Prentice Hall Geometry

Chapter 7 Similarity > 7-1 Ratios and Proportions

7-1 Ratios and Proportions

Objective

To write ratios and solve proportions

A Solve It problem analyzes wins and losses of a baseball team.
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In the Solve It, you compared two quantities for four years.

Essential Understanding You can write a ratio to compare two quantities.

A ratio is a comparison of two quantities by division. You can write the ratio of two numbers a and b, where b not equal to 0 comma in three ways: eh over b , comma eh colon b comma and a to b. You usually express a and b in the same unit and write the ratio in simplest form.

Problem 1 Writing a Ratio

Bonsai Trees The bonsai bald cypress tree is a small version of a full-size tree. A Florida bald cypress tree called the Senator stands 118 ft tall. What is the ratio of the height of the bonsai to the height of the Senator?

Express both heights in the same unit. To convert 118 ft to inches, multiply by the conversion factor 12 in . 1 ft . fraction 12 , in . , over 1 ft end fraction . .

118 ft = 118 ft 1 ⋅ 12 in . 1 ft = ( 118 ⋅ 12 ) in . = 1416 in . 118 , ft equals . fraction 118 cross out enclosing , ft , end crossout , over 1 end fraction . dot . fraction 12 , in . , over 1 cross out enclosing , ft , end crossout end fraction . equals . open . 118 dot 12 . close . in . equals , 1416 , in .

Write the ratio as a fraction in simplest form.

The equation reads: 118 feet = 118 feet over 1 all times 12 inches over 1 foot (cross out feet) = (118 times 12) inches = 1416 inches.

height of bonsai → height of Senator → 15 in . 118 ft = 15 in . 1416 in . = ( 3 ⋅ 5 ) in . ( 3 ⋅ 472 ) in . = 5 472 table with 2 rows and 1 column , row1 column 1 , heightofbonsai . rightwards arrow , row2 column 1 , heightofcap senator . rightwards arrow , end table . fraction 15 , in . , over 118 , ft end fraction . equals . fraction 15 , in . , over 1416 , in . end fraction . equals . fraction open , cross out enclosing , 3 , end crossout dot 5 , close . cross out enclosing , in , end crossout . , over open . cross out enclosing , 3 , end crossout dot 472 . close . cross out enclosing , in , end crossout . end fraction . equals , 5 over 472

The ratio of the height of the bonsai to the height of the Senator is 5 over 472 or 5 colon 472 .

✓ Got It?

A bonsai tree is 18 in. wide and stands 2 ft tall.

What is the ratio of the width of the bonsai to its height?

End ofPage 432

7-1 Ratios and Proportions

Lesson Vocabulary

Problem 1 Writing a Ratio

Think

✓ Got It?

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