Ratios

A ratio is a comparison of one quantity in relation to another of a same kind. Note that the word ‘is to’ in the ratio has the same meaning as the colon ‘:’.

        For example, if we have 10 apples and 2 oranges, then we can say that the ratio of apples to oranges is 10 to 2. It means that for every 10 apples we have 2 oranges (10:2) or scale it down and say, for every 5 apples we have 1 orange (5:1) or scale it up and say, for every 20 apples we will have 4 oranges (20:4). Thus the ratio of apples to oranges is ‘ten is to two’ and can be written as 10:2 or 10/2 or 10 to 2.

       For example, the pressure to altitude ratio of 2:1 would indicate that for every foot increase in altitude, the pressure would increase by 2 PSI.

 

Ratio between two quantities

Example 1

        In a basket there are 12 red balls and 4 blue balls. What is the ratio of red balls to blue balls?

                                Red balls : Blue balls (order is important)

12 : 4

                                            12/4 : 4/4 (General practice to simplify)

  3 : 1

        This answer can be written as 3:1 or 3/1 or 3 to 1.

 

Example 2

        In a basket there are 12 red balls and 4 blue balls. What is the ratio of blue balls to red balls?

        Here notice that the question is asking the ratio of blue balls to red balls.

Blue balls : Red balls

                                   4 : 12 (notice 4 comes first)

                                              4/4 : 12/4 (General practice to simplify)

1 : 3

        This answer can be written as 1:3 or 1/3 or 1 to 3.

 

Ratio between more than two quantities

Example

        In a hangar there are 20 Helicopters, 40 Engines and 60 Propellers. What is the ratio of helicopters to propellers to engines?

Helicopters : Propellers : Engines

     20     :      60      :     40

      20/20    :    60/20   :     40/20

(to simplify, find the largest number that can divide all three and in this case it is 20)

     1         :       3       :         2

        The answer is 1:3:2.

Note: Based on the answer given, if you are required finding the ratio of Engines to Helicopters to Propellers. Then the ratio order is written as 2:1:3.

 

Simplifying ratios

In general, the ratios are expressed in a simplified form. The ratio numbers are scaled down to smallest possible numbers. To scale down the ratio, divide both the sides by the largest possible number. Let us look at some of the examples to understand better.

Example 1

        A ratio 25:50 can be scaled down to 1:2 (divide both sides by 25)

 

Example 2

        A ratio 12:16 can be scaled down to 3:4 (divide both sides by 4)

 

Example 3

        To simplify the ratio 15:86, it is acceptable to scale it down to 1 and other as a whole numbers and decimals. Because in this case, it is not possible to find a common number that can scale it down resulting whole numbers.

                The scaled down ratio of 15:86 is

                                  15/15     :     86/15 (divide both sides by 15)

1        :       5.73

        Answer = 1:5.73

 

Ratio to quantities

If we know the ratio, then the following steps will explain on how to find the quantity (numbers).

Example 1

        The ratio of files to hammer in a toolbox is 2:3. How many files would be there if there are total of 25 tools?

                The ratio 2:3 shows that for a group of every 5 tools (2 + 3) there are 2 files and 3 hammers. In total there are 25 tools, which means that there are 25/5= 5 group of tools.

                Each group has 2 files. So in a group of 5 there should be 5 x 2 = 10 files.

 

Example 2

        The ratio of serviceable to unserviceable engines in a hangar is 1:4. The total number of engines is 120. Determine how many engines are serviceable?

     Serviceable   :   Unserviceable

1    :   4

                Total engines in a group = 1 + 4 = 5

                Total number of groups = 120/5 = 24

            Each group has one unserviceable engine. So, the total number unserviceable engines = 24 x 1 = 24 engines