2.6 Write Ratios and Proportions You will find ratios and write and solve proportions. Essential Question: How do you find ratios and write and solve proportions?

Warm-Up Exercises Write a ratio EXAMPLE 1 VOLLEYBALL A volleyball team plays 14 home matches and 10 away matches. a. Find the ratio of home matches to away matches. SOLUTION = 7 5 a. home matches away matches = b. Find the ratio of home matches to all matches. b. home matches all matches = = = 7 12

Warm-Up Exercises EXAMPLE 1 Derek and his brother decide to combine their CD collections. Derek has 44 CDs, and his brother has 52 CDs. Find the specified ratio. 1. The number of Derek ’ s CDs to the number of his brother ’ s CDs. 2. The number of Derek ’ s CDs to the number of CDs in the entire collection. GUIDED PRACTICE for Example ANSWER ANSWER

Warm-Up Exercises Solve a proportion EXAMPLE x 30 = Write original proportion. Multiply each side by = x Simplify. 55 = x Divide x 30 = x Solve the proportion 11 6 =.

Warm-Up Exercises EXAMPLE 2 Solve the proportion. Check your solution. GUIDED PRACTICE for Example w 35 = ANSWER

Warm-Up Exercises EXAMPLE 2 Solve the proportion. Check your solution. GUIDED PRACTICE for Example 2 m = ANSWER

Warm-Up Exercises EXAMPLE 2 Solve the proportion. Check your solution. GUIDED PRACTICE for Example z 54 = ANSWER

Warm-Up Exercises Solve a multi-step problem EXAMPLE 3 ELEVATORS The elevator that takes passengers from the lobby of the John Hancock Center in Chicago to the observation level travels 150 feet in 5 seconds. The observation level is located on the 94th floor, at 1029 feet above the ground. Find the time it takes the elevator to travel from the lobby to the observation level.

Warm-Up Exercises Solve a multi-step problem EXAMPLE 3 SOLUTION STEP 2 Solve the proportion. Write a proportion involving two ratios that compare the amount of time the elevator has ascended with the distance traveled. STEP 1 x 1029 = 5 Seconds 150 feet

Warm-Up Exercises Solve a multi-step problem EXAMPLE x 1029 = Write proportion =1029 x Multiply each side by = x Simplify = x Use a calculator. ANSWER The elevator travels from the lobby to the observation level in 34.3 seconds.

Warm-Up Exercises Solve a multi-step problem EXAMPLE 3 You can use a table to check the reasonableness of your answer. CHECK The solution, 34.3 seconds, is slightly less than 35 seconds, and 1029 feet is slightly less than 1050 feet. So, the solution is reasonable.

Warm-Up Exercises GUIDED PRACTICE for Example 3 WHAT IF ? In Example 3, suppose the elevator travels 125 feet in 5 seconds. Find the time it will take for elevator to travel from the lobby to the observation level. 6. ANSWER sec

Warm-Up Exercises GUIDED PRACTICE for Example 3 When two full moons appear in the same month. The second full moon is called a blue moon. On average, 2 blue moons occur every 5 years. Find the number of blue moons that are likely to occur in the next 25 years. 7. ASTRONOMY ANSWER 10 blue moons

Warm-Up Exercises Daily Homework Quiz 1. A chocolate chip cookie recipe calls for cups of flour and cup of brown sugar. Find the ratio of brown sugar to flour Solve the proportion. 2. a = ANSWER 1 3 3

Warm-Up Exercises Daily Homework Quiz = m ANSWER 4. A printer can print 12 color pages in 3 minutes. How many color pages can the printer print in 9 minutes? Write and solve a proportion to find the answer. ANSWER 12 3 = x 9 ; 36 color pages Solve the proportion.

You will find ratios and write and solve proportions. Essential Question: How do you find ratios and write and solve proportions? Ratios compare two quantities. A proportion states that two ratios are equivalent. When writing a proportion, put like quantities in the same location in each ratio, such as nuts = nuts ounces ounces A ratio is an expression that relates one quantity to another by division, while a proportion is an equation of two ratios. Solve proportions with unknown numbers in the same way as you solve equations, by isolating the variable.