Ratios and proportions
Ratio: A ratio can be written in three different ways and all are read as “the ratio of a to b”
- two equal fractions, or using a colon, a:b = c:d
A proportion is read as “a is to b as c is to d”
Example
You know that to make 20 cakes you have to use 2 eggs. How many eggs are needed to make 100 cakes?
Eggs | cakes | |
Small amount | 2 | 20 |
Large amount | x | 100 |
If we write the unknown number in the nominator then we can solve this as any other equation
Multiply both sides by 100
If the unknown number i.e. x is in the denominator, we can use another method that involves the cross product.
The cross product is the product of the numerator of one of the ratios and the denominator of the second ratio. The cross products of a proportion is always equal.
If we again use the example with the cookie mix used above
It is said that in a proportion if
If you look at a map it always tells you in one of the corners that 1 inch of the map correspond to a much bigger distance in reality. This is called a scaling. We often use scaling in order to depict various objects. Scaling involves recreating a model of the object and sharing its proportions, but where the size differs. One may scale up (enlarge) or scale down (reduce).
For example, the scale of 1:4 represents a fourth. Thus any measurement we see in the model would be 1/4 of the real measurement. If we wish to calculate the inverse, where we have a 20ft high wall and wish to reproduce it in the scale of 1:4, we simply calculate: