Evaluating Algebraic Expressions
5-2 Rates and Unit Rates
Warm UpDivide. Round answers to the nearest tenth.
1. 2.
3. 4.
23.3 3.5
23.8 23.9
420 18
73 21
380 16
430 18
Evaluating Algebraic Expressions
5-2 Rates and Unit Rates
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.
Evaluating Algebraic Expressions
5-2 Rates and Unit Rates
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
Evaluating Algebraic Expressions
5-2 Rates and Unit RatesAdditional Example 1: Finding Unit Rates
Geoff can type 30 words in half a minute. How many words can he type in 1 minute?
Write a rate.
=
Geoff can type 60 words in one minute.
Multiply to find words per minute.
60 words 1 minute
30 words minute
12
30 words • 2 minute • 212
Evaluating Algebraic Expressions
5-2 Rates and Unit RatesAdditional Example 2A: Chemistry Application
Five cubic meters of copper has a mass of 44,800 kilograms. What is the density of copper?
Copper has a density of 8,960 kg/m3.
44,800 kg5 m3
Write the rate.
Divide to find kilograms per 1 m3.
44,800 kg ÷ 55 m3 ÷ 5
8,960 kg1 m3
Evaluating Algebraic Expressions
5-2 Rates and Unit RatesAdditional Example 2B: Chemistry Application
A piece of gold with a volume of 0.5 cubic meters weighs 9650 kilograms. What is the density of gold?
Gold has a density of 19,300 kg/m3.
9650 kg0.5 m3
Write the rate.
Multiply to find kilograms per 1 m3.
9650 kg • 20.5 m3 • 2
19,300 kg1 m3
Evaluating Algebraic Expressions
5-2 Rates and Unit Rates
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.
Evaluating Algebraic Expressions
5-2 Rates and Unit Rates
Estimate each unit rate.
Additional Example 3B: Estimating Unit Rates
Choose a number close to 313 that is divisible by 8.
313 feet in 8 seconds
313 feet to 8 seconds is approximately 40 feet per second.
313 feet8 seconds
320 feet8 seconds
40 feet1 second
Divide to find feet per second.
Evaluating Algebraic Expressions
5-2 Rates and Unit Rates
Unit price is a unit rate used to compare price per item.
Evaluating Algebraic Expressions
5-2 Rates and Unit Rates
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.
Evaluating Algebraic Expressions
5-2 Rates and Unit Rates
Jamie can buy a 15 oz jar of peanut butter for $2.19 or a 20 oz jar for $2.78. Which jar has the lower unit price?
Additional Example 4B: Finding Unit Prices to Compare Costs
$2.1915
= $0.15
= $2.7820
$0.14
The 20 oz jar for $2.78 has the lower unit price.
price for jarnumber of ounces
price for jarnumber of ounces
Divide the price by the number of ounces.
Evaluating Algebraic Expressions
5-2 Rates and Unit RatesLesson Review: 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
Evaluating Algebraic Expressions
5-2 Rates and Unit RatesLesson Review: 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.