# Unit Rates and Ratios. Rates/ratios Can be written three different ways a to b a:b.

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Unit Rates and Ratios

Rates/ratios Can be written three different ways a to b a:b

Because ratios are fractions, they must always be reduced to simplest form A proportion is when two ratios (fractions) are equivalent.

Example The two ratios are proportional (equal)

Example On average, a baseball team scores 3 runs to every 7 hits. Write a ratio for the situation

Example On average, a baseball team scores 3 runs to every 7 hits. Write a ratio for the situation 3 to 7 3:7

Using the ratio If the number of hits and runs is proportional, how many hits did the team have if they scored 6 runs?

Finding a value in a proportion Just like making an equivalent fraction. What you do to the top you must do to the bottom

You

Example Tell whether the ratios are proportional

You Try

2 3 5 x = Using Cross Products to Find a Missing Value

6 8 x 12 = Using Cross Products to Find a Missing Value

9 4 x 10 = Using Cross Products to Find a Missing Value

8 10 12 x = You

6 8 8 x =

1.5 5 x 10 = You

0.5 4 5 x = You

How many students in here are left handed? If our school has 1,000 students, how many would we expect to be left handed based off of our classroom data and assuming the relationship is proportional?

Unit Rates This is the value per unit. You use these all the time: At the grocery store For cars At your job Speed

Unit Rates The denominator must be 1 How much for 1? How long for 1?

Example What is the unit rate: \$15 for a 5oz package of cashews. (how much per oz)

You A car can go 270 miles on 9 gallons of gas. What is the unit rate?

You Jim can type 500 words in 10 minutes. What is the unit rate?

You A plane can fly 480 miles per hour. What is the rate in minutes?

Think Pair Share Value-Mart is advertising a Back-to-School sale on pencils. A pack of 30 sells for \$7.97 whereas a 12-pack of the same brand cost for \$ 4.77. Which is the better buy? How do you know?

Pack of 30Pack of 12 Ratio: Rate: Unit Rate: Unit of Measure:

Pack of 30Pack of 12 Ratio:\$7.97 for every 30 pencils \$15.94 for every 60 pencils \$4.77 for every 12 pencils \$23.85 for every 60 pencils Rate: 7.97/30, or approx. 0.27 dollars per pencil 4.77/12, or approx. 0.40 dollars per pencil Unit Rate:0.270.40 Unit of Measure:dollars per pencil

How is finding an associated rate or unit rate helpful when making comparisons between quantities?

Video

Exit Ticket 1. At the conclusion of the video, your classmate takes out his calculator and says, “Wow that was amazing! That means the dog went about 5 meters in 1 second!” Is your classmate correct and how do you know? 2. After seeing this video, another dog owner trained his dog, Lightning, to try to break Tillman’s skateboarding record. Lightning’s fastest recorded time was on a 75-meter stretch where it took him 15.5 seconds. Based on this data, did Lightning break Tillman’s record for fastest dog? Explain how you know.

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