Ratios, Rates, and Unit Rates across the Universe

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Ratios, Rates, and Unit Rates across the Universe
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RATIOS

• A ratio makes a comparison of two quantities
  using division. 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 using division.
  Ratios can be written in three different ways.
• 3 to 4
• 34

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Find Each Ratio
1. Purple to total
2. Green to total
3. Purple to green
4. Green to purple
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Using Tape Diagrams to Solve
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Using Table to Solve
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Think About It

• This recipe has a ratio of 3 cups of flour to 4
  cups of sugar, so there is 3/4 cup of flour for
  each cup of sugar.
• 3cups 4 cups

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Think About It

• 52 wings26 beaks
• The ratio of wings to beaks in the bird house at
  the zoo was 21, because for every 2 wings there
  was 1 beak.

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Write the ratios in simplest form.

• 1. 5 to 13
• 2. 7 to 35
• 3. 6 to 9
• The ratio of wins to losses for a team with 14
  wins and eight losses.

5/13 because it cannot be simplified.
1/5 because you can divide both by 7.
2/3 because you can divide both by 3.
14 14/2 7 wins 8 8/2 4 losses
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Ratio- Real Life Application

• You are painting a room and want to mix red and
  blue to make purple. The ratio should be 15 oz.
  red to 20 oz. blue. 1520 Put this in simplest
  terms

15 15/5 3 oz. red20 20/5 4 oz. blue
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Solve
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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 Per means DIVIDE 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. We need to find out how fast he can walk
in 1 hours.
Divide 2/2 to get 1 hour. Then divide 10/2 to get
5. 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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Think About It

• "We paid 75 for 15 hamburgers, which is a rate
  of 5 per hamburger." How do we know if this is
  right? 75 15 5

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Real Life Application

• A car traveled 300 miles on 10 gallons of gas.
  What is the unit rate (miles per gallon)?

300 300/10 30 miles 10 10/10 1
gallon of gas(30 miles per gallon)
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Solve It

• JoJo earned 50 in five hours cutting grass. What
  is the unit rate?

50 50/5 10 dollars 5 1
1 hour (10 per hour)
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Real Life Application

• On vacation, Mike hiked 30 miles in six hours.
  What is the unit rate?

30 30/6 5 miles 6 6/6 1
hour (five miles per hour)
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Find the unit rate.

• 1) 84 students in 4 classrooms
• 84 students x
• 4 classrooms 1

21 students/per classroom

• 2) 30 for 8 lunches

3.75/per lunch
30 x 8 1
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Find the unit rate

• 3) 15,000 cars sold by 2000 dealers
• 15,000 x
• 2,000 1
• 4) Your heart beats 70 beats/min. How many beats
  per hour is this?

7.5 cars/dealer
4200 beats/hour