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

• Basic Concept of Ratios
• Important Properties of Ratios
• Ratio in Lowest Term
  
• Types of Ratios
• Comparing Ratios
• Arranging Ratios
  
• Dividing into a Given Ratio
  
• Divide a Number into Three Parts in a Given Ratio
• Dividing a Quantity into Three Parts in a Given Ratio
  
• Problems on Ratio
  
• Worksheet on Ratio in Lowest Term
  
• Worksheet on Types of Ratios
  
• Worksheet on Comparison on Ratios
• Worksheet on Ratio of Two or More Quantities
  
• Worksheet on Dividing a Quantity in a Given Ratio
• Word Problems on Ratio
  
• Proportion
  
• Definition of Continued Proportion
  
• Mean and Third Proportional
  
• Word Problems on Proportion
  
• Worksheet on Proportion and Continued Proportion
  
• Worksheet on Mean Proportional
  
• Properties of Ratio and Proportion

10th Grade Math

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