This document discusses ratios and how they are used in cycling gear ratios, cooking recipes, making gold jewelry, and other examples. It provides definitions of ratios, such as how they compare two items and can be written in shorthand form using a colon. It also explains that for ratios the items being compared must be in the same units.

2. 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 needed 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.

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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!

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Ratios are also important in making gold for jewelery.
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

5. A Ratio is a comparison or a relationship between two items.
The Ratio of Blue Circles to Pink Circles is five blue circles
compared to three pink circles.
We can write this in any three of the following ways:
Blue to Pink = 5 to 3 or 5:3 or 5/3

6. We can express our Ratio comparison in two ways :
Blue Circles to Pink Circles or
Pink Circles to Blue Circles
Blue to Pink = 5 to 3 or 5:3 or 5/3
Pink to Blue = 3 to 5 or 3:5 or 3/5

7. If we double our circles we now have 10 Blue circles to
6 Pink circles. There are still 5 Blue Circles for every three
Pink circles. We simply now have two of these groupings.
This means the simplest Ratio we can write for our situation
is Blue to Pink = 5 : 3.
The Ratios 10 : 6 and 5 : 3 are said to be “Equivalent”.

8. What is the Ratio of Cats to Snakes in this Picture ?
There are two cats and one snake, so the ratio is 2 to 1.
The Ratio answer is Cats : Snakes = 2 : 1
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9. What is the Ratio of Apples to Bananas ?
There are 5 apples and 6 bananas, so the ratio is 5 to 6.
The Ratio is Apples : Bananas = 5 : 6
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10. What is the Ratio of Boys to Girls ?
There is one boy and three girls, so the ratio is 1 to 3 .
The Ratio is Boys : Girls = 1 : 3
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11. Write 10kg to 3kg in “shorthand ratio” form.
There are ten kilograms compared to three kilograms .
The “Shorthand Ratio” = 10 : 3
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12. 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, days are smaller than weeks, and so on.

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