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Geometry 7.1SWLT: Use Ratios and Proportions

Key Terms

Ratio: A comparison of two nonzero numbers Can be written three different ways

3 to 4, 3:4, or

Proportion: A comparison of two equal ratios

Simplifying Ratios

Example 1:

20 cm : 60 cm

Write as a Fraction

Simplify

Can be read in fraction form or 1:3 or 1 to 3

Example 2

3 ft. : 18 in.

Make sure the quantities are measured in the same units!

Solving Proportions

5(9) = 3x

45 = 3x

x = 15

Cross Multiply

Solve for x (Divide)

Map Activity

2011 Green Bay Packers

Wild Card – Philadelphia

Divisional Round – Atlanta

Conference Championship – Chicago

Super Bowl – Arlington Texas

2013 Baltimore Ravens

Wild Card – Indianapolis

Divisional Round – Denver

Conference Championship – Boston

Super Bowl – New Orleans

Using maps and string, set up proportions to find out which Super Bowl Winner traveled the most. The scale on the provided maps is 4.2 cm to 150 miles.

Using Ratios…Geometry

The perimeter of a rectangle is 80 feet. The ratio of the length to the width is 7:3. Find the the length and width of the rectangle Use the perimeter formula

P = 2l + 2w

Substitute the given values for length, width and perimeter. 80 = 2(7x) + 2(3x) 80 = 14x + 6x 80 = 20x x = 4 Length = 7(4) = 28 Width = 3(4) = 12

7x

3x

Using Proportions… Word Problems

Critics say that Ryan Howard is on track for his least productive full season since he hit 31 HR’s in 2010. He’s hit 5 HR to 70 At Bats.

If Ryan Howard bats 570 times, are his critics right?

Use the given ratio of HR : At Bats to set up a proportion

Solve the proportion

5(570) = 70HR

2850 = 70HR

HR ≈ 40.7

Ryan Howard is on pace to hit 41 Home Runs