1. Algebra 1 Chapter 2 Section 5

2. 2-5: Solving Proportions A ratio is a comparison of two quantities. The ratio of a to b can be written a:b or a/b, where b ≠ 0. A statement that two ratios are equal, such as 1/12 = 2/24, is called a proportion.

3. Example 1: Using Ratios The ratio of faculty members to students at a college is 1:15. There are 675 students. How many faculty members are there? faculty→1 students→ 15 1 = x 15 675 x = 45 There are 45 faculty members. Write a ratio comparing faculty to students. Write a proportion. Let x be the number of faculty members. Since x is divided by 675, multiply both sides by 675. 675

4. Proportions are used to create scale drawings and scale models. A scale is a ratio between two sets of measurements, such as 1 in:5 mi. A scale drawing or scale model uses a scale to represent an object as smaller or larger than the actual object. A map is an example of a scale drawing.

5. A common application of proportion is rates. A rate is a ratio of two quantities with different units, such as 34mi. 2 gal. Rates are usually written as unit rates. A unit rate is a rate with a second quantity of 1 unit, such as 17 mi. or 17 mi./gal. 1 gal. You can convert any rate to a unit rate.

6. Example 2: Finding Unit Rates Jesus Jaramillo of Mexico ate 53.5 hot dogs in 12 minutes to win a contest. Find the unit rate. Round your answer to the nearest hundredth. 53.5 = x 12 1 4.458333 = x 4.46 ≈ x Write s proportion to find an equivalent ratio with a second quantity of 1. Divide on the left side to find x.

7. In the proportion a/b = c/d, the products a d and bc are called cross products. You can solve a proportion for a missing value by using the Cross Products Property.

8. Example 3: Solving Proportions Solve each proportion. A. 5 = 3 9 w 5w = 39 5w = 27 5 5 w = 27 5 B. 8 = 1 x+10 12 8 12 = 1(x +10) 96 = x + 10 - 10 - 10 86 = x Cross multiply. Solve the equation.

9. Another common application of proportions is percents. A percent is a ratio that compares a number to 100. For example, 25% = 25/100. You can use the proportion part = percent total 100 to find unknown values.

10. Example 4: Percent Problems A. Find 50% of 20. part = percent total 100 x = 50 20 100 x 100 = 50 20 100x = 1000 100 100 x = 10 Use the percent proportion. Let x represent the part. Find the cross products. Since x is multiplied by 100, divide both sides by 100 to undo the multiplication.

11. B. 440 is what percent of 400? 440 = x 400 440 = 400x 400 400 1.1 = x 110% = x 440 is 110% of 400 Write an equation. In math, is means =, what percent is x, and of means multiply ( ). Solve the equation. Now, move the decimal point two places to the right to change it to percent.