Ratios and Rates 4 : 7 100 km/h __ 3 4 11 : 14

By definition: A ratio is a fraction that compares two numbers with the same units. A rate compares two numbers with different units

In this classroom, write the ratio for: Boys to girls Dark hair to light hair Short hair to long hair

From a pocket full of change, write the ratios for - Dimes to quarters – Nickels to dimes – Loonies to pennies –

Rates compare numbers of different units: 100 km / h (401) $50.00 / week (allowance) $8.00 / person (movies)

Ratios can be used to analyze information Consider 2 baseball players: Player 1 77 hits in 149 bats Player 2 189 hits in 417 bats Who is the better hitter?

Player 2 189 hits in bats 417 bats Player 1 77 hits in 149 bats Who is the better hitter? 77 149 189 417 = 0.517 = 0.453

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?

Which is the better deal? 200g of popcorn for $1.00 or 750g of popcorn for $2.70

RRs are in lowest terms when the GCF is 1 4 : 8 = 1 : 2 10 : 25 = 2 : 5 6 : 48 = 1 : 8 7 : 21 = 1 : 3 Equivalent ratios form a proportion Proportions can be solved for unknown amounts

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Proportions

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

How much mix will you need to go with 10 cups of water = Water 1 = 4 X 10 4X = 10 1 4X = 10 4 4 1 X = 10 4 X = 2.5

Proportions can be reduced to a unit rate. Proportions can then be compared

Sheets

Rates For this assignment: Copy down all the text in black Answer the homework questions assigned on the last slide Show Mr. Stokes both when you are finished

A ratio compares 2 numbers in the same unit (3:4 or 2:13) A rate compares two numbers in different units

Speed limit on the 401 Pay at McDonald’s 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

Rates are most useful when they are written as a unit rate Rates are most useful when they are written as a unit rate. To determine the unit rate, use division

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

Suppose 12 CDs cost $14.99 How much does 1 CD cost? cost CD 14.99 12 = = $1.25 / CD

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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Rates Spending money…

By definition: A ratio is a fraction that compares 2 numbers with the same units. A rate compares 2 numbers with different units

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

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)

A: 11.99 Price $1.20/CD = = 10 CD B: 12.99 Price $1.08/CD = = 12 CD B is a better deal!

Ex 2: Laundry soap comes in 3 sizes and prices. Determine the best buy: Size (loads) Cost ($) A: 10 5.49 B: 20 8.49 C: 37 9.99

The best buy will have the lowest cost per load.

A: 5.49 Price $0.55/load = = 10 load B: 8.49 Price $0.42/load = = 20 load C: 9.99 Price $0.27/load = = 37 load

C is the best deal

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