1. Chapter 6: Ratio, Proportion and Percent
Chapter 6 Lesson 1
Ratios and Rates
Pgs
What you will learn:
Write ratios as fractions in simplest form
Determine unit rates

2. Vocabulary
Ratio (264): a comparison of two numbers by division. Ratios
can be written in the following three ways:
2 to : 4
Remember that a fraction bar represents division. When the
First number being compared is less that the second, the ratio
Is usually written as a fraction in simplest form.
Rate (265): a ratio of two measurements having different kinds
of units.
Ex) 65 miles in 3 hours miles and hours are
different kinds of units
$16 for 2 pounds Dollars and pounds are

3. Unit Rate (265): when a rate is simplified so that it has a
denominator of 1.
Ex) $5 per pound, which means $5 per 1 pound
Example Uno: Write Ratios as Fractions
Express the ratio 9 goldfish out of 15 fish in simplest form
9 = Divide the numerator and denominator
by the GCF, 3
The ratio of goldfish to fish is 3 to 5. This means that for every
5 fish, 3 of them are goldfish

4. When writing a ratio involving measurements, both quantities
Should have the same unit of measure.
Example Dos: Write Ratios as Fractions
Express the ratio 3 feet to 16 inches as a fraction in simplest form.
3 feet = inches Here we convert feet to inches
16 inches inches
Simplify: inches = 9 inches We divide the numerator
16 inches inches & denominator by the
GCF of 4. “Inches”
cancel with each other.
Written in simplest form, the ratio is 9 to 4.

5. Example Tres: Find Unit Rate
A package of 20 recordable CDs costs $18, and a package of
30 recordable CDs costs $28. Which package has the lower
cost per CD?
Recall the definition of Unit Rate (265): when a rate is
simplified so that it has a denominator of 1.
Ex) $5 per pound, which means $5 per 1 pound
18 dollars = Divide the numerator and
20 CDs 1 CD denominator of 18 by 20 so the 20
new denominator will = 1
Do the same with the second rate:
28 dollars = Divide the numerator & denomintor
30 CDs CD by 30 to get a denominator of 1.

6. Now compare the two unit rates:
For the 20-pack, the unit rate is $.90 per CD.
For the 28-pack, the unit rate is $.93 per CD.
So the package that contains 20 CDs has the lower
cost per CD.
Concept Check: Is $50 in 3 days a rate or a unit rate? Explain.
Since the ratio doesn’t have a denominator of 1, it is a rate.

7. To convert a rate such as miles per hour to a rate such as feet
per second, you can use dimensional analysis (Lesson 5-3).
remember that this is the process of carrying units throughout
a computation.
Example Cuatro: Convert Rates
A grizzly bear can run 30 miles in 1 hour. How many
feet is this per second?
You need to convert 30 miles to  ft
1 hr s
There are 5280 ft in 1 mile and 3600 seconds in 1 hour.
30 mi = 30 mi  5280 ft  3600s Convert feet to miles and hours to seconds
1 hr hr mi hr
= 30 mi  ft  1 hr Remember, use the reciprocal when
1 hr mi s dividing fractions
= 30 mi  5280 ft  1 hr
1 hr mi s Divide the common factors and units

8. 44 1
= 30 mi  5280 ft  1 hr
1 hr mi s Divide the common factors and units
= 44 ft s
So, 30 miles per hour is equivalent to 44 feet per second.
When working on problems like this, work carefully and
logically think through what you are doing!!
120 1

9. Your Turn!!
Express each ratio as a fraction in simplest form.
18 cups to 45 cups
9 pounds to 16 tons (2000 pounds/ton)
155 apples to 75 oranges
Express each ratio as a unit rate, round to nearest tenth if needed
$3 for 6 cans of tuna
68 meters in 15 seconds
236.7 miles in 4.5 days
18 = 6 = 2
9 = 9
,000
155 = 31
$0.50/can
4.5 m/sec
52.6 mi/day

10. Take a practice sheet & see me during study hall if you
have questions !!