![Page 1: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/1.jpg)
Ratios, Rates, and Unit Rates across the Universe
![Page 2: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/2.jpg)
RATIOSA 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.
![Page 3: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/3.jpg)
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.
![Page 4: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/4.jpg)
RATIOS A ratio makes a
comparison using division. Ratios can be written in three different ways.
3 to 4
3:4 4
3
![Page 5: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/5.jpg)
Find Each Ratio
1. Purple to total
2. Green to total
3. Purple to green
4. Green to purple
![Page 6: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/6.jpg)
![Page 7: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/7.jpg)
![Page 8: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/8.jpg)
Using Tape Diagrams to Solve
![Page 9: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/9.jpg)
Using Table to Solve
![Page 10: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/10.jpg)
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
![Page 11: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/11.jpg)
Think About It
• 52 wings:26 beaks
• “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.”
![Page 12: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/12.jpg)
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
![Page 13: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/13.jpg)
![Page 14: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/14.jpg)
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. 15:20 Put this in simplest terms:
•15 = 15/5 = 3 oz. red20 20/5 4 oz. blue
![Page 15: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/15.jpg)
Solve
![Page 16: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/16.jpg)
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.
![Page 17: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/17.jpg)
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…..
5
100 Miles
Seconds
![Page 18: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/18.jpg)
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 packPer means DIVIDE
What other examples of rates can your group think of?
![Page 19: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/19.jpg)
UNIT RATESMost 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.
2
10 Miles
Hours 1
5 Miles
Hour=
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.
![Page 20: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/20.jpg)
UNIT RATESA unit rate compares a quantity to one unit of
another quantity. These are all examples ofunit rates.
2 eyes per alien1 foot per leg
6 tentacles per head1 tail per body
3 windows per spaceship3 riders per spaceship
2 people riders per dog rider
![Page 21: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/21.jpg)
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
![Page 22: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/22.jpg)
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)
![Page 23: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/23.jpg)
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)
![Page 24: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/24.jpg)
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)
![Page 25: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/25.jpg)
![Page 26: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/26.jpg)
![Page 27: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/27.jpg)
Find the unit rate.• 1) 84 students in 4 classrooms
84 students x
4 classrooms = 1
• 2) $30 for 8 lunches
$30 = x 8 1
21 students/per classroom
$3.75/per lunch
![Page 28: Ratios, Rates, and Unit Rates across the Universe](https://reader036.vdocuments.us/reader036/viewer/2022070401/56813650550346895d9dd1b6/html5/thumbnails/28.jpg)
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