Ratios and Proportions Algebra I Mastery. There’s lots of differences between the classes in your school – … Some have more boys than girls … Less USC.

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Presentation transcript:

Ratios and Proportions Algebra I Mastery

There’s lots of differences between the classes in your school – … Some have more boys than girls … Less USC fans than Clemson fans … More cat-lovers than dog-lovers … Less pizza-munchers than chicken-dippers

You are a USC fan. Which class would you choose to be in. Let’s take a class vote. Class One has 30 students with 10 USC fans and 20 Clemson fans Class Two has 18 students with 9 USC fans and 9 Clemson fans

Carolina Clemson If you were in Class One, there would be 10 Carolina fans out of the 30 students in the class. 10/30 = 1/3 If you were in Class Two, there would be 9 Carolina fans out of the 18 students in the class. What would our fraction be in this case? So it would be better to be in Class Two because 1 out of every 2 students is a Carolina fan and 1 out of every 3 are Carolina fans in Class One.

Jeannine has a bag with 3 videocassettes, 4 marbles, 7 books, and 1 orange. How many total items does she have? How many books does she have out of this total? How many marbles does she have compared to books?

What is a ratio? Ratio- a comparison of two numbers by division x to y x : y x / y These are all ways to write out a ratio

Ratios How can we write the ratio of squares to circles?

Ratios How can we write the ratio of slices of pizza to milkshakes?

When we have two ratios that that are equal, that has a special name. We call these ratios a proportion. A proportion is an equation stating that two ratios are equal. For example: 1/2 =2/4 or 2/6 = 1/3

Proportions Look at our pizza to milkshake ratio: 6/4 Look at our squares to circles ratio: 3/5 Does 6/4 = 3/5? So are they proportional or are they not proportional? Why or why not? Are 5/15 and 1/3 proportional?

Try These Are these proportional? Why or why not? 4/9 and 12/27 1/6 and 3/7 8/10 and 16/20

Proportions Jack and Jill went up the hill to pick apples and pears. Jack picked 10 apples 15 pears and Jill picked 20 apples and some pears. The ratio of apples to pears picked by both Jack and Jill were the same. Determine how many pears Jill picked.

Proportions JackJill Apples X = the number of pears Jill has = Pears 15 X Use cross multiplication: 10x=20*15 Solve for x using linear equation strategies: 10x=300 X=30 So Jill has 30 pears

Proportions- Try This A basketball team scores 17 points in the first 8 minutes of play. At this rate how many points will the team score in a 32 minute game?

17 x 8 32 x = total points in a game 17*32 = 8x 544 = 8x x = 68 points in a 32 minute game =

Closing- Try This Three out of every ten students in the fifth grade own a CD player. There are 50 students in the fifth grade. How many fifth grade students own a CD player?