“Rational Number Riddles” Complete the Project worksheet “Rational Number Riddles.” Once you have completed #1 a-h, complete #2 and create your own riddles. Make sure you also come up with the solutions. C. 7/8 H. 73/200 A. 11/30 R. 5/12 C. 19/40 O. 17/25 A. 87/100 L. 7/8

Chapter 6 “Ratio, Proportion, and Probability” Section 6.1 “Ratios and Rates” Section 6.2 “Writing and Solving Proportions” Section 6.3 “Solving Proportions Using Cross Products” Section 6.4 “Similar and Congruent Figures” Section 6.5 “Similarity and Measurement” Section 6.6 “Scale Drawings” Section 6.7 “Probability and Odds” Section 6.8 “The Counting Principle”

Do Now In your notebook, name several sports teams in which an athlete’s success is described in terms of his or her number of successes at some task.

Objective SWBAT find ratios and unit rates

Section 6.1 “Ratios and Rates” uses division to compare two quantities of the SAME MEASURE. You can write ratios three different ways: a b a to b a:b

Ratios What is the ratio of: 1/17 6/7 7/3 3/1 Blue to total Yellow to green green to red Red to blue

Try It Out… VOLLEYBALL A volleyball team plays 14 home matches and 10 away matches. a. Find the ratio of home matches to away matches. b. Find the ratio of home matches to all matches. SOLUTION = 7 5 a. home matches away matches 14 10 b. home matches all matches 14 14 + 10 = 24 7 12

RATIO- a comparison of two numbers by division. The two numbers must have the same unit of measure. 5 ft Find the ratio of the height to the width. 9 ft Find the ratio of the width to the height. Are the ratios the same? NO!!

Find the Ratio… On a set of house plans, an architect wants to represent a 30ft length of a room by a 5 inch segment. What is the ratio of the length of the segment to the length of the room? A comparison of two numbers by division. The two numbers must have the same unit of measure Length of segment 5 inches 5 1 Length of room 30 ft (x 12 inches) = 360 72 Convert feet to inches. 12 inches in 1 foot. The ratio is 1 to 72.

RATE- “Rates” 45miles hour 5 meters second 8 dollars hour a fraction in which the numerator and the denominator have different units of measure. Examples of rates: speed & distance, wages 45miles hour 5 meters second 8 dollars hour

1 = UNIT RATE- 45 miles 1 hour a rate with a denominator of 90miles 2 hours ÷ 2 = = UNIT RATE

Finding a Unit Rate A car travels 110 miles in 2 hours. Find the unit rate. 110 miles 2 hours = 1 hour 55 miles 2 hours 2 110 miles 2

Finding a Unit Rate Arnold and Jena went mountain biking on some trails in their town. Based on the information below, which one of them rode at a faster pace? Arnold rode 23 miles in 4 hours. Jena rode 16 miles in 3.5 hours. Arnold 23 miles 4 hours = 1 hour 5.75 miles 4 hours 4 23 miles 4 Jena 16 miles 16 miles ÷ 3.5 4.6 miles 3.5 hours 3.5 hours ÷ 3.5 1 hour

Your basic monthly charge for cell phone service is $30, which includes 300 free minutes. You pay a fee for each extra minute you use. One month you paid $3.75 for 15 extra minutes. Find your total bill if you use 22 extra minutes. STEP 1 Calculate the unit rate. 15 3.75 = 0.25 1 = $.25 per minute STEP 2 Write a verbal model and then an expression. Let m be the number of extra minutes. 30 + 0.25 m STEP 3 Evaluate the expression when m = 22. 30 + 0.25(22) = 35.5 Total Bill: $35.50

“Rate or Ratio?” Rate Ratio

Writing Equivalent Rates If you are walking 5 meters in 1 second, how many meters will you walk in a hour? If you can buy 3 pounds for a $1, how many ounces can you buy for a $1? There are 60 seconds in a minute and 60 minutes in a hour, so multiply 5 meters by 3600. There are 16 ounces in a pound, so multiply 3 pounds by 16.

Puzzler A rope ladder is hanging over the side of a boat so that half of the ladder is under water. The tide is rising at a rate of 8 inches per hour. In how many hours will the entire ladder be under water? Explain.