Ratios, Rates and Proportions
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Transcript of Ratios, Rates and Proportions
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Ratios, Rates and Proportions
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Write the ratios:
Shaded to Unshaded,
Unshaded to total,
Total to Shaded,
Shaded to Total
Write equivalent ratios
with 100 in the denominator
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Ratio: Comparison of 2 quantities - fraction form.
Apples to apples or oranges to oranges. It could be Granny Smith to Red delicious or Temple oranges to Navel oranges
Example: 5/6 (no units)
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Write each ratio in simplest form. REDUCE!
2015
43
= 3036
56
270220 220 270
10 2710 22
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Rate: Comparison of two numbers with different units
Example: Dollars to ounces
Example: Miles to gallons
Reduce fraction
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Unit Rate
Rate Comparison of the numeratorto 1 in the denominatorDivide by the denominator
Example: A car traveled 600 miles in 10 hours.
600/10 = 60 mph
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Unit Rate Examples:
You purchased 5 pounds of cat food for $2.75.
What was the per pound cost?
$2.75 ÷ 5 pounds
75.25
55.
025250
2575.25
$ per pound
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The Concept of ProportionsThe Proportion has a fraction on each side of an equal sign. The fractions have the same value.
6448
43
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Write a proportion to express the following:
5 is to 7 as 15 is to 21 2115
75
Write one for: 6 is to 8 as 9 is to 12
129
86
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Determine if a Proportion Is True or False byMultiplying diagonally across the equal sign
216
144
)6(14)21(4 84=84 True
Products are equal
4/14 could have been reduced first.
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If the cross-products are not equal, statement is false.
231174
2116
16(231)?21(174) 16(231)?21(174) 3 3
16(77) ? 7 ( 174) =16(11) ? 174 176=174
Or 16 * 231 = 3696 21*174=3654
3696 is not the same as 3654 = false
7 7
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Solving Proportions
144125 n
144*512 n
12144*5
1212
n
6012*5
nn
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n150
2125
150*2125 n
125150*2
125125
n
2525
125
150*2N
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4.25225/12
56
12
56*2
n
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Applied Proportion ProblemsA car assembly line made 243 engines on Monday. 27 were defective.
If that rate holds true for each day, how many of the 4131 engines made in a month are defective?
Method: 1. Determine unit rate - How many engines per defective unit. Divide that into the total engines. Divide engines by engines.
Method: 2. Write proportion, cross multiply and divide.You need to keep units corresponding
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APPLIED PROPORTION PROBLEMS
Write the proportion keeping units corresponding.
Cross multiply.
Divide by the coefficient of the variable
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Create a table to keep units corresponding:
413124327total
x
defective
monthyesterday
27*4131/243= x
11537/243=459 defective
Or reduce first: 27*4131/243(27/27)=4131/9
27*4131=243x
Never multiply the same units together. If you have, you have set up your equation wrong.
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A 10-speed bike has a gear ratio of 3 revolutions of the pedal for every two revolutions of the bike wheel. If the bike wheel turns at 65 revolutions per minute,how many times must she pedal per minute.
wheel pedalgear ratio 2 3 65 x
2x=65*3
2195
22
x
X = 97.5 rpm
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When there are 8500 passengers a day, Tim rents 340 bikes.The next projection is for 10,300 passengers. How many bikes should Tim plan on renting?
passengers bikes 8500 340 10300 x
8500x = 340*10300
85x = 340 * 103
x = 340* 103/ 85
X = 412 bikes
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A biologist caught 42 fish in a lake and tagged them.She returned them to the lake. After a few days, she caught 50 fish and 7 were tagged. How many fish are in the lake?
caught tagged 50 7 x 42
7x = 50 * 42
x = 50 * 6 = 300 fish
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A park ranger an Alaska forest captures and tags 50 bears. He releases them to range through the forest. Later,he recaptures 50. Four have tags. Estimate the numberof bears in the forest.
caught tagged 50 4 x 50
4x = 50*50
X = 2500 / 4 = 625 bears