sol 7.4, 8.3a use measures expressed as rates (e.g., speed, density) and measures expressed as...
TRANSCRIPT
SOL 7.4, 8.3a Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer.
Objective: Finding Unit Rates Finding Unit Prices to Compare Costs
Rate Movie
Ratio: 903
Rate: 90 miles3 hours
Read as “90 miles per 3 hours.”
A rate is a comparison of two quantities measured in different units.
Notes
Unit rates are rates in which the second quantity is 1.
unit rate: 30 miles,1 hour
or 30 mi/h
The ratio 903
can be simplified by dividing:
903
= 301
Notes
Check It Out! Example 1
Penelope can type 90 words in 2 minutes. How many words can she type in 1 minute?
90 words 2 minutes
Write a rate.
=
Penelope can type 45 words in one minute.
90 words ÷ 2 2 minutes ÷ 2
Divide to find words per minute.
45 words 1 minute
Estimate each unit rate.
Additional Example 3A: Estimating Unit Rates
Choose a number close to 468 that is divisible by 91.
468 students to 91 computers
468 students to 91 computers is approximately 5 students per computer.
468 students91 computers
455 students91 computers
5 students1 computer
Divide to find students per computer.
Estimate each unit rate.
Check It Out! Example 3A
Choose a number close to 583 that is divisible by 85.
583 soccer players to 85 soccer balls.
583 soccer players to 85 soccer balls is approximately 7 players per soccer ball.
583 players85 soccer balls
595 players85 soccer balls
7 players1 soccer ball
Divide to find players per soccer ball.
Pactice
• Estimate each unit rate– 121 students in 3 buses
– 31.50 for 4 hours
Unit price is a unit rate used to compare price per item.
Pens can be purchased in a 5-pack for $1.95 or a 15-pack for $6.20. Which pack has the lower unit price?
Additional Example 4A: Finding Unit Prices to Compare Costs
Divide the price by the number of pens.
price for packagenumber of pens
=$1.955
= $0.39
price for packagenumber of pens
= $6.2015
$0.41
The 5-pack for $1.95 has the lower unit price.
Check It Out! Example 4B
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
Divide the price by the number of ounces.
Lesson Quiz: Part I
1. Meka can make 6 bracelets per half hour. How many bracelets can she make per hour?
2. A penny has a mass of 2.5 g and a volume of approximately 0.360 cm3. What is the approximate density of a penny?
Estimate each unit rate.
3. $2.22 for 6 stamps
4. 8 heartbeats in 6 seconds
$0.37 per stamp
≈ 6.94 g/cm3
1.3 beats/s
12
Lesson Quiz: Part II
Find each unit price. Then tell which has the
lower unit price.
5. A half dozen carnations for $4.75 or a dozen
for $9.24
6. 4 pens for $5.16 or a ten-pack for $12.90.
a dozen
They cost the same.