Objective 12/09/09

Objective 12/09/09Objective 12/09/09

The students will be able to The students will be able to solve for the missing value solve for the missing value in a proportion and solve in a proportion and solve word problems by using word problems by using cross-products.cross-products.

A PowerPoint Presentation

by Mrs. Mary Angel Alim- Flores

Making Iced TeaMaking Iced Tea

Cups of Cups of waterwater 11 22 33 44 1010

Iced Iced TeaTea

(tsp)(tsp)

Making Iced TeaMaking Iced Tea

Cups of Cups of waterwater 11 22 33 44 1010

Iced Iced TeaTea

(tsp)(tsp)

44

Making Iced TeaMaking Iced Tea

Cups of Cups of waterwater 11 22 33 44 1010

Iced Iced TeaTea

(tsp)(tsp)

44 88

Making Iced TeaMaking Iced Tea

Cups of Cups of waterwater 11 22 33 44 1010

Iced Iced TeaTea

(tsp)(tsp)

44 88 1212

Making Iced TeaMaking Iced Tea

Cups of Cups of waterwater 11 22 33 44 1010

Iced Iced TeaTea

(tsp)(tsp)

44 88 1212 1616

Making Iced TeaMaking Iced Tea

Cups of Cups of waterwater 11 22 33 44 1010

Iced Iced TeaTea

(tsp)(tsp)

44 88 1212 1616 4040

Two equal ratios form a Two equal ratios form a PROPORTION.PROPORTION.

Ex. 5 : 10 = 20 : 40Ex. 5 : 10 = 20 : 40 5656 = = 77 64 864 8

2 Ways of Writing a Proportion2 Ways of Writing a Proportion

1. 1. Colon FormColon Form

3:4 = 12: 163:4 = 12: 16

2. 2. Fraction FormFraction Form

3 3 = = 1212

4 164 16

ExtremesExtremes

16: 8 = 20:4016: 8 = 20:40Means

To check if two ratios are equal or not:To check if two ratios are equal or not:

Fraction formFraction form Use cross-products Use cross-products

Ex. Ex. 3 3 = = 1515

4 204 20

(3x20=60) (4x15=60)(3x20=60) (4x15=60)

Therefore, the two ratios form a Therefore, the two ratios form a proportion.proportion.

2. Colon form2. Colon form

Check if the product of the means and Check if the product of the means and product of the extremes are equal. product of the extremes are equal.

Ex. 4: 6 _____ 12: 18Ex. 4: 6 _____ 12: 18

(6x12= 72) (18x4= 72)(6x12= 72) (18x4= 72)

Therefore, the two ratios are equal.Therefore, the two ratios are equal.

To solve for the missing value.To solve for the missing value.

Use cross productsUse cross products

55 = = 6060

10 x10 x

55 = = 606010 x10 x

11stst Step: 5(x)= 5x Step: 5(x)= 5x22ndnd Step: 10 (60)= 600 Step: 10 (60)= 60033rdrd Step: Step: 5x5x = = 600600 5 55 5Answer: x= 120Answer: x= 120

12:36 = 3: m 12:36 = 3: m

11stst Step: 12 (m)= 12m Step: 12 (m)= 12m22ndnd Step: 36 (3)= 108 Step: 36 (3)= 10833rdrd Step: Step: 12m12m = = 108108 12 1212 12Answer: m= 9Answer: m= 9

Solving Word ProblemsSolving Word Problems

Grace and James are on a Grace and James are on a swimming team. Their swim swimming team. Their swim training is 200 meters and training is 200 meters and usually takes them 3 minutes. usually takes them 3 minutes. How long, at this rate, would it How long, at this rate, would it take them to complete an 800-take them to complete an 800-meter swim? meter swim?

1. 1. Set up the proportion:Set up the proportion:

metersmeters 200200 = = 800800

minutes 3 nminutes 3 n

2. Use cross-products2. Use cross-products

200(n)= 200 n then 3(800)= 2400. 200(n)= 200 n then 3(800)= 2400.

3. Divide both sides by 2003. Divide both sides by 200

n=12n=12

Answer: 800-meter swim will take them 12 minutes.Answer: 800-meter swim will take them 12 minutes.

A car travels 125 miles A car travels 125 miles in 3 hours. How far in 3 hours. How far would it travel in 5 would it travel in 5 hours?hours?

A car travels 125 miles in 3 hours. How far A car travels 125 miles in 3 hours. How far would it travel in 5 hours?would it travel in 5 hours?

Step 1 Set up the proportion.Step 1 Set up the proportion.

miles miles 125125 = = hh

hours 3 5hours 3 5

Step 2 Solve for the missing value (h).Step 2 Solve for the missing value (h).

125(5) = 625 then, 3(h)=3h125(5) = 625 then, 3(h)=3h

Step 3 Divide both 625 and 3h by 3Step 3 Divide both 625 and 3h by 3

Answer: 208.33 or 208 1/3 milesAnswer: 208.33 or 208 1/3 miles

RECAPRECAPToday I learned…Today I learned…

The steps in solving proportions are…The steps in solving proportions are…

Trip Around the WorldTrip Around the World

1. 1. U.S.AU.S.A2. Philippines2. Philippines3. Australia3. Australia4. Canada 4. Canada 5. Japan 5. Japan

EXIT TICKETEXIT TICKET

A 380- cubic cm sample of A 380- cubic cm sample of titanium has a mass of 1710 g. titanium has a mass of 1710 g. Find the weight of a titanium Find the weight of a titanium sample that has a volume of sample that has a volume of 532 cubic cm. Explain how you 532 cubic cm. Explain how you got your answer.got your answer.