Ratios and Rates

4 : 7100 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

• Player 1

• 77 hits in 149 bats

Consider 2 baseball players:

• Player 2

• 189 hits in 417 bats

• Who is the better hitter?

• 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

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 or750g of popcorn for $2.70

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…

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

Mix

=

Water

1

=

4

X

10

4X = 10

4X = 10

4 4 X = 10

4 X = 2.5

1

1

Proportions can be reduced to a unit rate.

Proportions can then be compared

Sheets

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

• 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

– 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.

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

HomeworkPage

180 - 181

RatesSpending 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)

PriceCD

=

A:

11.9910

=$1.20/CD

PriceCD

=

B:

12.9912

= $1.08/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

B: 20

C: 37

5.49

8.49

9.99

The best buy will have the lowest cost per load.

Priceload

=

A:5.4910

= $0.55/load

Priceload

=

B:8.4920

= $0.42/load

Priceload

=

C:9.9937

= $0.27/load

C is the best deal

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