Transcript RATIO
DO NOW (not later): Compare the number of boys to girls in the class. Free powerpoints at http://www.worldofteaching.com The number of boys = The number of girls = If we compare boys to girls we get ___ boys to _____ girls. What do we call a comparison between two or more quantities? RATIO We just found the RATIO of boys to girls. Is the ratio of girls to boys the same ? No, when writing a ratio, ORDER matters. AIM: What is a ratio? It’s 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? Every ratio can be written in 3 ways: 4 to 6 First quantity to Second quantity 4:6 First quantity : Second quantity 4 6 First quantity divided by the second quantity (as a fraction). 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 4 = 4/4 8 8/4 =1 = 1 to 2 2 GCF = 4 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 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. Write the ratio of yellow to blue marbles in Yellow : Blue form. : Red is4 : 24 can : 2 be : 3 simplest simplified to 2 : 1 2)Since What the ratio of yellow to red marbles? any is multiple of this is an equivalent ratio, this 4 : 3 can also be written as 4x : 2x: 3x 3) How many yellow marbles are there? 1) 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, b) Write the ratio in simplest form. 2 3 20 30 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 (1)28 / 56 = 1 / 2 simplest form. The ratio of boys to girls is 1 to 2 2) Explain what this ratio (2) For every 1 boy there are 2 tells us. 1) 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?