Ratio Table

A ratio table shows the relation between two variables across different measurements. It is a tabular form of representing a group of data in two variables in a readily identifiable way.  

For example, Phillips recorded the distance covered by him with the amount of time taken till he reached home, which is at a distance of 10 km from his start point. The result he got is given below in the form of a table.

Distance Covered (d)	Time Taken (t)
2 km	30 mins
4 km	60 mins
6 km	90 mins
8 km	120 mins
10 km	1500 mins

Every one of those pairs of numbers in the table represents a ratio where two numbers or quantities are compared. The ratio is written in the fraction form (d/t), such as ${\dfrac{2}{30}}$, ${\dfrac{4}{60}}$, ${\dfrac{6}{90}}$ such that each ratio is equivalent to the other.

Thus, a ratio table is a structured list of equivalent (equal value) ratios that establish the relationship between the ratios and the numbers.

How to do Ratio Tables

Let us consider Glen is curious to know how his heart works to pump blood through his arteries and starts calculating how fast his heart is beating and if it is normal.

As we know, heartbeat is rhythmic, and thus the ratio between the two parameters will always give an equivalent fraction.

Step 1: Making a table with two rows

Step 2: Labeling the table and input the values

Number of Heartbeats	160	320	480	640
Time (in minutes)	2	4	6	8

Step 3: Writing in the form of an equivalent ratio

To check whether the heart is beating uniformly, we will divide the number of heartbeats by time for each observation.

${\dfrac{160}{2}}$ = 80

${\dfrac{320}{4}}$ = 80

${\dfrac{480}{6}}$ = 80

${\dfrac{640}{8}}$  = 80

Step 4: Check the values in each case to find your answer.

Yes, the heart is functioning correctly at a uniform rate.

It works for similar cases where we need to calculate uniformity in the speed of a vehicle, the number of customers in a store, and the volume of water flowing out of a pipe. 

How to Complete a Ratio Table

We can add the missing values in a ratio table by:

1. Adding or subtracting each ratio
2. Multiplying or dividing each number in the equivalent ratios by the same value

Consider the table given below:

Number of Boys	3	6	9	12
Number of Girls	5	10	15	20

Here, the first quantity of each ratio is obtained by adding 3, and the second quantity by adding 5.

Similarly, in the following table:

Number of Butterflies	6	12	18	24	30
Number of Moths	10	20	30	40	50

Here, the first quantity of each ratio is obtained by multiplying 6 by 2, 3, 4, and 5. Similarly, the second quantity of each ratio is obtained by multiplying 10 by 2, 3, 4, and 5.

Using the same concept, we can complete a ratio table. An example is given below:

Number of Chairs	10	15
Number of Tables	4		6

Since the original ratio is ${\dfrac{10}{4}}$ = ${\dfrac{5}{2}}$, we will add 5 to the first row each time and add 2 repeatedly to the second row

Thus the table becomes:

Number of Chairs	10	15	20	25	30	35
Number of Tables	4	6	6	8	10	12

Let us some practice problems using the above concepts.

Solved Example

E.g. 1. Complete the given equivalent ratio table.

Number of Dogs	8	12				28
Number of Cats	6	9		15

Since the original ratio is ${\dfrac{8}{6}}$ = ${\dfrac{4}{3}}$, we will add 4 to the first row each time and add 3 repeatedly to the second row

Thus the table becomes:

Number of Dogs	8	12	16	20	24	28
Number of Cats	6	9	12	15	18	21

E.g. 2. If 7 books cost $14, use a ratio table to calculate the cost of 8 books.

As we know,

Unit cost = Total cost/Number of units = 7/21 = 3

Thus, 8 × 3 = 24

Number of Books	7	1	8
Cost (in $)	21	3	24

Thus, the cost of 8 books is $24.