1. Terra Alta/East Preston School Presents Proportions

2. Proportions

3. Warm Up 1) Your friend worked at the record store for 1 hour and got paid $7.00. You worked there for 3 hours. How much should you get paid? $21.00

4. Warm Up 2) Last time you were at the video store, you rented 3 movies and paid $6.00. This time you are renting 2 movies. How much will you have to pay? $4.00

5. Introduction The idea of getting paid a “fair” amount for work in the music store, and paying a “fair” amount for the movie rental is called: The idea of getting paid a “fair” amount for work in the music store, and paying a “fair” amount for the movie rental is called: PROPORTIONAL REASONING * It seems only fair to get paid 3 times as much for 3 times the work.

6. Definition & Details Proportion – a statement that two ratios are equal. Proportion – a statement that two ratios are equal. If the ratios are equal, then the cross products are equal. If the ratios are equal, then the cross products are equal. If the cross products are NOT EQUAL then it is NOT A PROPORTION! If the cross products are NOT EQUAL then it is NOT A PROPORTION!

7. Can these form a proportion? 120 = 120 TRUE 864 = 848 FALSE 204 = 120 FALSE 90 = 90 TRUE

8. Sometimes it’s not so simple. Ex: If you travel on your summer vacation, ? You can solve this by setting up ratios that are equal to each other. 540 miles in 3 days 540 miles 3 days = 10 days X miles how many miles could you travel in 10 days how many miles could you travel in 10 days

9. It’s called a proportion. 540 miles = x miles 3 days 10 days You can solve for x using CROSS PRODUCTS. 540 * 10 = 3 * x 5400 = 3x 1800 = x You could go 1800 miles!

10. Another Situation A recipe for chocolate chip cookies calls for 2.25 cups of flour and.75 cups of sugar. You only have 1.5 cups of flour. How much sugar should you use? A recipe for chocolate chip cookies calls for 2.25 cups of flour and.75 cups of sugar. You only have 1.5 cups of flour. How much sugar should you use? 2.25 c. flour =.75 c. sugar 1.5 c. flour x c. sugar 2.25 x = 1.125 x =.5

11. Now you try (set up a proportion and solve using cross products) 1) For a model train, 1 inch on the model stands for 87 inches on the real train. If the engine on the model train is 8 inches long, how long is the real engine? 1 in. = 87 in. 8 in. x in. 1x = 696 696 58 feet

12. Now you try (set up a proportion and solve using cross products) 1) If a 24oz jar of sauce costs $1.59, how much does 6oz cost? 24oz. = $1.59. 6oz. x 24x = $9.54 0.3975 0.40

13. Now you try (set up a proportion and solve using cross products) Jordon sneezed 15 times in 4 minutes. How many times can you expect him to sneeze in half an hour? Jordon sneezed 15 times in 4 minutes. How many times can you expect him to sneeze in half an hour? 15 = x_ 430 450 = 4x 112.5 = x 112 or 113 times!

14. Watch out for numbers that don’t matter!!! There are about 210 students in the 8th grade. If 1 out of 5 are left handed, how many are left handed? There are about 210 students in the 8th grade. If 1 out of 5 are left handed, how many are left handed? 1 = x_ 5210 210 = 5x 42= x 42 are left handed There are about 210 students in the 8th grade. If 1 out of 5 are left handed, how many are left handed? There are about 210 students in the 8th grade. If 1 out of 5 are left handed, how many are left handed?

15. Now you try (set up a proportion and solve using cross products) In 10 classes, Clint slept 7 times. How many classes will it take for him to sleep 35 times? In 10 classes, Clint slept 7 times. How many classes will it take for him to sleep 35 times? 10 = x_ 735 350 = 7x 50= x In 50 classes he will have slept 35 times! In 10 classes, Clint slept 7 times. How many classes will it take for him to sleep 35 times? In 10 classes, Clint slept 7 times. How many classes will it take for him to sleep 35 times?