Ratios, Rates, and Unit Rates across the Universe

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Ratios, Rates, and Unit Rates across the Universe

• An introduction

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RATIOS

• A ratio makes a comparison. There
• are 3 green aliens and 4 purple
• aliens. The ratio of
• green aliens to
• purple aliens is
• 3 to 4.

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RATIOS

• A ratio makes a comparison. The
• ratio of green aliens to total aliens
• is 3 to 7. The ratio of
  
• total aliens to purple
• aliens is 7 to 4.

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RATIOS

• A ratio makes a comparison. Ratios
• can be written in three different
• ways.
• 3 to 4
• 34

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RATES

• A rate is a ratio that compares quantities that
• are measured in different units.

This spaceship travels at a certain speed.
Speed is an example of a rate. Speed can be
measured in many different ways. This spaceship
can travel 100 miles in 5 seconds. 100 miles in
5 seconds is a rate.
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RATES

• A rate is a ratio that compares quantities that
• are measured in different units.

Rates are often written in fraction form. 100
miles in 5 seconds is a rate. It can be written
as..
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RATES

• A rate is a ratio that compares quantities that
• are measured in different units.

One key word that often identifies a rate is
PER. Miles per gallon, Points per free
throw, Dollars per pizza, Sticks of gum per
pack What other examples of rates can your group
think of?
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UNIT RATES

• Most of the time when we work with rates we
• use a unit rate. A unit rate compares a quantity
• to one unit of another quantity.

This alien can walk at a rate of 10 miles in 2
hours. His speed is a unit rate of 5 miles per 1
hour or simply 5 miles per hour.
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UNIT RATES

• A unit rate compares a quantity to one unit of
• another quantity. These are all examples of
• unit rates.

6 tentacles per head 1 tail per body
2 eyes per alien 1 foot per leg
3 windows per spaceship 3 riders per spaceship 2
people riders per dog rider
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Examples
Rate
150 space miles
2 minutes
Unit Rate (Divide to get it)
150 2 75 space miles per minute.
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Find the Unit Rate
Ashytn can read 88 pages in 4 hours. What is the
unit rate? (How many pages can she read per hour?)
88 pages
22 pages / hour
4 hours
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Using Unit Rates

• You can find the missing terms of equal ratios.
• Use the unit rate, and set it equal to another
  ratio.
• Solve for what is missing by dividing or
  multiplying.

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Example
Alissas car goes 25 miles per gallon of
gasoline. How far can it go on 8 gallons of
gasoline?
x 8
25 miles

Unit Rate
8 gallons
1 gallon
x 8
25 x 8 200. Alissas car can go 200 miles on 8
gallons of gas.
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Comparing Unit Prices

• Use division to find the unit prices of the two
  products in question.
• The unit rate that is smaller (costs less) is the
  better value.

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Example
Juice is sold in two different sizes. A 48-fluid
ounce bottle costs 2.07. A 32-fluid ounce
bottle costs 1.64. Which is the better buy?
2.07
0.04 per fl.oz.
0.043125
48 fl.oz.
1.64
0.05 per fl.oz.
0.05125
32 fl.oz.
The 48 fl.oz. bottle is the better value.
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Comparing Unit Prices

• Use division to find the unit prices of the two
  products in question.
• The unit rate that is smaller (costs less) is the
  better value.

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HOMEWORK TIME