Do Now 2/24/11Do Now 2/24/11 Take out HW from last night.Take out HW from last night.

Text p. 272, #10-36 evens, #44, & #47Text p. 272, #10-36 evens, #44, & #47

Copy HW in your planner.Copy HW in your planner. Text p. 278, #10-30 evens, #35Text p. 278, #10-30 evens, #35

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 5 pounds for a $1, If you can buy 5 pounds for a $1, how many ounces can you buy for how many ounces can you buy for a $1?a $1?

1$

?

1$

5 ozlb

Writing Equivalent RatesWriting Equivalent Rates

If you are walking 5 If you are walking 5 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

5

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 5 in a hour, so multiply 5 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

000,18

sec1

5

1$

48

1$

3 ozlb

HomeworkHomeworkText p. 272, #10-36 evens, Text p. 272, #10-36 evens,

#44, & #47#44, & #47 10) No; 3 to 4; 3/4, 3:410) No; 3 to 4; 3/4, 3:4 12) No; 5 to 1; 5/1; 5:112) No; 5 to 1; 5/1; 5:1 14) No; 7 to 2; 7/2; 7:214) No; 7 to 2; 7/2; 7:2 16) Yes; 64 to 3; 64/3; 16) Yes; 64 to 3; 64/3;

64:364:3 18) 4/2, 11 to 2, 36:5, 18) 4/2, 11 to 2, 36:5,

22:3, 30/422:3, 30/4 20) 1/2, 6:10, 7:11, 20) 1/2, 6:10, 7:11,

8:12, 7:48:12, 7:4 22) 35 words / 1 minute22) 35 words / 1 minute 24) 32 oz / 1 serving24) 32 oz / 1 serving

26) $80 / 1 person26) $80 / 1 person 28) 1 3/5 muffins / $128) 1 3/5 muffins / $1 30) 79,20030) 79,200 32) 23,40032) 23,400 34) 30134) 301 36) a. 4/136) a. 4/1

b. That the adult b. That the adult frog is 4 times frog is 4 times smaller than the smaller than the tadpoletadpole

44) 1/344) 1/3 47) 1 1/11 minutes47) 1 1/11 minutes

ObjectiveObjective

SWBAT write and solve proportionsSWBAT write and solve proportions

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

3

2

9

n==

You need to find You need to find a a value of n so thatvalue of n so thatis equivalent to is equivalent to

9

n

3

2

3

3

9

6==

3

2

Use Algebra to Solve Use Algebra to Solve ProportionsProportions

1111 66

xx3030== Write original proportion.Write original proportion.

Multiply each side by Multiply each side by 30.30.

330330 66

== xx Simplify.Simplify.

5555 = = xx Divide.Divide.

1111 66

xx3030==3030 3030

xx3030Solve the proportion Solve the proportion 1111

66 == ..

How can weHow can we get ‘x’ by itself?get ‘x’ by itself?

Try It Out…Try It Out…

xx 1212

2288== Write original proportion.Write original proportion.

Multiply each side by 12Multiply each side by 12..

2424 88

Simplify.Simplify.

x = 3x = 3 Divide.Divide.

xx 1212

22 88==1212 1212

22 88Solve the proportion Solve the proportion xx

1212 == ..

x = x =

How can weHow can we get ‘x’ by itself?get ‘x’ by itself?

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

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

Solving Equations with Solving Equations with RatiosRatios

You are making a scale drawing of a You are making a scale drawing of a room. The actual room has a width of 18 room. The actual room has a width of 18 ft and a length of 24 ft. Your scale ft and a length of 24 ft. Your scale drawing of the room has a length of 4 in. drawing of the room has a length of 4 in. What is the width of the room on the scale What is the width of the room on the scale drawing? drawing?

roomoflength

roomofwidthdrawingoflength

drawingofwidth

4

3==

6

6

24

18

ft

ft

24

18

.4

.

in

inx

HomeworkHomeworkText p. 278, #10-30 evens, #35Text p. 278, #10-30 evens, #35