evaluating algebraic expressions 5-2 rates and unit rates california standards mg1.3 use measures...
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Evaluating Algebraic Expressions
5-2 Rates and Unit Rates
California Standards
MG1.3 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.
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 RatesCheck 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
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 RatesCheck It Out! Example 2A
Four cubic meters of precious metal has a mass of 18,128 kilograms. What is the density of the precious metal?
The precious metal has a density of 4,532 kg/m3.
18,128 kg4 m3
Write the rate. Divide to find kilograms per 1 m3.
18,128 kg ÷ 44 m3 ÷ 4
4,532 kg1 m3
Evaluating Algebraic Expressions
5-2 Rates and Unit RatesCheck It Out! Example 2B
A piece of gemstone with a volume of 0.25 cubic meters weighs 3540 kilograms. What is the density of the gemstone?
The gemstone has a density of 14,160 kg/m3.
3540 kg0.25 m3
Write the rate.
Multiply to find kilograms per 1 m3.
3540 kg • 40.25 m3 • 4
14,160 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
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.
Evaluating Algebraic Expressions
5-2 Rates and Unit Rates
Estimate each unit rate.
Check It Out! Example 3B
Choose a number close to 271 that is divisible by 3.
271 yards in 3 hours
271 yards to 3 hours is approximately 90 yards per hour.
271 yards3 hours
270 yards3 hours
90 yards1 hour
Divide to find yards per hour.
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 Rates
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?
Check It Out! Example 4A
Divide the price by the number of balls.
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.
Evaluating Algebraic Expressions
5-2 Rates and Unit RatesCheck 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.