FINDING RATIOS FROM TABLES

Ratio is a comparison of two quantities with same kind. In this section, we are going to see, how to find ratios from the tables. 

Example :

Students in Mr. Webster’s science classes are doing an experiment that requires 250 milliliters of distilled water for every 5 milliliters of ammonia. The table shows the amount of distilled water needed for various amounts of ammonia.

Question 1 : 

Use the numbers in the first column of the table to write a ratio of distilled water to ammonia.

Answer : 

100 ml distilled water / 2 ml ammonia  (or)  100 : 2

Question 2 : 

How much distilled water is used for 1 milliliter of ammonia?

Answer : 

From the first column of the table, the ratio  of distilled water to ammonia is 

100 ml water / 2 ml ammonia

To find the quantity of distilled water used for 1 milliliter of ammonia, we have to make the second quantity (ammonia) as 1. 

100 ml distilled water : 2 ml ammonia  =  (100 ÷ 2) / (2 ÷ 2)

100 ml distilled water : 2 ml ammonia  =  50 / 1

That is,

50 ml distilled water / 1 ml ammonia  

The quantity of distilled water used for 1 milliliter of ammonia is 50 ml.

Question 3 : 

Use your answer from question 2, write another ratio of distilled water to ammonia.

Answer : 

To write another ratio from the answer of question 2, we have find an equivalent ratio to 50 : 1.

To find equivalent ratio of the given ratio, we have to multiply both the terms of the ratio by the same non zero number, say "2".

Then, we have 

(50x2) : (1x2)  =  100 : 2

Therefore, another ratio of distilled water to ammonia is 100 : 2

Question 4 : 

Check whether the two ratios from answers of question 1 and question 2 are equivalent or not equivalent. 

Answer : 

The two ratios from the answers of question 1 and 2 are 

100 : 2 and 50 : 1 

Let us check, whether two rations 100 : 2 and 50 : 1 are equivalent or not equivalent. 

From the above working, it is clear that the two ratios 100 : 2 and 50 : 1 are equivalent.

Question 5 :

Complete the table. What are the equivalent ratios shown in the table ?

Answer : 

For the first blank :

(100 ÷ 2) / (2 ÷ 2)  =  50 / 1

(50 x 3) / (1 x 3)  =  150 / 3

For the second blank :

(100 ÷ 2) / (2 ÷ 2)  =  50 / 1  

(50 ÷ 2) / (1 ÷ 2)  =  25 / 0.5

(25 x 7) / (0.5 x 7)  =  175 / 3.5

For the third blank :

(100 x 2) / (2 x 2)  =  200 / 4

Then, we have

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