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Name _____________________________________ Hour ________________ Ratio and Proportion Study Guide Ratios: A ratio is a number pair that compares two quantities. The numerator is the first term mentioned and the denominator is the second term mentioned. Remember to simplify all fractions and do not make improper fractions into mixed numbers. Rob’s sister Luann has 6 compact discs and 38 DVDs. Write the ratio of as a fraction in lowest terms. 1. Luann’s compact discs to DVDs. ______________ 2. Luann’s DVDs to compact discs. ______________ 3. Compare compact discs to the total number of Luann’s collection. _________ Equal Ratios: You can write equal ratios by multiplying or dividing both terms of the ratio by the same nonzero number. Write three equal ratios for each situation. 4. 3 guitars to 2 keyboards _______________ 5. 40 country CDs to 30 classical CDs _______________ 6. 8 Mozart compact discs to 4 Beethoven compact discs __________________ Proportions: A proportion is formed when two ratios are equal. A quick way to determine if two ratios are a proportion is to find the cross products. If the cross products are equal the two ratios form a proportion. You can also simply the ratios. If the ratios are simplified to same ratio it is a proportion. Tell whether these ratios equivalent (yes or no)? 7. 21 = 75 28 100 ____________ 8. 70 = 110 84 320 _____________ Use a proportion to solve. Show all work. 9. If 3 pairs of socks cost $3.30, how much will 5 pairs of socks cost? Solving proportions: To solve proportions look to see if you can multiply or divide by numbers that are up and down or left and right. If you are unable to multiply or divide you must use cross products. Multiply two numbers diagonally and divide by the number with the variable. Solve each proportion and show work. 10. 7 = 8 35 n 11. n = 20 9 4 __________ 12. 4 = n 3 78 __________ ___________ 13. 8 = 9 4 n ____________ 14. Of the students in Ms. Yadav’s fourth-period math class, 16 are wearing athletic shoes, 10 are wearing boots, and 4 are wearing other kinds of shoes. a. What fraction of Ms. Yadav’s students are wearing boots? b. Suppose 1200 students attend the middle school where Ms. Yadav teaches. How many students are wearing athletic shoes? Similar Figures: To find the missing side of a similar figure set up a proportion and solve. Remember to match corresponding sides. The polygons in each pair are similar. Write a proportion, then find each missing length. 15. 16. 17. 18. The shadow of a flagpole is 9.6 meters long. The shadow of a meter stick is 1.2 meters long. What is the height of the flagpole? Hint: Make a picture. 19. Elena wants to enlarge some of the photographs from her trip to China. The original photographs are 4 inches wide and 6 inches long. The length of the enlargements will be 15 inches. How wide will the enlargements be? Scale Drawings: Make a proportion and solve. Remember the scale can be written as a ratio to begin the proportion. The length and width on a scale drawing of some rooms at the Science Center are listed below. Find the actual length and width of each rectangular room. Use the scale: 1cm = 1.5 m. 20. Auditorium: length = 14 cm 21. Office: length = 3.2 cm width = 16 cm width = 2.8 cm 22. The dinosaur exhibit at the Science Center includes a model of a stegosaurus. The scale of the model is 20 centimeters to 2.5 meters. actual height of a stegosaurus was about 3.5 meters. How tall is the model? The