Ratio and Proportion

Writing and Simplifying Ratios A ratio is a comparison of numbers by division. A ratio can be written with the word to, with a colon (:), or as a fraction. The first number in ratio is the numerator (top number). The second number is the denominator (bottom number). [Remember to simplify to the lowest terms] The fraction method is most common.

Example Solve Write the ratio of 2 pounds of hamburger for 3 people as a fraction. Simplify 20:25 Write the ratio with a colon (:) and simplify. $24 for 2 tickets

Group Work Solve Write the ratio of 5 runs in 9 innings with a colon (:). Simplify 27:36 Write the ratio with a colon (:) and simplify. 400 pieces in 12 hours

Ratio of Measurement To compare units of measure, express them in the same terms. To compare minutes and hours, change hours to minutes.

Example Write each ratio as a fraction and simplify. 24 minutes to an hour 4 inches to 1 foot 1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 ft = 36 in 1 mile (mi) = 5,280 ft = 1,760 yd

Group Work Write each ratio as a fraction and simplify. 2,640 feet to 1 mile 4 yards to 6 feet Jane’s workbench is 30 inches wide and eight feet long. What is the ratio of the width to the length? 1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 ft = 36 in 1 mile (mi) = 5,280 ft = 1,760 yd

Writing Proportions A proportion is a statement that two ratios are equal. The statement is a proportion. A proportion is the same as two equal fractions. Each of the four numbers in a proportion (or a pair of equal fractions) is called a term. The cross products in a proportion are equal. This means that the top term of the first ratio times the bottom term of the second equals the bottom term of the first ratio times the top term of the second. 6 8 3 4 = For the proportion on the slide both cross products equal 24

Solving Proportions 8 28 14 s = Proportion is a useful way to solve many word problems. In most proportion problems, one of the four terms is missing. Use a letter to stand for the missing term. When a term is missing in a proportion, only one cross product can be completed. The other cross product is incomplete. To find the missing term, divide the completed cross product by the number in the incomplete cross product. S = 49 You may also cancel before you multiply as a shortcut so you can work with smaller numbers. 8 28 14 s =

Example Solve each proportion for the letter. 1 12 9 8 s = 2 2 7 x 28

Group Work Solve each proportion for the letter. The ratio of games won to games lost for the Westport Warriors was 5:2. The team won 15 games. How many games did they lose? 1 3 3 5 9 n 16 y 2 3 = = 2 4 6 z 15 4 14 3 s 6 = =