Introduction to Ratios

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If you have ridden a bike lately, then you will know that for going downhill very fast, we use a Rear Cog that does not have as many teeth compared to the Front Chain Ring.

This gives us a “Very High” Gear Ratio of 53 to 11.

Front / Rear gear measurement uses two numbers (e.g. 53/11) where the first is the number of teeth in the front chain ring and the second is the number of teeth in the rear sprocket.

Low Gear Ratios are used for going up hills, and a low gear Rear / Front Ratio might typically be 34 / 23, or 34 teeth on the rear cog, compared to 23 teeth on the front chain ring.

In Low Gear the chain ring will rotate more times than the cog, which gives us more power supplied to a single revolution of the rear wheel.

This makes it easier to get up a big hill.


kid making cookies
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Ratios are very important in Cooking.

If a recipe calls for 1 egg and 2 cups of flour, the relationship of eggs to cups of flour is 1 to 2.

Add the wrong ratios of ingredients to a baked cookies recipe, and the resulting salty rock hard cookies will not be a hit with anyone.


woman with jewellery in shop
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Ratios are also important in making gold for jewellery.

For example 14 carat Gold can be made by combining 6 parts Gold with two and a half parts Copper, and one and a half parts Silver.

The Ratio of Gold to Copper to Silver = 6 to 2.5 to 1.5


Definition of a Ratio

A Ratio is a comparison or a relationship between two items.

It is represented using a colon ‘:’, the word ‘to’ or using a fraction ‘/’.

For example, in the following diagram, the ratio of red cirles to blue circles is 5 to 3.

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The order we write a ratio in is important. For our situation we can express the comparison Ratio in two different ways.

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This means that we need to read math questions very carefully to see which order the Ratio needs to be written in.

If the question asked us to “write the Ratio of Blue Circles to Pink Circles”, then we would need to write 5 : 3 or 5 to 3.

The Ratio of Blue Circles to Pink Circles as 5 to 3 indicates that for every five Blue circles, we have three Pink Circles.

If we double our circles, we will have 10 Blue circles to 6 Pink circles.

There are still five Blue Circles for every three Pink circles. We simply now have two of these groupings.

We say that the ratio of 10 : 6 is “Equivalent”, (or means the same thing as), to 5 : 3 .

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Introductory Video on Ratios


Determining Ratios Examples

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Units for Ratios

The items being compared in a Ratio must always be in the same units.

For example: 1km to 300m needs to be written as 1000m to 300m, which in shorthand form is 1000 : 300

123 days to 1.2 years needs to be converted into 123 days to (1.2 x 365) days = 123 : 438

27 minutes to 2 hours needs to be converted into 27 minutes to (2 x 60) minutes = 27 : 120

Note that we always convert both items into the smaller unit.

(Meters are smaller than kilometers, days are smaller than years, minutes are smaller than hours, and so on).

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Related Items

Fibonacci Sequence in Music


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