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February 16, 2012 Activities Review for Chapter 5 test dsf February 16, 2012 Ratios Ratio: A comparison of two quantities by division. Part to Part Part to Whole Whole to Part Boys to Girls Boys to Class Class to Boys 3 ways to write a ratio: 5 to 12 5 : 12 5 12 How to Compare Ratios 5 12 45 108 1. Multiply the numbers diagonally (From bottom to top). 2. Check the products (your answers) to see if they are the same or not. February 16, 2012 Boardwork Are these Ra*o equivalent? Yes or No 1. 12:24 , 50:100 Yes or No 3. 2 to 3 , 24 to 36 2. 22:1 , 1:22 Yes or No 4. 8 to 18 , 4 to 9 Yes or No 9. From 280 to 126 Yes or No 10. From 59 to 127 February 16, 2012 Ratios How to Make Equivalent Ratios 5 12 24 30 1. Multiply the top and bottom numbers by any number. 2. Divide the top and bottom numbers by any number. February 16, 2012 Boardwork Find an Equivalent Ratio 1. 12:24 3. 2 to 3 2. 22:1 4. 8 to 18 February 16, 2012 February 16, 2012 Unit Rate & Proportional Reasoning Rate: A ratio that compares two quantities Unit Rate:The rate for one unit of a given quantity. Finding a Unit Rate. EX: A package of cheddar cheese contains 15 servings and has a total of 147 grams of fat. Find the unit rate of grams of fat per serving. 1. Write the quantities as a ratio according to what the problem asks. grams serving Find the unit rate of grams of fat per serving. 2. Set up your rate as a proportion. (Make sure the 2nd rate has a denominator of 1.) 3. Multiply diagonally and then divide by the remaining number. February 16, 2012 1. Find the Unit rate for 210 heart beats in 3 minutes. 2. Find the unit rate for $33 for 4 hours of work. February 16, 2012 Unit Rate & Proportional Reasoning Rate: A ratio that compares two quantities Unit Rate:The rate for one unit of a given quantity. Finding Unit Cost by using Unit Rate. EX: Dog food costs $.35/lb. How much does a 20 lb. bag cost? 1. Write the Unit Rate as a ratio. ( BE SURE TO LABEL) 2. Set up your rate as a proportion. (Extra information in problem creates the 2nd ratio) 3. Multiply diagonally and then divide by the remaining number. Which bottle of Apple juice is the better buy: 48 fl oz for $3.05 or 64 fl oz for $3.59? February 16, 2012 February 16, 2012 Proportions * A Proportion is an equations stating that two ratios are equal of two ratios. Ex 3 4 2 5 = = 6 8 16 40 6 = 8 9 12 Check a proportion by multiplying cross products. 3• 8 and 4 • 6 1. Multiply diagonally. Start with the bottom number and go to the top number. 2. Compare your answers to determine if they are a proportion. February 16, 2012 Determine whether the ratios form a proportion. 1. 3 6 = 16 8 2. 4 6 = 6 9 3. 5 4 = 9 8 February 16, 2012 February 16, 2012 Solving Proportions If postcards cost $2.45 for 5 cards. How much will 13 cards cost? To find a missing number. 1. Make sure you line up labels 2. Circle diagonals and multiply the two numbers. 3. Divide answer by the third remaining number in the proportion. 3 4 = 20 x February 16, 2012 Solve each proportion. 1. 4. 12 x = 21 15 2. d 16 = 51 30 20 3. 110 = 35 m Swimming goggles cost $84.36 for 12. How much will new goggles for 17 members of a swimming team? February 16, 2012 February 16, 2012 Similar Figures How to find a missing measure. 10 3 15 x Small left side Small long side = = Big right side 1. Make labels and match sides. Big long side 2. Fill in the measures. EF 24 18 DC = 16 • 18 ÷ 24 = x x 3. Solve for missing measure. Multiply diagonally then divide. February 16, 2012 Similar Figures How to find a missing measure. Practice 32 cm Y X 40 cm 24 cm 30 cm 18 cm X Y 14 cm 6 cm February 16, 2012 February 16, 2012 February 16, 2012 Scale Drawings The scale on a map is 1 in. = 40 miles. If it is 11 inches on a map from Bemidji to Chicago, how many miles is it to Chicago? = 1. Write your scale as a fraction with the labels. = 2. Add the measurement that you are given from the problem. = 3. Solve. Multiply diagonally then divide. EF 24 Check to see if they form a proportion. 18 DC 16 • 18 ÷ 24 = x x February 16, 2012 February 16, 2012 The distance from Atlanta to Macon is about 75 mi. The scale on the map is 1 in. : 17 mi. What is the approximate map distance between these two cities? February 16, 2012