Ratios and Rates
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Transcript of Ratios and Rates
Ratios and RatesSection 5.1 & 5.2
Objectives:• Solve problems involving average
speed, distance, and time. (AF 4.2)
• Choose an appropriate unit measure and use ratios to convert within and between measurement systems. (MG 1.0)
• Compare measures within and between measurement items (MG 1.1)
Words to know ~• Ratio – a comparison of a number “a” and a
nonzero number “b” using division.
ExampleExample – – 12 games to 7 games ; 12 games to 7 games ;
12 to 7; 12:712 to 7; 12:7
• Rate – a type of ratio that compares two
• quantities that have different kinds of units of measure.
ExampleExample – – 100 miles in 2 hours100 miles in 2 hours
• - 6 pencils for $1.40- 6 pencils for $1.40
Writing a Ratio • Voting – Barack Obama won 333 electoral
votes while John McCain won 156. What’s the ratio of Obama’s votes to McCain’s votes?
• Ratio – Obama votes =
McCain votes
Ratio can be written also as 111:52 , or “111 to 52”
Rewriting with the same units
• A map shows the distance between the classroom and the bathroom as 16 inches. In reality, the distance is 4 yards.
MUST CONVERT TO THE SAME UNIT OF MEASURE!!!
Finding a RateFinding a Rate• You and your family drove 400 miles in 8
hours.
• What was the average rate of speed?
Reduce the numbers.
Summary:
Ratio is ….
Rate is ….
Finding a Unit Rate
• A 6 pack of soda costs $1.60. A 12 pack of soda costs $ 3.00. Which is the better buy?
Finding a Unit Finding a Unit RateRate
Golf balls can be purchased in a 3-pack for $4.95 or a 12-pack for $18.95. Which pack has the lower unit price?
price for packagenumber of balls
$4.953
= $1.65
price for packagenumber of balls
= $18.9512
$1.58
The 12-pack for $18.95 has the lower unit price.
Finding a Unit Finding a Unit RateRate
John can buy a 24 oz bottle of ketchup for $2.19 or a 36 oz bottle for $3.79. Which bottle has the lower unit price?
$2.1924
$0.09
$3.7936
$0.11
The 24 oz jar for $2.19 has the lower unit price.
price for bottlenumber of ounces
price for bottlenumber of ounces
=
=
PracticeIdentify if the problems are rates or ratios.
Practice• Write each fraction in simplest terms.
SummarySummary• Remember that a ratio is a comparison of two numbers.
Example = number of A’s compared to the number of B’s
• Remember that a rate is a type of ratio that compares two quantities that have different kinds of units of measure.• Example = 2 pairs of pants for $25. (comparing the number of
pants to the dollar amount.)
Lesson QuizLesson QuizWrite each ratio in simplest form.Write each ratio in simplest form.
1. 22 tigers to 44 lions
2. 5 feet to 14 inches
12
307
3. Meka can make 6 bracelets per half hour. How many bracelets can she make per hour?
12Estimate each unit rate.
4. $2.22 for 6 stamps
5. 8 heartbeats in 6 seconds
$0.37 per stamp
1.3 beats/s
Find each unit price. Then tell which has the lower unit price.
6. A half dozen carnations for $4.75 or a dozen for $9.24
7. 4 pens for $5.16 or a ten-pack for $12.90.
a dozen
They cost the same.
Activity• Using the grocery store flyers (with a partner), create 3
rates and 3 ratios.
• Exchange them with another team.
• Solve the other team’s rates and ratios.