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# Rates, Ratios, Proportions

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by

## Eddie Perez

on 25 September 2013

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#### Transcript of Rates, Ratios, Proportions

By: Eduardo,Aaron,Brianna,Obed
Check it out #1
The ratio of games won to games lost for a baseball team is 3:2. The team won 18 games. How many games did the team lose?
Example 3
Converting Rates...
Example 3 continued...
B.
Example 2
Finding Unit Rates...
Check it out #2
Cory earns \$52.50 in 7 hours. Find the unit rate.
Why learn this?
Ratios and proportions are used to draw accurate maps.
Example 1
Using Ratios...
Rates, Ratios, Proportions

Rates,Ratios, and Proportions

Ratio-
Rate-
Scale-
Unit rate-
Conversion Factor-
Proportion-
Cross products-
Scale drawing-
Scale model-
A ratio of two quantities with different units
A comparison of two quantities by division
A ratio between two sets of measurements
A arithmetical multiplier for converting a quantity expressed in one set of units into an equivalent expressed in another
Vocabulary
A rate with a second quantity of 1 unit
A statement that two ratios are equivalent
Two equal products obtained by multiplying the second term of each ratio by the first term of the other ratio in a proportion
Both a scale to represent an object as smaller or larger than the actual object
The ratio of faculty members to students at a college is 1:15. There are 675 students. How many faculty members are there?
faculty
------------
students
----->
1
15
----->
----
1.) Write a ratio comparing faculty to students
1/15
=
X/675
2.) Write a proportion. Let X= the # of faculty members
<-----
<-----
3.) Multiply both sides of the equation by 675 since x is divided by 675
<-----

675(x/675) = 675(1/15)
x = 45
Takeru Kobayashi of Japan ate 53.5 hot dogs in 12 minutes to win a contest. Round you answer to the nearest hundreth.
53.5/12
=
x/1
1.) Write a proportion to find an equivalent ratio with a second quantity of 1
4.46 = x
2.) Divide on the left side to find x
<-----
<-----
A.
As you go deeper underground, the earth's temperature increases. In some places, it may increase by 25 Degrees Celcius per kilometer. What in this rate in degrees per meter?
25C/1km * 1km/1000 m
C = Degrees Celcius
0.025C/1m
The rate is 0.025C per meter
To convert the second quantity in a rate, multiply by a conversion factor with that unit in the first quantity
<-----
There are 45 faculty members.
The dwarf sea horse Hippocampus zosterae swims at a rate of 52.68 feet per hour. What is this speed in inches per minute
Step 1
Convert the speed to inches per hour
52.68ft/1h * 12in/1ft
To convert the first quanitity in a rate, multiply by a conversion factor with that unit in the second quanitity
632.16in/1h
<------
The speed is 632.16 inches per hour
Step 2
Convert this speed to inches per minute
632.16in/1h * 1h/60in

The speed is 10.536 inches per minute
To convert the second quanity in a rate, multiply by a conversion factor with that unit in the first quanitity.
<------
10.536in/1min
Solving Proportions...
5/9 = 3/w
5/9 = 3/w
5(w) = 9(3)
5w = 27
5w/5 = 27/5
w = 27/5
A.
B.
Use cross products
<--
Divide both sides by 5
<--
8/x+10 = 1/12
8/x+10 = 1/12
8(12) = 1(x + 10)
96 = x + 10
-10 -10
86 = x
<---
<---
Check it out #4
-5/2 = y/8
4a.
4b.
g+3/5 = 7/4
Example 5
A. On the map, the distance from Chicago and Waukeganis 4 mi. What is the distance on the map?
map
------
actual
---->
---->
1in
------
18 mi
1/18 = 0.625/x

x*1 = 18(0.625)
x = 11.25
The actual distance is 11.25mi
Write the scale as a fraction
Let x be the actual distance
Use cross products to solve
<----
<----
<----
Example 5 continues...
The actual distance between North Chicago and Waukegan is 4 mi. What is the distance on the map?
map
actual
---------
----->
----->
1in
-----
18mi
1/18
=
x/4
4 = 18x
4/18 = 18x/18
0.2 = x
Write the scale as a fraction
<---
Let x be the distance on the map
<---
Use cross products to solve the proportion.
<---
Since x is multiplied by 18 , divide both sides by 18 to undo the multipication.
The distance on the map is about 0.2in
Example 4
The unit rate is approximateley 4.46 hot dogs per minute.
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