Transcript Chapter 6: Ratio, Proportion and Percent

Chapter 6: Ratio, Proportion
and Percent
Chapter 6 Lesson 1
Ratios and Rates
Pgs. 264-268
What you will learn:
Write ratios as fractions in simplest form
Determine unit rates
Vocabulary
Ratio (264): a comparison of two numbers by division. Ratios
can be written in the following three ways:
2 to 4
2:4
2
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
different kinds of units
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 = 3
15
5
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
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
=
16 inches
Simplify:
36 inches
16 inches
36 inches =
16 inches
Here we convert feet to inches
9 inches
4 inches
We divide the numerator
& denominator by the
GCF of 4. “Inches”
cancel with each other.
Written in simplest form, the ratio is 9 to 4.
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 = 0.9
20 CDs
1 CD
Divide the numerator and
denominator of 18 by 20 so the
20
new denominator will = 1
Do the same with the second rate:
28 dollars = .93 Divide the numerator & denomintor
30 CDs
1 CD by 30 to get a denominator of 1.
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.
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
1s
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
1 hr
1 mi
1 hr
= 30 mi  5280 ft  1 hr Remember, use the reciprocal when
1 hr
1 mi
3600 s dividing fractions
= 30 mi  5280 ft  1 hr
1 hr
1 mi 3600 s
Divide the common factors and units
44
1
= 30 mi  5280 ft  1 hr
1 hr
1 mi 3600 s
120
1
= 44 ft
s
Divide the common factors and units
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!!
Your Turn!!
Express each ratio as a fraction in simplest form.
A. 18 cups to 45 cups
18 = 6 = 2
45 15 5
9 = 9
B. 9 pounds to 16 tons (2000 pounds/ton) 16 32,000
C. 155 apples to 75 oranges 155 = 31
75
15
Express each ratio as a unit rate, round to nearest tenth if needed
D. $3 for 6 cans of tuna
$0.50/can
E. 68 meters in 15 seconds
4.5 m/sec
F. 236.7 miles in 4.5 days
52.6 mi/day
Take a practice sheet & see me
during study hall if you
have questions !!