Ratios and Proportions

Well, it's pretty much a fraction. Like 1/4, 1/3, 1/2, and so on. 

A proportion is a name we give to a statement that two ratios are equal. It can be written in two ways:

• two equal fractions, 

  • • or,

• using a colon,    a:b = c:d

When two ratios are equal, then the cross products of the ratios are equal.

That is, for the proportion, a:b = c:d ,  a x d = b x c

EXAMPLE-> 2:10=1:5 , 2x5=10x1 , 10=10.  This would be the same thing as-> 2/10=1/5 , 2x5=10x1.

In problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. We can also use cross products to find a missing term in a proportion. 

EXAMPLE-> 20/50=30/X , 20xX=50x30 , 20X=1500 , X=1500/20 , X=75.

Ratios can also be used to find a relationship between two amounts.

EXAMPLE –> If there are 100 kids in a room, and 60% of them are girls.

        Therefore there are 60 girls and 40 boys.

        The ratio of girls to boys would be 60:40 or reduced into its simplest form by dividing each number by 20. The ratio is 3:2. There are 3 girls for every 2 boys.

EXAMPLE –> What are the dimensions of a rectangle that is four times larger than a rectangle with a width of 3 and a length of 5.

        The ratio (width:length) of the smaller rectangle would be 3:5.

        To find the larger rectangle we would take (3:5)•4 = 3•4:5•4 = 12:20.

        The width of the larger rectangle would be 12 and the length would be 20. The two rectangles are proportional.

For more information: http://www.purplemath.com/modules/ratio.htm