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: 90 3 Rate: 90 miles 3 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 90 3 can be simplified by dividing: 90 3 = 30 1

Evaluating Algebraic Expressions 5-2 Rates and Unit Rates Additional 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 words 2 minute

Evaluating Algebraic Expressions 5-2 Rates and Unit Rates 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

Evaluating Algebraic Expressions 5-2 Rates and Unit Rates Additional 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/m 3. 44,800 kg 5 m 3 Write the rate. Divide to find kilograms per 1 m 3. 44,800 kg ÷ 5 5 m 3 ÷ 5 8,960 kg 1 m 3

Evaluating Algebraic Expressions 5-2 Rates and Unit Rates Additional 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/m kg 0.5 m 3 Write the rate. Multiply to find kilograms per 1 m kg m ,300 kg 1 m 3

Evaluating Algebraic Expressions 5-2 Rates and Unit Rates Check 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/m 3. 18,128 kg 4 m 3 Write the rate. Divide to find kilograms per 1 m 3. 18,128 kg ÷ 4 4 m 3 ÷ 4 4,532 kg 1 m 3

Evaluating Algebraic Expressions 5-2 Rates and Unit Rates Check 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/m kg 0.25 m 3 Write the rate. Multiply to find kilograms per 1 m kg m ,160 kg 1 m 3

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 students to 91 computers 468 students to 91 computers is approximately 5 students per computer.  468 students 91 computers 455 students 91 computers  5 students 1 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 feet in 8 seconds 313 feet to 8 seconds is approximately 40 feet per second.  313 feet 8 seconds 320 feet 8 seconds  40 feet 1 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 soccer players to 85 soccer balls. 583 soccer players to 85 soccer balls is approximately 7 players per soccer ball.  583 players 85 soccer balls 595 players 85 soccer balls  7 players 1 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 yards in 3 hours 271 yards to 3 hours is approximately 90 yards per hour.  271 yards 3 hours 270 yards 3 hours  90 yards 1 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 package number of pens = $ =$0.39 price for package number of pens = $  $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  $ = $0.15 = $  $0.14 The 20 oz jar for $2.78 has the lower unit price. price for jar number of ounces price for jar number 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 $ Which pack has the lower unit price? Check It Out! Example 4A Divide the price by the number of balls. price for package number of balls  $ =$1.65 price for package number of balls = $  $1.58 The 12-pack for $18.95 has the lower unit price.

Evaluating Algebraic Expressions 5-2 Rates and Unit Rates 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?  $ = $0.09 = $  $0.11 The 24 oz jar for $2.19 has the lower unit price. price for bottle number of ounces price for bottle number of ounces Divide the price by the number of ounces.