Ratio and Proportion Ratio - Given two numbers x and y, y  0, a ratio is the quotient x divided by y. A ratio can be written as x to y, x:y, or x/y. All of these ratios are read x to y. Extended Ratios – Ratios that compare three or more numbers, such as a:b:c. Proportion - A proportion is the equality of two ratios. In symbols, a/b = c/d or a:b = c:d. It is read a is to b as c is to d.

Example 1-1b The country with the longest school year is China with 251 days. Find the ratio of school days to total days in a year for China to the nearest tenth. (Use 365 as the number of days in a year.) Answer: 0.7

Example 1-2d Multiple- Choice Test Item In a triangle, the ratio of the measures of three sides is 3:4:5, and the perimeter is 42 feet. Find the measure of the longest side of the triangle. A 10.5 ft B 14 ft C 17.5 ft D 37 ft Answer: C

Ratio and Proportion Terms - Each number in a proportion is called a term. Extremes - The first and fourth terms in a proportion are called the extremes. Means - The second and third terms in a proportion are called the means. Proportions are solved by cross-multiplying - which is multiplying the means by each other and the extremes by each other.

Ratio and Proportion Properties of Proportions 1. Means-extremes property a/b = c/d is equivalent to a  d=b  c. 2. Means or extremes can be interchanged. a/b = c/d is equivalent to a/c = b/d and a/b = c/d is equivalent to d/b = c/a.

Example 1-3c Answer: 4.5 Answer: 9 Solve each proportion. a. b.

Example 1-4c Two large cylindrical containers are in proportion. The height of the larger container is 25 meters with a diameter of 8 meters. The height of the smaller container is 7 meters. Find the diameter of the smaller container. Answer: 2.24 m