Objective:
Ratio and Proportion
In this lesson you will review how to set up and work
with ratios, percents, and proportions.
For any words used that you are unsure of for its
definition, please go to the glossary found by clicking
on the Glossary button at the bottom of the page.
- Ratio
- Proportion
- Percent
- Product
- Similar Triangles
| The ratio of the number a to the number
b can be written in the following ways: using
words - a to b, using a colon - a
: b, and using a fraction - a / b.
Since division by zero is undefined, the second number,
b, cannot be 0. Since a fraction represents division,
this tells us that a ratio compares two numbers using
division. The fraction 5 / 6 means 5 divided by 6. |
A proportion shows one ratio equal to another
ratio and can be written in the following ways:
3/6 = 15/30, 3:6 = 15:30, or 3:6 :: 15:30. When
reading a proportion, you use the words "is
to" to replace the / or : . The
'=' and '::' are read with the word
"as". This example would be read as, 3
is to 6 as 15 is to
30. Remember to set up your proportion with the
top numbers of both ratios representing the same
type as the bottom number of the ratios should be
the same type as well. For example, if there are
5 apples to 7 oranges and we know that there are
10 apples to 14 oranges we need to be sure to set
up the proportion apples to apples and oranges to
oranges. 5 apples / 7 oranges = 10 apples / 14 oranges
A proportion is made up of four numbers.
If we know three of the numbers, we can solve to
find the fourth number.
To solve a proportion, we set the two ratios
equal to each other and find their cross products.
Two ratios are equal if their cross products are
equal. Thus in a proportion, the cross products
are equal. For example:
3/4 = x/24
We find the cross product and find
the missing value, x, by getting it by itself on
one side of the equation.
(diagram of 3/4 = x/24 with an
arrow going from 3 down to 24 and an arrow from
x down to 4)
3 * 24 = 4 * x
72 = 4x
18 = x
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The symbol % is used to mean percent. The
percent of a number can be written as a decimal or
a fraction. For example, 25% is represented by .25
as a decimal. We move the decimal that is after the
ones place value in our percent two places to the
left. As a fraction it would be written as 25/100
and then reduced to lowest terms would be 1/4.
When working with percents and other mathematical
equations and statements, remember that the word "of"
means multiplication and the word "is"
means equals to. For example in the question, what
number is 35% of 150, we can translate this into mathematical
terms, x (what number) = (is) .35 (35% written as
decimal) * (of) 150, x = .35 * 150 would be our equation
to solve.
Remember, 100% of anything is the total number of
outcomes. For example, if there are 12 pieces of
pizza, 100% of the pizza would be 12 of the 12 pieces. |
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