Chapter 3.5-3.6 Notes: Write Ratios and Proportions

Goal: You will find ratios and write and solve proportions.

• Ratios:• A ratio uses division to compare two quantities.

• You can write the ratio of two quantities a and b, where b is not equal to 0, in three ways.

a to b a : b

• Each ratio is read “the ratio of a to b.” Ratios should be written in simplest form.

a

b

Ex.1: A volleyball team plays 14 home matches and 10 away matches. a. Find the ratio of home matches to away matches.b. Find the ratio of home matches to all matches.

Ex.2: Derek and his brother decide to combine their CD collections. Derek has 44 CDs, and his brother has 52 CDs. Find the specified ratio.a. The number of Derek’s CDs to the number of his brother’s CDs.b. The number of Derek’s CDs to the number of CDs in the entire collection.

Ex.3: At a carwash fundraiser, 18 ninth grade students and 14 tenth grade students worked the first shift. a. Find the ratio of ninth grade students to tenth grade students.b. Find the ratio of ninth grade students to all students.

• Setting Up a Proportion:• There are different ways to set up a proportion.

i.e. A recipe for tomato salsa calls for 30 tomatoes to make 12 pints of salsa. How many tomatoes are needed to make 4 pints of salsa.

Ex.4: The elevator that takes passengers from the lobby of the John Hancock Center in Chicago to the observation level travels 150 feet in 5 seconds. Find the time the elevator takes to travel from the lobby to the observation level.

Ex.5: A backpacker in the Sierras hikes 5.5 miles in 2 hours. If the hiking rate remains the same, how far will the backpacker hike in 7 hours? Write and solve a proportion to find the answer.

Ex.6: Each day, the seals at an aquarium are each fed 8 pounds of food for every 100 pounds of their body weight. A seal at the aquarium weighs 280 pounds. How much food should the seal be fed per day?

Ex.7: Georgia is making her own potting soil. For every 4 buckets of peat moss, she mixes in 3 buckets of perlite. Suppose she uses 10 buckets of peat moss. How many buckets of perlite should she use? Write and solve a proportion to find the answer.

Scale Drawings and Scale Models:

• A scale drawing is a two-dimensional drawing of an object in which the dimensions of the drawing are in proportion to the dimensions of the object.

i.e. A floor plan of a house is an example of a scale drawing.

• A scale model is a three-dimensional model of an object in which the dimensions of the model are in proportion to the dimensions of the object.

i.e. A small model of an actual size house is a scale model.

• The scale of a scale drawing or scale model relates the drawing’s or model’s dimensions and the actual dimensions.

– A scale is written in the form:

scale measure : actual measure

– i.e. 1 in : 20 ft means 1 in. in the floor plan represents an actual distance of 20 ft.

Ex.8: Use a metric ruler and the map of California to estimate the distance between Sacramento and Los Angeles.

Ex.9: The ship model kits sold at a hobby store have a scale of 1 ft : 600 ft. A completed model of the Queen Elizabeth II is 1.6 feet long. Estimate the actual length of the Queen Elizabeth II.

Ex.10: On a map, the distance between Red River Gorge and Pine Bluff is 3.8 centimeters. If the map scale is 1 cm = 25 km, estimate the actual distance between Red River Gorge and Pine Bluff.