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Ratios and Rates
4 : 7100 km/h
3__4 11 : 14
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By definition:
•A ratio is a fraction that compares two numbers with the same units.
•A rate compares two numbers with different units
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In this classroom, write the ratio for:
• Boys to girls
• Dark hair to light hair
• Short hair to long hair
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From a pocket full of change, write the ratios for -
• Dimes to quarters –
• Nickels to dimes –
• Loonies to pennies –
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Rates compare numbers of different units:
• 100 km / h (401)
• $50.00 / week (allowance)
• $8.00 / person (movies)
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Ratios can be used to analyze information
• Player 1
• 77 hits in 149 bats
Consider 2 baseball players:
• Player 2
• 189 hits in 417 bats
• Who is the better hitter?
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• Player 1
• 77 hits in 149 bats
• Player 2
• 189 hits in bats 417 bats
• Who is the better hitter?
77
149
189
417
= 0.517 = 0.453
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When rates are expressed as unit rates, comparisons can be made.
For Example:$67.50 for 6 hours work or$85.00 for 7 hours work
Which is the better job?
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Which is the better deal?
200g of popcorn for $1.00 or750g of popcorn for $2.70
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RRs are in lowest terms when the GCF is 1
• 4 : 8 = 1 : 2 • 10 : 25 =
2 : 5
• 7 : 21 = 1 : 3 • 6 : 48 = 1 : 8
Equivalent ratios form a proportion
Proportions can be solved for unknown amounts
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odd28,2931,37,3942,46Hand in…
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Proportions
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Find the unknown quantity:• Orange juice powder and water
must be mixed in the ratio 1:4
• If you have 3 cups of mix, how much water do you need?
Mix
=
Water
1
=
4
3
X
1X = 12
X = 12
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How much mix will you need to go with 10 cups of water
Mix
=
Water
1
=
4
X
10
4X = 10
4X = 10
4 4 X = 10
4 X = 2.5
1
1
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Proportions can be reduced to a unit rate.
Proportions can then be compared
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Sheets
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RatesFor this assignment:
1. Copy down all the text in black
2. Answer the homework questions assigned on the last slide
3. Show Mr. Stokes both when you are finished
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• A ratio compares 2 numbers in the same unit (3:4 or 2:13)
• A rate compares two numbers in different units
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• Speed limit on the 401
– 100 km / hour
– km are one unit and hours are the other
• Pay at McDonald’s
– $7.00 / hour
– Dollars are one unit and hours are the other
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Rates are most useful when they are written as a unit rate.
To determine the unit rate, use division
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• Suppose you make $45.00 in 5 hours.
• How much do you make per hour?
• To find pay per hour:
Pay
hour=
45
5= $9 / hour
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• Suppose 12 CDs cost $14.99
• How much does 1 CD cost?
cost
CD
14.99
12=
= $1.25 / CD
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Rates can be expressed in unit rates (used for comparisons)
• 180 km in 2 hours
• 180 / 2 = 90 km / h
• $3.60 for 6 muffins
• 3.60 / 6 = $.60 / muffin
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HomeworkPage
180 - 181
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RatesSpending money…
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By definition:
•A ratio is a fraction that compares 2 numbers with the same units.
•A rate compares 2 numbers with different units
![Page 27: Ratios and Rates](https://reader035.vdocuments.us/reader035/viewer/2022070403/568139bc550346895da15fe7/html5/thumbnails/27.jpg)
For comparisons, it is usually better to express
the numbers in a unit rate
To determine the unit rate, divide the 2 quantities being examined
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For example:
A: 10 pack of CDs costs $11.99.
B: 12 pack of CDs costs $12.99.
Which is the better deal? (price/CD)
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PriceCD
=
A:
11.9910
=$1.20/CD
PriceCD
=
B:
12.9912
= $1.08/CD
B is a better deal!
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Ex 2: Laundry soap comes in 3 sizes and prices. Determine the best buy:
Size (loads) Cost ($)
A: 10
B: 20
C: 37
5.49
8.49
9.99
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The best buy will have the lowest cost per load.
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Priceload
=
A:5.4910
= $0.55/load
Priceload
=
B:8.4920
= $0.42/load
Priceload
=
C:9.9937
= $0.27/load
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C is the best deal
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