# Ratios and proportions

Ratio: A ratio can be written in three different ways and all are read as “the ratio of a to b”

tb
a:b
a/b
Proportion: A proportion is an equation which says that two ratios are equivalent. it can be written in two ways:
• two equal fractions, or using a colon,  a:b = c:d
For example, if one package of cookie mix results in 20 cookies than that would be the same as to say that two packages will result in 40 cookies.
20/1=40/2

A proportion is read as “a is to b as c is to d”

a/b=c/d wherb,d0
If one number in a proportion is unknown you can find that number by solving the proportion.

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
eggs/cakes=eggs/cakeocakes/eggs=cakes/egg

If we write the unknown number in the nominator then we can solve this as any other equation

x/100=2/20

Multiply both sides by 100

100⋅ x/100=1002/20
x=200/20
x=10

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

20/1=40/2
140=220=40

It is said that in a proportion if

a/b=c/d where b,d0