A grade has 81 girls and 72 boys. the grade is split into groups that have the same ratio of girls to boys as the whole grade. how many girls are in a group that has 16 boys? complete the ratio table to solve the problem.

The big keyword here is the word RATIO. Ratio of what? The ratio of girls to boys in the entire grade. A ratio is just the two amounts divided by each other (you can also call it the slope, but ignore that if that makes it more confusing). 

(81 girls)/(72 boys) 

Simplify it by breaking it up a bit. 
81 = 9 * 9 
72 = 9 * 8

[tex] \frac{9*9}{9*8} [/tex]

Cross out similar terms to gain the result of: 
[tex] \frac{9 girls}{8 boys} [/tex]

What they want from us is the ratio of girls if a group has 16 boys. So set it up like this: 
[tex] \frac{x girls}{16 boys} = \frac{9 girls}{8 boys} [/tex]

Just by looking at this you may be able to solve for "x" if you have a good understanding of fractions, but instead let's do the long way.

First off is to get "x" alone by multiplying 16 boys on both sides. 

x = [tex] \frac{9*16}{8} [/tex]


Remember that: 
16 = 8*2

x = [tex] \frac{9*8*2}{8} [/tex]

Cancel out the like terms (8) to give you: 
x = 18 girls