Unit Rates and Ratios

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Unit Rates and Ratios
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Rates/ratios

• Can be written three different ways
• a to b
• ab

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

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Example
The two ratios are proportional (equal)
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Example

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

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Example

• On average, a baseball team scores 3 runs to
  every 7 hits. Write a ratio for the situation
• 3 to 7
• 37

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Using the ratio

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

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Finding a value in a proportion
Just like making an equivalent fraction. What
you do to the top you must do to the bottom
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You
10
You
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Example

• Tell whether the ratios are proportional

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You Try
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Using Cross Products to Find a Missing Value
2
5

x
3
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Using Cross Products to Find a Missing Value
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x

12
8
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Using Cross Products to Find a Missing Value
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x

10
4
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You
12
8

x
10
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You
6
8

x
8
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You
1.5
x

10
5
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You
0.5
5

x
4
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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?

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Unit Rates

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

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Unit Rates

• The denominator must be 1
• How much for 1?
• How long for 1?

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Example

• What is the unit rate 15 for a 5oz package of
  cashews. (how much per oz)

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You

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

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You

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

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You

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

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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?

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Pack of 30 Pack of 12
Ratio
Rate
Unit Rate
Unit of Measure
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Pack of 30 Pack 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 0.27 0.40
Unit of Measure dollars per pencil dollars per pencil
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• How is finding an associated rate or unit rate
  helpful when making comparisons between
  quantities?

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Video
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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
  Tillmans skateboarding record.
• Lightnings fastest recorded time was on a
  75-meter stretch where it took him 15.5 seconds.
  Based on this data, did Lightning break Tillmans
  record for fastest dog? Explain how you know.