

47 = 4×87×8 = 3256 and 58 = 5×78×7 = 3556

Clearly, 3556 > 3256

58 > 47

⟹ 5 : 8 > 4 : 7

Hence, 5 : 8 > 4 : 7


Ratios in Ascending Order

4. Write the following ratios in ascending order 4 : 3, 7 : 10, 4 : 7.

Solution:

4 : 3 = 43;   7 : 10 = 710 and  4 : 7 = 47.

LCM of 3, 7 and 10 = 210

43 = 4×703×70 = 280210

710 = 7×2110×21 = 147210

47 = 4×307×30 = 120210


Now 120210 < 147210 < 280210 

47 < 710 < 43

4 : 7 < 7 : 10 < 4 : 3

Hence, 4 : 7 < 7 : 10 < 4 : 3


Comparing Ratios

Worksheet on Comparing Ratios:

1. Which of the following ratio is larger?

(i) 3 : 4 or 9 : 16

(ii) 15 : 16 or 24 : 25

(iii) 4 : 7 or 5 : 8

(iv) 9 : 20 or 8 : 13

(v) 1 : 2 or 13 : 27


Answer:

1. (i) 3 : 4 > 9 : 16

(ii) 15 : 16 < 24 : 25

(iii) 4 : 7 < 5 : 8

(iv) 9 : 20 < 8 : 13

(v) 1 : 2 > 13 : 27

● Ratio and proportion






10th Grade Math

From Comparing Ratios to HOME




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. 5th Grade Circle Worksheet | Free Worksheet with Answer |Practice Math

    Jul 11, 25 02:14 PM

    Radii of the circRadii, Chords, Diameters, Semi-circles
    In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl…

    Read More

  2. Construction of a Circle | Working Rules | Step-by-step Explanation |

    Jul 09, 25 01:29 AM

    Parts of a Circle
    Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

    Read More

  3. Combination of Addition and Subtraction | Mixed Addition & Subtraction

    Jul 08, 25 02:32 PM

    Add and Sub
    We will discuss here about the combination of addition and subtraction. The rules which can be used to solve the sums involving addition (+) and subtraction (-) together are: I: First add

    Read More

  4. Addition & Subtraction Together |Combination of addition & subtraction

    Jul 08, 25 02:23 PM

    Addition and Subtraction Together Problem
    We will solve the different types of problems involving addition and subtraction together. To show the problem involving both addition and subtraction, we first group all the numbers with ‘+’ and…

    Read More

  5. 5th Grade Circle | Radius, Interior and Exterior of a Circle|Worksheet

    Jul 08, 25 09:55 AM

    Semi-circular Region
    A circle is the set of all those point in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is known

    Read More