This document discusses several math concepts including ratios, percentages, fractions, and tree diagrams. It explains that ratios compare two numbers, percentages are fractions written with a percent sign meaning divided by 100, fractions have a numerator and denominator, and tree diagrams visualize possible outcomes of sequential events.

1. Math
By Michael Du
(Lucy the Unicorn)

2. Ratios
• A ratio is a statement of how two numbers
compare. It is a comparison of the size of
one number to the size of another
number. All of the lines below are
different ways of stating the same ratio. If
you fill in one of the lines below, this
selection will explain a few things about
your ratio.

3. Percentages
If you just remember these rules as “move the decimal two
places to the left” and “move the decimal two places to the
right,” you are very likely to get them confused. If you
accidentally move the decimal in the wrong direction it will
end up four places off from where it should be, which means
that your answer will be either ten-thousand times too big or
ten-thousand times too small. This is generally not an
acceptable range of error. It is much better to remember these
rules by simply remembering the meaning of the percent sign,
namely that “ % “ means “ /100.” If you just write the problem
that way, you should be able to see what you need to do in
order to solve it.

4. Fractions
• Numerator: the top number in the fraction that is the amount it has outta the denominator
• Denominator : the bottom number in the fraction usually the number hat is needed to make
the whole number
Examples: 4/5 = 80% or 0.8
Some fractions are called improper fractions which means the numerator is greater than the
denominator example: 11/10

5. Tree Diagram
Tree diagrams are useful for organizing and visualizing the different possible
outcomes of a sequence of events. For each possible outcome of the first event,
we draw a line where we write down the probability of that outcome and the
state of the world if that outcome happened. Then, for each possible outcome of
the second event we do the same thing.