Equivalent Ratio – Concept and Its Uses

Introduction:

Definition of equivalent ratio: 

The ratio which we get by multiplying or dividing by the same non-zero number to the two terms of the given ratio is called an equivalent ratio. Equivalent ratios are ratios that express the same relationship. 

Obtaining an equivalent fraction: 

To get a ratio equivalent to the given ratio, we begin by representing the ratio in the form of a fraction. Then multiplying and dividing the first term and second term by the same non-zero number, we get an equivalent ratio. At last, it is represented in the ratio form. 

Example: 

Find an equivalent ratio of 3/2

. 

Solution: The fractional form of the ratio given is 3/2

. 

Step 1: Multiply by a non-zero number to both numerator and denominator. In this case, let us take. 

3 × 4 / 2 × 4= 12 / 8

           

Step 2: Write the equivalent fraction in the ratio form, i.e., 12:8. 

Therefore, 12:8 is the equivalent ratio of 3:2. 

5.2.1 Finding equivalent ratios using multiplications 

Example 1: Write three equivalent ratios to 5:6. 

Solution: The fractional form of the ratio given is 5/6

. 

Step 1: Multiply by a non-zero number to both numerator and denominator. In this case, let us take 2, 3 and 4 since we are finding three equivalent ratios. 

5 × 2 / 6 × 2=10/12

5 × 3 / 6 × 3=15/18

5 × 4 / 6 × 4=20/24

Step 2: Write the equivalent fraction in the ratio form, i.e., 10:12, 15:18 and 20:24. 

Therefore 10:12, 15:18 and 20:24 are the equivalent ratios of 5:6. 

Example 2: A team of disaster response force consists of 6 doctors for every 25 nurses. If the ratio remains constant and there are 30 doctors, find the numbers of nurses the team must have. 

Solution: 

First method: Make a table with equivalent ratios. We know that ratio of doctors to that of nurses is 6:25.  

Step 1: Multiply both terms of ratio by same non-zero number till we obtain 30 doctors. 

Step 2: Check the corresponding nurses when the doctors are 30. Hence, 125 nurses have to be arranged for 30 doctors. 

Second method:   

Solution: 

Ratio of doctors to that of nurses is 6:25. Guess the non-zero number by which 6 is to be multiplied to get 30. Use the same number to multiply 25 as well. In this case, take 5.  

Step 1: Write the ratio as a fraction and multiply 5 to both terms. 

6 / 25 =6 × 5 / 25 × 5 =30/125

5.2.2 Finding equivalent ratios using divisions 

Example 1: Jane is sharing pens. The table below shows you the ratio in which they are shared. If Jane keeps the ratio same and gives 7 black pens to his friend, then find how many blue pens he must also share. 

Solution: 

Step 1: Divide 56 and 32 by the same non-zero number until we get 7 black pens; let’s start by 4. 

We get 56 ÷ 4 = 14 and 32 ÷ 4 = 8. 

Step 2: Divide 56 and 32 by the same non-zero number until we get 7 black pens; let’s take 8. 

We get 56 ÷ 8 = 7 and 32 ÷ 8 = 4. 

Therefore, we understand that Jane gives 4 blue pens and 7 black pens. 

Example 2: Shawn needs 180 kilograms of meat to feed his 8 pet dragons. Find the quantity of meat Shawn needs to feed 2 dragons only.  

Solution:  

Step 1: Divide 180 and 8 by the same non-zero number until we get 2 dragons; let’s start by 2. 

We get 180 ÷ 2 = 90 and 8 ÷ 2 = 4. 

Step 2: Divide 90 and 4 by the same non-zero number until we get 2 dragons; let’s start by 2. 

We get 90 ÷ 2 = 45 and 4 ÷ 2 = 2. 

Therefore, we understand that Shawn needs 45 kilograms of meat. 

5.2.3 Finding equivalent ratios 

Example 1: Which of the following ratios are equivalent to 16:20: 

2:3, 4:5, 18:22, 20: 25 

Solution: 

Step 1: Make a table of equivalent ratios, take the given ratio and reduce it to the lowest possible value. Take 4 and divide both the terms. 

Step 2: Make equivalent ratios with the now reduced form, i.e., 4:5. 

Therefore, 4:5, 20:25 are the equivalent ratios to 16:20. 

Example 2: Which of the following ratios are equivalent to 45:81: 

30:54, 14:5, 18:20, 35: 25 

Solution: 

Step 1: Make a table of equivalent ratios, take the given ratio and reduce it to the lowest possible value. Take 9 and divide both the terms.  

Step 2: Make equivalent ratios with the now reduced form, i.e., 5:9. 

Therefore, 5:9, 30:54 are the equivalent ratios to 45:81.

What have we learned?

• Understanding equivalent ratios

• Find equivalent ratios using multiplications

• Find equivalent ratios using divisions

• Find equivalent ratios

Mind Map :