In mathematics, a ratio is a comparison of two numbers by
division.
For example, the ratio of 15 and 10 can be expressed in the following three ways.
15 to 10 15:10 
You can express in simplest form as 
.
An equation stating that two ratios are equal is called a proportion.
So, 
is a proportion. Every proportion has
two equal cross products.
You can use cross products to solve proportions. Sometimes
you’ll use the Distributive Property.
Example
Solve each proportion.
You can use proportions to find equivalent measurements
within the English or metric systems.
Example
Convert each measurement as indicated.
3. 72 ounces to pounds
Alternative
Solutions :
16
ounces = 1 pound
Let x
represent the number of pounds. Write a proportion.
4.
15 meters to centimeters
Alternative
Solutions :
1
meter = 100 centimeters
Let x
represent the number of pounds. Write a proportion.
A rate is a ratio
of two measurements having different units of measure. For example, 120 miles
in 2 hours is a rate. When a rate is simplified so it has a denominator of 1,
it is called a unit
rate. To find the unit rate of 120 miles in 2 hours, divide by 2.
The result is a unit rate of 60 miles in 1 hour, or 60 miles per hour.
To solve
problems involving rates, you can use dimensional analysis. This is the process of
carrying units throughout a computation.
Example
Science Link
5. Density is a measure of the amount of matter that occupies a given
volume. The density of wood is 0.71 gram per cubic centimeter. Suppose you have
a piece of wood whose volume is 50 cubic centimeters. How many grams of wood
does it contain?
Alternative
Solutions :
Multiply
the unit rate by the number of cubic centimeters of wood.
So, the
piece of wood contains 35.5 grams of wood.
Example
Travel Link Link
6. Juanita’s family drove 400 miles in 8 hours. The next day, they need to
drive another 700 miles. At the same rate, how long will it take them to drive
the 700 miles?
Alternative
Solutions :
Explore
You know that the family drove
400 miles in
8 hours. You need to find how long it will take
to drive 700 miles farther.
Plan Write the rate 400 miles in 8
hours as a unit rate.
Then divide 700 miles by the unit rate.
Solve
Examine
It takes 8 hours to
travel 400 miles. A trip of
700 miles would take nearly twice as long.
So, 14 hours is reasonable.
Sumber
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