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. Ratioscan 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 ratioIs usually written as a fraction in simplest form.

Rate (265): a ratio of two measurements having different kindsof units.

Ex) 65 miles in 3 hours miles and hours aredifferent 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 Divide the numerator and denominator15 5 by the GCF, 3

The ratio of goldfish to fish is 3 to 5. This means that for every5 fish, 3 of them are goldfish

When writing a ratio involving measurements, both quantitiesShould 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 = 36 inches Here we convert feet to inches 16 inches 16 inches

Simplify: 36 inches = 9 inches We divide the numerator 16 inches 4 inches & 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 of30 recordable CDs costs $28. Which package has the lowercost per CD?

18 dollars = 0.9 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 = .93 Divide the numerator & denomintor 30 CDs 1 CD by 30 to get a denominator of 1.

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

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 lowercost 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 feetper second, you can use dimensional analysis (Lesson 5-3).remember that this is the process of carrying units throughouta computation.

Example Cuatro: Convert Rates

A grizzly bear can run 30 miles in 1 hour. How manyfeet is this per second? You need to convert 30 miles to ft

1 hr 1 sThere 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

= 30 mi 5280 ft 1 hr 1 hr 1 mi 3600 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!!

1

120

44

1

Your Turn!!

Express each ratio as a fraction in simplest form.

A. 18 cups to 45 cups

B. 9 pounds to 16 tons (2000 pounds/ton)

C. 155 apples to 75 oranges

Express each ratio as a unit rate, round to nearest tenth if needed

D. $3 for 6 cans of tuna

E. 68 meters in 15 seconds

F. 236.7 miles in 4.5 days

18 = 6 = 245 15 5

9 = 9 16 32,000

155 = 31 75 15

$0.50/can

4.5 m/sec

52.6 mi/day

Take a practice sheet & see me during study hall if youhave questions !!