Do Now 1/5/12Do Now 1/5/12 Take out HW from last night.Take out HW from last night.

Text p. 156, #14-38 evens, 43, 48, 49 Text p. 156, #14-38 evens, 43, 48, 49 

Copy HW in your planner.Copy HW in your planner. Text p. 160, #6-32 evens, 39, 40, 44, & 45Text p. 160, #6-32 evens, 39, 40, 44, & 45 Quiz sections 4.1-4.3 Monday Quiz sections 4.1-4.3 Monday

In your journal, decide which is the better In your journal, decide which is the better buy? 350 minutes for $39.99 or 600 buy? 350 minutes for $39.99 or 600 minutes for $52.99. How much money are minutes for $52.99. How much money are you saving per minute?you saving per minute?

.min1

11.0$

.min350

99.39$

.min1

09.0$

.min600

99.52$

HomeworkHomework Text p. 156, #14-38 evens, 43, Text p. 156, #14-38 evens, 43,

48, 4948, 49 14) yes14) yes 16) no16) no 18) yes18) yes 20) yes20) yes 22) 27/60 = 9/2022) 27/60 = 9/20 24) 121/99 = 11/924) 121/99 = 11/9 26) 5/22 = 15/6626) 5/22 = 15/66 28) 27/72 = 3/828) 27/72 = 3/8

30) 8, 24, 3230) 8, 24, 32 32) 3:1, 9:332) 3:1, 9:3 34) 2:1, 4:234) 2:1, 4:2 36) 1/5, 2/1036) 1/5, 2/10 38) 2 to 20, 3 to 3038) 2 to 20, 3 to 30 43) a. 8 to 543) a. 8 to 5

b. Mill Pond & Clear b. Mill Pond & Clear PondPond

48) D48) D 49) H49) H

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 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”

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

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

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

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

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.

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

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.

HomeworkHomework Text p. 160, #6-32 evens, 39, 40, 44, Text p. 160, #6-32 evens, 39, 40, 44,

& 45& 45

NJASK7 PrepNJASK7 Prep