# Arranging Ratios

We will learn how to solve different types of problems on arranging ratios in ascending order and descending order.

When a ratio is expressed in fraction or in decimal we first need to convert the ratio into whole number to compare the ratios.

The order of a ratio is important to compare two or more ratios. By reversing the antecedent and consequent of a ratio are different ratio is obtained.

Solved problems on comparing and arranging ratios in ascending and descending order:

1. Compare the ratios 1$$\frac{1}{3}$$ : 1$$\frac{1}{5}$$ and 1.6 : 1.2

Solution:

1$$\frac{1}{3}$$ : 1$$\frac{1}{5}$$ and 1.6 : 1.2

= $$\frac{4}{3}$$ : $$\frac{6}{5}$$ and $$\frac{16}{10}$$ : $$\frac{12}{10}$$

= $$\frac{4}{3}$$ × 15 : $$\frac{6}{5}$$ × 15 and $$\frac{16}{10}$$ × 10 : $$\frac{12}{10}$$ × 10

= 20 : 18 and 16 : 12

= $$\frac{20}{18}$$ and $$\frac{16}{12}$$

= $$\frac{10 × 2}{9 × 2}$$ and $$\frac{4 × 4}{3 × 4}$$

= $$\frac{10}{9}$$ and $$\frac{4}{3}$$

= 10 : 9 and 4 : 3

Now, $$\frac{10}{9}$$ and $$\frac{4}{3}$$ are to be compared. L.C.M. of 9 and 3 = 9

$$\frac{10}{9}$$ = $$\frac{10 × 1}{9 × 1}$$ and $$\frac{4}{3}$$ = $$\frac{4 × 3}{3 × 3}$$

= $$\frac{10}{9}$$ and $$\frac{12}{9}$$

Since, $$\frac{10}{9}$$ < $$\frac{12}{9}$$

Therefore, 10 : 9 < 4 : 3

Hence, 1$$\frac{1}{3}$$ : 1$$\frac{1}{5}$$ < 1.6 : 1.2

2. Compare the ratios 14 : 23, 5 : 12 and 61 : 92 in ascending order.

Solution:

Given ratios can be written as $$\frac{14}{23}$$, $$\frac{5}{12}$$ and $$\frac{61}{92}$$

L.C.M. of the denominators 23, 12 and 92 = 276

$$\frac{14}{23}$$ = $$\frac{14 × 12}{23 × 12}$$ = $$\frac{168}{276}$$

$$\frac{5}{12}$$ = $$\frac{5 × 23}{12 × 23}$$ = $$\frac{115}{276}$$

and

$$\frac{61}{92}$$ = $$\frac{61 × 3}{92 × 3}$$ = $$\frac{183}{276}$$

Since, $$\frac{115}{276}$$ < $$\frac{168}{276}$$ < $$\frac{183}{276}$$

Therefore, $$\frac{5}{12}$$ < $$\frac{14}{23}$$ < $$\frac{61}{92}$$

Hence, 5 : 12 < 14 : 23 < 61 : 92

3. Arrange the ratios 1 : 3, 5 : 12, 4 : 15 and 2 : 3 in descending order.

Solution:

Given ratios can be written as $$\frac{1}{3}$$, $$\frac{5}{12}$$, $$\frac{4}{15}$$ and $$\frac{2}{3}$$

L.C.M. of the denominators 3, 12, 15 and 3 = 60

$$\frac{1}{3}$$ = $$\frac{1 × 20}{3 × 20}$$ = $$\frac{20}{60}$$

$$\frac{5}{12}$$ = $$\frac{5 × 5}{12 × 5}$$ = $$\frac{25}{60}$$

$$\frac{4}{15}$$ = $$\frac{4 × 4}{15 × 4}$$ = $$\frac{16}{60}$$

and

$$\frac{2}{3}$$ = $$\frac{2 × 20}{3 × 20}$$ = $$\frac{40}{60}$$

Since, $$\frac{40}{60}$$ > $$\frac{25}{60}$$ > $$\frac{20}{60}$$ > $$\frac{16}{60}$$

Therefore, $$\frac{2}{3}$$ > $$\frac{5}{12}$$ > $$\frac{1}{3}$$ > $$\frac{4}{15}$$

Hence, 2 : 3 > 5 : 12 > 1 : 3 >  4 : 15.

● Ratio and proportion

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.

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

## Recent Articles

1. ### Addition of Three 1-Digit Numbers | Add 3 Single Digit Numbers | Steps

Sep 19, 24 12:56 AM

To add three numbers, we add any two numbers first. Then, we add the third number to the sum of the first two numbers. For example, let us add the numbers 3, 4 and 5. We can write the numbers horizont…

2. ### Adding 1-Digit Number | Understand the Concept one Digit Number

Sep 18, 24 03:29 PM

Understand the concept of adding 1-digit number with the help of objects as well as numbers.

3. ### Addition of Numbers using Number Line | Addition Rules on Number Line

Sep 18, 24 02:47 PM

Addition of numbers using number line will help us to learn how a number line can be used for addition. Addition of numbers can be well understood with the help of the number line.

4. ### Counting Before, After and Between Numbers up to 10 | Number Counting

Sep 17, 24 01:47 AM

Counting before, after and between numbers up to 10 improves the child’s counting skills.