Transcript Ratios and Unit Rates Notes

Ratio Notes
A ratio is a comparison of two numbers
by division. Each number in a ratio is
called a term.
Ratios can be written three ways and
SHOULD ALWAYS BE SIMPLIFIED.
Ex: The ratio 4 to 5 can be written
1. 4 to 5
2. 4:5
3. 4/5
• Equal Ratios are ratios that name the
same number. They have the same
simplest form.
•
To find equal ratios, multiply or
divide both the numerator and
denominator of a ratio by the same
number
4/7 = 8/14
• Ratios are proportional if they simplify to
the same ratio.
Ex:
8:10 = 12:15 because
both simplify to 4:5
Write a ratio in three ways to compare each.
1. Lions to deer
_______________________
2. Parrot to swans _______________________
3. Swans to lions
_______________________
4. Deer to parrot
________
5. Swans to deer
________
6. Deer to swans
_______________________
Write each ratio as a fraction in simplest form.
(4 pumpkins, 2 watermelon, 12 bananas)
1. Watermelon to pumpkins
_________
2. Pumpkins to bananas
_________
3. Pumpkins to watermelon
_________
4. Watermelon to bananas
_________
5. Bananas to watermelon
_________
6. Bananas to pumpkins
Unit Rates
• A Rate is a ratio that compares two
quantities measured in different units.
• Ex. 150 heartbeats to 2 minutes
• A unit rate is the rate for one unit of a
given quantity. Always has the denominator
of 1.
• 150 divided by 2 = 75 The unit rate is 75
heartbeats per minute.
• Unit Price – a unit rate that gives the cost
per unit.
Finding Unit Rates
If you are given the price of many items, but you
need the price for one item individually, then
you need to know the unit rate. Or if you are
given the rate for 20 laps around a track, but
you want to know the speed PER LAP – you
need to know a unit rate.
•
You are finding “how many” in 1.
Practice with Unit Rates
You want to break these down into the “unit”
rate. How many miles in 1 min? How
many dollars you make in 1 hour? Etc.
*Hint: Divide the first by the second*
•
•
•
•
760 miles in 30 min
$42.50 in 8 hours
450 yards gained in 3 football games
286 shots made in 20 basketball games
Proportions
• A proportion is two equivalent ratios. We say that two
ratios are “proportional” to one another.
• Use cross products to determine if two ratios are
proportional.
• You can also use proportions to find a missing value in a
problem.
– You will actually use cross multiplication here, and an algebra
equation to solve for missing values.
4 = X
7
35
• 1. There are 54 boys and 48 girls in the Leopard
team. What is the ratio of girls to boys?
• 2. Tell me if the following ratios form a
proportion. Show your work.
3
15
5
35
3. Solve to find the missing value in the
following proportion:
4 = X
7
35
EXAMPLES:
• Example:
You can buy 20 CD’s in a pack for $30.00.
How much does each individual CD cost?
Proportion:
Division:
Find the unit rate for each situation.
• $80 for 10 shirts
• $20 for 4 toys
• $56 for 8 hours
• $120 for 5 shirts
• $45 for 9 boxes
Write the unit rate as a ratio. Then find an equal ratio.
•
The cost is $4.25 for 1 item. Find the cost of 4 items.
•
The cost is $10.10 for 1 item. Find the cost of 10 items.
•
The cost is $8.50 for 1 item. Find the cost of 4 items.
•
There are 2.54 cm in 1 inch. How many cm are in 6 inches?
•
There are 365 days in 1 year. How many days are in 2 years?