• Proportions
Proportions are two ratios that are equal.  A ratio is a comparison of two quanities.  For example:

x x x x o o o o o o o

What is the ratio of x's to o's

The question asks for the x's first, so we count the x's which is 4
Next we count the o's which is 7

There are three ways to write a ratio

1) 4 to 7
2) 4 : 7
3) 4/7 This looks like a fraction but it really is the comparison of two quanities.  This is also the most common way to write a ratio when solving problems with proportion

Proportions are very similar to equivalent fractions

1/4 = x/8
Cross multiply the numbers
4 (x) = 1 (8)
Now solve it like you would an equation
Determine the operation, which is multiplication
Perform the opposite operation, which is division.  You must divide both sides with the number attached to the variable.  In this case it is 4
4(x)/4 = 8/4
The four with the variable counsels out leaving x
x=8/4
Eight divided by 4 is 2
Therefore x = 2
Substitue 2 for the variable in the original problem
4 (2) = 1 x 8
8 = 8  Your ratios are now equivalent
so 1/4 =2/8