1. A ratio is a comparison of two quantities by division.
Ratios
The ratio of a to b can be written as:
Example: If there are 12 males and 17 females in a class,
then the ratio of males to females is:
Simplifying a Ratio
Step 1. Write the ratio in fraction notation.
Step 2. Simplify if possible.
Example 1. Simplify each ratio if possible.
a) 12 to 15 b) 17 to 51
Answers:
Your Turn Problem #1
Simplify each ratio if possible.
a) 18 to 36 b) 63 to 81
Answers:

2. Simplifying a Ratio That Contains Decimals
Step 1. Write the ratio in fraction notation.
Step 2. Multiply numerator and denominator by a power of 10 to make each a whole number. (It must be the same power of 10 for both.)
Stated also as: move the decimal point in the numerator and denominator to the right the same number of places to make each a whole number
Step 3. Simplify if possible.
Example 2. Simplify each ratio if possible.
a) 0.48 to b) 0.4 to 5
Move the decimal point to the right 2 places.
Move the decimal point to the right 1 places.
Answers:
Your Turn Problem #2
Simplify each ratio if possible.
a) 0.36 to 0.4 b) 2.75 to 0.5
Answers:

3. Simplifying a Ratio That Contains Fractions and Mixed Numbers
Step 1. Write the ratio in division form. a to b written as a  b.
Step 2. Perform the division and simplify if possible.
Answer:
Example 3. Simplify the ratio if possible:
1. Write as a division problem.
2. Convert mixed numbers to improper fractions. Convert to multiplication and invert 2nd fraction.
Your Turn Problem #3
Simplify the ratio if possible:
Answer:

4. Writing a ratio of converted measurement units
If a comparison is made between two measurements, it must be written in the same units if possible.
For example; if one measurement is in inches and the other in feet, convert the feet to inches. It is usually easier to convert the larger units to the smaller units.
Answer:
Since 4 feet = 48 inches
(Since the units are identical, they divide out)
Your Turn Problem #4
Answer:

5. When a ratio is used to compare two different kinds of measure, we call it a rate.
Rates
Rates are written in fraction notation with the units included. We include the units because they are different and therefore do not divide out.
Finding a unit rate
Procedure: Finding a Unit Rate
Step 1. Write the rate in fraction notation with the units included.
Step 2. Divide the numerator by the denominator.
Example 5. Find the unit rate.
a) 780 miles in 12 hours b) 500 people in 4 days
Answers:
Your Turn Problem #5
Find the unit rate.
a) $3600 in 9 months
b) words on 12 pages
Answers:
a) $400 per month
b) 420 words per page

6. Unit Price
A unit price is the ratio of price to the number of units.
Example 6. Find the unit price for a 12 oz bottle that sells for $0.75.
= $0.06
(round to the hundredths place since we are dealing with money.)
Your Turn Problem #6
Find the unit price
$3.29 for 16 ounces
Answers:
$0.21 per ounce
The End
B.R.
6-4-08