Do Now 12/11/13Do Now 12/11/13 Take out HW from last night.Take out HW from last night.

Text p.152, #6-24 evens, 27, 31, & 32Text p.152, #6-24 evens, 27, 31, & 32

Copy HW in your planner.Copy HW in your planner. Text p. 156, #16-36 multiples of 4; & #43Text p. 156, #16-36 multiples of 4; & #43 Text p. 160, #6-30 evens, 39, 40, 44, & 45Text p. 160, #6-30 evens, 39, 40, 44, & 45

In your journal, write 2 ratios that are In your journal, write 2 ratios that are equivalent to the given ratios.equivalent to the given ratios.

27

321

18

8

5

Write 2 fractions that are equivalent Write 2 fractions that are equivalent to the given fraction.to the given fraction.

27

3

21

18

8

5

9

1270

30

54

6

63

54

42

36

7

6

16

10

24

15

40

25

HomeworkHomework Text p.152, #6-24 evens, Text p.152, #6-24 evens,

27, 31, & 3227, 31, & 32 6) 18 minutes / 1 pound6) 18 minutes / 1 pound 8) the 64 ounce 8) the 64 ounce

containercontainer 10) $115 per feet²10) $115 per feet² 12) 13 songs per CD12) 13 songs per CD 14) 54 words per minute14) 54 words per minute 16) $2.16 per pound16) $2.16 per pound 18) 11 m per s18) 11 m per s 20) 16,000 km per hour20) 16,000 km per hour 22) 800 minutes for 22) 800 minutes for

$62.99 is the better buy$62.99 is the better buy

24) $3.55, $3.70; 24) $3.55, $3.70; $24.80/8 yds is the $24.80/8 yds is the better buybetter buy

27) 289, 328, 609; 27) 289, 328, 609; France, Poland, France, Poland, GermanyGermany

31) D31) D 32) 5 cuts at a rate of 32) 5 cuts at a rate of

36 seconds per cut36 seconds per cut

ObjectiveObjective

SWBAT identify and write SWBAT identify and write proportionsproportions

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 4.2 “Identifying and Section 4.2 “Identifying and Writing Proportions” Writing Proportions”

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

If two ratios are equivalent, If two ratios are equivalent, they are said to be they are said to be PROPORTIONALPROPORTIONAL or or PROPORTIONATE.PROPORTIONATE.Determine whether the ratios are proportional

9

6,

3

2

3

2

3

3

9

6

3

2

3

2

Proportional because 2/3 is equal to 2/3.

20

6,

24

8

10

3

2

2

20

6

3

1

8

8

24

8

Not proportional because 1/3 is not equal to 3/10.

Determine whether the ratios are proportional

24

14,

8

7

12

7

2

2

24

14

8

7

8

7

Not proportional because 7/8 is notequal to 7/12.

180

81,

20

18

20

9

9

9

180

81

10

9

2

2

20

18

Not proportional because 9/10 is not equal to 9/20.

21

6,

7

2

7

2

3

3

21

6

7

2

7

2

Proportional because 2/7 is equal to 2/7.

4

6,

14

21

2

3

2

2

4

6

2

3

7

7

14

21

Proportion

al because 3/2 is equal to 3/2.

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

Method #1

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

Cross ProductsCross Products

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 bcad , then

Method #2

Section 4.3 Section 4.3 ““Solving Proportions” Solving Proportions”

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

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.

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.

Density is the ratio of a substance’s mass to its Density is the ratio of a substance’s mass to its volume. The density of ice is 0.92 g/mL. What is volume. The density of ice is 0.92 g/mL. What is the mass of 3 mL of ice?. the mass of 3 mL of ice?.

Write and solve a proportion to find Write and solve a proportion to find the mass of 3 mL of icethe mass of 3 mL of ice..

== xx 3 mL3 mL

0.92 g0.92 g1 mL1 mL

Cross products propertyCross products property

x x = 2.76 g= 2.76 g Simplify.Simplify.

1 1 · x· x = 3 = 3 ·· 0.92 0.92

SOLUTIONSOLUTION

The mass of 3 mL of ice is 2.76 grams.

NJASK7 PrepNJASK7 Prep

Text p. 156, #16-36 multiples of 4; & #43Text p. 156, #16-36 multiples of 4; & #43 Text p. 160, #6-30 evens, 39, 40, 44, & 45Text p. 160, #6-30 evens, 39, 40, 44, & 45

  

HomeworkHomework