Do Now 3/30/11Do Now 3/30/11 Take out HW from last night.Take out HW from last night.

Scavenger Hunt worksheetScavenger Hunt worksheet

Copy HW in your planner.Copy HW in your planner. Text p. 278, #10-24 evensText p. 278, #10-24 evens Text p. 283, #20-34 evens, #38 & 40Text p. 283, #20-34 evens, #38 & 40 Quiz sections 6.1-6.3 Friday Quiz sections 6.1-6.3 Friday

In your notebook, use the following unit In your notebook, use the following unit rates to answer the following questions.rates to answer the following questions.

If you are walking 7 meters in 1 If you are walking 7 meters in 1 second, how many meters will you second, how many meters will you walk in a hour?walk in a hour?

h

mm

1

?

sec1

7

If you can buy 3 pounds for a $1, If you can buy 3 pounds for a $1, how many ounces can you buy for how many ounces can you buy for a $1?a $1?

1$

?

1$

3 ozlb

Writing Equivalent RatesWriting Equivalent Rates

If you are walking 7 If you are walking 7 meters in 1 second, how meters in 1 second, how many meters will you many meters will you walk in a hour?walk in a hour?

h

mm

1

?

sec1

7

There are 60 seconds in There are 60 seconds in a minute and 60 minutes a minute and 60 minutes in a hour, so multiply 7 in a hour, so multiply 7 meters by 3600. meters by 3600.

If you can buy 3 pounds If you can buy 3 pounds for a $1, how many for a $1, how many ounces can you buy for a ounces can you buy for a $1?$1?

1$

?

1$

3 ozlb

There are 16 ounces in a There are 16 ounces in a pound, so multiply 3 pound, so multiply 3 pounds by 16.pounds by 16.

h

mm

1

200,25

sec1

7

1$

48

1$

3 ozlb

Ratio/Rate Scavenger Ratio/Rate Scavenger HuntHunt

1) 60 miles /1 hour1) 60 miles /1 hour 2) $1.48 / 1 lb.2) $1.48 / 1 lb. 3) 57 miles / 1 hour3) 57 miles / 1 hour 4) $0.14 / 1 lb.4) $0.14 / 1 lb. 5) 9 weeks / 26 weeks5) 9 weeks / 26 weeks 6) 5 / 16) 5 / 1 8) 3 / 88) 3 / 8 9) 3.08 ft. / 1 sec.9) 3.08 ft. / 1 sec. 10) 4 / 110) 4 / 1 11) 3 / 1611) 3 / 16 12) 60 words / 1 min.12) 60 words / 1 min. 13) 1 / 5 13) 1 / 5 14) 9000 cars / 1 year14) 9000 cars / 1 year

RateRateRateRateRateRateRateRateRatioRatioRatioRatioRatioRatioRateRateRatioRatioRatioRatioRateRateRatioRatioRateRate

ObjectiveObjective

SWBAT write and solve proportionsSWBAT write and solve proportions

SWBAT solve proportions using SWBAT solve proportions using cross productscross products

RATERATE – –

a fraction in which the numerator and a fraction in which the numerator and the denominator have different units the denominator have different units of measure. of measure.

RATIO-RATIO- uses division to compare two uses division to compare two

quantities of the quantities of the SAME MEASURE.SAME MEASURE.

Proportion-Proportion- an equation that states an equation that states that two ratios/rates are that two ratios/rates are equivalent.equivalent.

d

c

b

a

Section 6.2 “Writing and Section 6.2 “Writing and Solving Proportions” Solving Proportions”

““a is to b asa is to b asc is to d”c is to d”

Solving a ProportionSolving a Proportion

Solve a proportionSolve a proportion by finding the by finding the value of the variable.value of the variable.

One way to solve a proportion is to One way to solve a proportion is to write both fractions with the same write both fractions with the same denominator (think of equivalent denominator (think of equivalent fractions).fractions).

93

2 n

Solve the Following Solve the Following Proportions:Proportions:

15

x==5

3

7

x==28

16

9

y==3

10

15

9==5

33

3

7

4==28

164

4

9

30==3

103

3

x = 9

x = 4

y = 30

Solving Equations with Solving Equations with RatesRates

A punch recipe calls for 4 cups of A punch recipe calls for 4 cups of orange juice. The recipe will serve 8 orange juice. The recipe will serve 8 people. You are making punch for a people. You are making punch for a party of 32 people. How many cups party of 32 people. How many cups of orange juice do you need? of orange juice do you need?

people

cupsx

32

people

cups

8

4

people

cups

32

16==

8

4

4

4

Solve the ProportionSolve the Proportion

d

c

b

a bcad If , then

33

11

12

xIf , then )11)(12()33)(( x

13233 x

Divide both sides by 33Divide both sides by 33

33

132

33

33

x

4x

Section 6.3 “Solving Proportions Section 6.3 “Solving Proportions Using Cross Products”Using Cross Products”

Proportion Cross Products PropertyProportion Cross Products Property

A A CROSS PRODUCTCROSS PRODUCT is the product of the is the product of the numerator of one ratio and the denominator of the numerator of one ratio and the denominator of the other ratio in a proportion. other ratio in a proportion.

d

c

b

aIf , then bcad

Write original proportion.Write original proportion.

8 15 = 8 15 = x x 66

Solve the proportion Solve the proportion ==88 xx

661515

Cross products propertyCross products property

Simplify.Simplify.120 = 6120 = 6xx

Divide each side by Divide each side by 66..2020 == xx

==88 xx

661515

aa2929 ==

21217 7

Cross products propertyCross products property 21 21 · 29· 29 = = 7 7 a a

609 = 7a609 = 7a SimplifySimplify

Divide both sides by 7. Divide both sides by 7. 87 = a87 = a

Solve the proportionSolve the proportion

aa2929 ==

21217 7

Write original proportion.Write original proportion.

Cross products propertyCross products property

Distrubutive propertyDistrubutive property

Solve the proportionSolve the proportion

6

8

7

2

x

6

8

7

2

x

87)6(2 x

56122 x-12 -12

442 x

22x

The ship model kits sold at a hobby store have The ship model kits sold at a hobby store have a scale of a scale of 1 ft : 600 ft.1 ft : 600 ft. A completed model of the A completed model of the Queen Elizabeth II is Queen Elizabeth II is 1.61.6 feet long. Estimate the feet long. Estimate the actual length of the Queen Elizabeth II. actual length of the Queen Elizabeth II.

Write and solve a proportion to find Write and solve a proportion to find the length the length gg of the Queen Elizabeth of the Queen Elizabeth IIII..

==1.61.6 gg

11600600

Cross products propertyCross products property

g g = 960= 960 Simplify.Simplify.

1 1 · · g g = 600 = 600 ·· 1.6 1.6

SOLUTIONSOLUTION

The actual length of the Queen Elizabeth II is about 960 feet.

HomeworkHomework Text p. 278, #10-24 evensText p. 278, #10-24 evens Text p. 283, #20-34 evens, #38 & 40Text p. 283, #20-34 evens, #38 & 40