Ratio and Proportion Most of the power point was taken from  Instructions  Read and work through the following power point.  Be sure to work through and understand the terms and methods for solving proportional problems.  Do the questions that are indicated for your class. Pass in your problems to Mrs. Vass on the answer sheet provided.  You will receive a mark for these problems for the term.

What do we call a comparison between two or more quantities? RATIO If we were to compare the ratio of Boys to Girls in our class it would be _______ to ______ When writing a ratio, ORDER does matter.

AIM: What is a ratio?

How many basketballs to footballs are there? For every 4 basketballs there are 6 footballs. The ratio is 4 to 6.

What are some other ways we can write the ratio of basketball to footballs? 4 to 6 4 : First quantity to Second quantity First quantity : Second quantity First quantity divided by the second quantity (as a fraction). Every ratio can be written in 3 ways: Careful!! Order matters in a ratio. 4 to 6 Is NOT the same as 6 to 4

Write the ratio of sandwiches to coke bottles 3 different ways. 6:8, 6 to 8, and 6 8 Since a fraction can be simplified, We can simplify the ratio 6/8 to 3/4. The ratio of sandwiches to coke bottles can also be expressed as 3 : 4 or 3 to 4. In other words, ratios can be simplified to form equivalent ratios.

Equivalent Ratios can be formed by multiplying the ratio by any number. For example, the ratio 2 : 3 can also be written as –4 : 6 (multiply original ratio by by 2) –6 : 9 (multiply original ratio by by 3) –8 : 12 (multiply original ratio by by 4) The ratio 2 : 3 can be expressed as 2x to 3x (multiply the original ratio by any number x)

Compound Ratios A ratio that compares more than 2 quantities is called a compound ratio. Example: –A cake recipe says the ratio of cups of milk, sugar, and batter are 1:2:4. This means that there is one cup of milk for every two cups of sugar and four cups of batter.

A bag contains 18 yellow, blue, and red marbles. The ratio of yellow to blue to red marbles is 4 : 2 : 3. 1)Write the ratio of yellow to blue marbles in simplest form. 2)What is the ratio of yellow to red marbles? 3)How many yellow marbles are there? 4 : 2 can be simplified to 2 : 1 4 : 3 Yellow : Blue : Red is 4 : 2 : 3 Since any multiple of this is an equivalent ratio, this can also be written as 4x : 2x: 3x Let 4x = yellow, 2x = blue, 3x = red 4x + 2x+ 3x = 18 9x = 18 X= 2 Since the question asks for yellow marbles, there are 4x or 4 (2) = 8 yellow marbles.

Practice problem # 1 (1) You have 100 different shirts. The ratio of blue to black shirts is a) Write the ratio of blue to black shirts 3 different ways. b) Write the ratio in simplest form. c) Explain what this ratio tells us. d) How many black shirts do you have?

Solution - # 1 You have 100 different shirts. The ratio of blue to black shirts is 20 / 30 a) Write the ratio of blue to black shirts 3 different ways. 20 to 30, 20 : 30, b) Write the ratio in simplest form. 2 3 c) Explain what this ratio tells us. For every two blue shirts, there are 3 black shirts. d) How many black shirts do you have? 2x + 3x = 100 5x = 100 x = 20 There are 3x black shirts so 3 (20) = 60 black shirts

Problem for (903 & 904 only) Be sure to go to the last problem for all classes (1)Mindy has 72 candy bars. If the ratio of Mars to Snickers is 8:4, Find the number of each type of candy. (2)Pass in your answer to Mrs. Vass. Be sure to show all work. Make sure to put your name on your answer sheet.

Problem # 3 ( 905 only) The school has 162 t-shirts. The ratio of red t-shirts to blue t-shirts is 8 :10 How many of each colour do you have?

Problem for All Classes You have a box of Smarties that contains 135 Smarties. The ratio of red to orange to brown Smarties is 7:3:5. How many of each colour of Smarties do you have? Be sure to show your work.