unit rates and ratios mr. swaner. rates/ratios can be written three different ways a to b a:b
TRANSCRIPT
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Unit Rates and Ratios
Mr. Swaner
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Rates/ratios
• Can be written three different ways
a to b
a:b
a
b
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• Because ratios are fractions, they must always be reduced to simplest form
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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
3:7
3
7
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Using the ratio
• We can use the ratio to find the runs or the hits for a scenario. – The team scored 6 runs, how many hits did
they have?
3 6
7
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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
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Example
• What is the unit rate: $15 for a 5oz package of cashews. (how much per oz)
$15
5oz
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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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The Hamburglar Strikes Again!
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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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Trial Number Passed
Time Ratio Rate Unit Rate
1
2
3
4
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Class # of boys # of girls Ratio of boys to girls
1
2
3
5
6
Are the ratios of boys to girls in the two classes equivalent?
What could these ratios tell us?
If there is a larger ratio of boys to girls in one class than in the grade as a whole, what does that mean must be true about the boy/girl ratio in other classes?
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• 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 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.