Its Friday night and your friends are having a party…… The ratio of girls to guys is 2 to 12. Would you want to attend the party?
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 : 6 4 6 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 Simplify the following ratios: 4 to 8 10 to 8 8 to 10 Step 1 – Write the ratio as a fraction Step 2 – Simplify the fraction (Find the greatest common factor (GCF) of both numbers and divide the numerator and denominator by the GCF). Step 3 – Write the equivalent ratio in the same form as the question 4=4= 4 / 4 = 1 = 1 to 2 8 8 / 4 2 GCF = 4
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 20. 30 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, 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 2x black shirts so 2 (20) = 40 black shirts
Practice Word Problems You go to a party where the ratio of boys to girls is 28 to 56. Express the ratio of boys to girls in simplest form. Explain what this ratio tells us. (1)28 / 56 = 1 / 2 The ratio of boys to girls is 1 to 2 (2) For every 1 boy there are 2 girls at the party.
Practice Word Problems (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) Explain what this ratio tell us.
Challenge Question The perimeter of a rectangle is 500 feet. The ratio of the base and height is 3:2. What is the measure of the height?