Name:,
2-6 Rates, Ratios and Proportions
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Ratio -
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Examples:
Ex 1: There are 486 students in a middle school and 27 teachers in the school. What is the
student to teacher ratio?
Proportion-
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Examples:
CROSS PRODUCTS PROPERTY
Numbers
a
In a proportion, cross
products are equal
2
-
3
is equal to:
5 3
= -.
9 HI
Example 1: Solve -
Algebra
4
--
If
b-
-
c
d
and b ;t 0 and d;t 0,
6
then
Example 2: Solve --
8
x+l0
= -.1
12
2-6 Notes
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Example 3: Solve -
2
y
Example 4: Solve
= -.
8
a+3
_0 -
5
7
=- .
4
Using Proportions: The ratio of professors to students at a college is 1:15. There are 675
students enrolled in the college.
How many professors are there?
Steps
1. Write a ratio comparing what we know
2. Write a proportion using a variable as the unknown keeping units lined up.
3. Solve the proportion (equation)
The ratio of sugar to water in fruit punch is 1: 1o. You
How many cups of fruit punch can you make with three cups of
More practice with proportions:
have 3 cups of sugar.
sugar?
Rate-
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Examples:
2-6 Notes
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UnitRate-
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Examples:
Finding unit rates:
Joey Chestnut ate 66 hot dogs in 12 minutes to set the world record. Find
the unit rate. Round your answer to the nearest hundredth. (hint: write a proportion to
solve this problem)
A bullet makes 24 revolutions in its flight that went 96 feet. What is the twist rate of the barrel on
the gun? (revolutions per foot)
More Practice with Rates
Ex 1: A Chevy Malibu goes 83 miles in 1 % hours. Find the unit rate at which it was traveling.
Ex 2: A secretary typed a 500 word essay in 8 minutes.
Find the unit rate at which he was typing.
Ex 3: A girl walked home from school. Her home is 2.5 miles away from the school and it took her
45 minutes to walk home. Find the unit rate at which she walked home.
2-6 Notes
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Conversionfactor-
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Examples:
Converting Units
Example 1: Convert 1200 inches to yards.
Example 2: Convert 96 cups to gallons.
Example 3: Convert 2.34 hours to seconds.
Example 4: Convert 500 in2 to
fe.
Example 5: Convert 82 ml to ern".
Example 6: Convert 18 m2 to cm2.
2-6 Notes
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Converting Rates
Example 7: As you go deeper underground, the earth's temperature increases. In some places,
it may increase by 25° C per kilometer. What is this rate in degrees per meter? (Hint you
want to multiply by a conversion factor with a unit that will cancel out the unit you want to changein
the first one)
Example 8: You are traveling in a car in and the speed limit is 55mph. Unfortunately you are
driving an imported car that only has metric speeds on the speedometer (i.e. 10 kmph).
What is the fastest speed in kmph that you can drive this car? (1 mile 1.6 km)
=
r: Example 9: A cyclist travels 56 miles in 4 hours. What is the cyclist's speed in feet per second?
Round your answer to the nearest tenth.
Example 10: A certain cup holds 1 pint. How many milliliters will it hold?
(1 oz
= 29.6
ml, 1 pint
= 16 oz)
Example 11: A car weights 3 tons. The hydraulic jack at the garage can support 2700 kg. Will
the jack support the car? (1 ton = 2000 lbs, 1 kg = 2.2 Ibs)
2-6 Notes
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Scale -
--:-
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Scale Drawing I Scale Model-
Example 1: On the map, the distance from Chicago to Evanston is
0.625 inches. What is the actual distance?
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....
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1 ~: 18,.·
Example 2: The actual distance between North Chicago and Waukegan is 4 miles. What is this
distance on the map? Round to the nearest tenth.
Example 3: A scale model of a human heart is 16 ft long. The scale is 32: 1. How many inches
long is the actual heart is represents?
2-6 Notes
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