1. Do Now: 1) Given triangle UAF with coordinates U(O, 4), A(8, -9), and F(-IO, -12), find the image of point A after a reflection in the y- axis. 2) After a reflection in the y-axis, (-1,-1) is the image of point B. What is the original location of point B? EQ: How do I use ratios to compare numbers HWK: WB p 42, even, p43, odd:

2. Learn to identify, write, and compare ratios and find units and compare unit rates, such as average speed and unit price.. Course 2 5-1 Ratios, Rates and Unit Rates M7P1.b Solve problems that arise in mathematics and in other contexts; M7P1.d Monitor and reflect on the process of mathematical problem solving

3. Vocabulary A ratio is a comparison of two quantities by division. Insert Lesson Title Here Course 2 5-1 Ratios A rate is a ratio that compares two quantities measured in different units. A unit rate is a rate whose denominator is 1. To change a rate to a unit rate, divide both the numerator and denominator by the denominator.

4. Course 2 5-1 Ratios Sometimes a ratio can be simplified. To simplify a ratio, first write it in fraction form and then simplify the fraction.

5. Course 2 5-1 Ratios To compare ratios, write them as fractions with common denominators. Then compare the numerators.

6. Course 2 5-2 Rates An average rate of speed is the ratio of distance traveled to time. The ratio is a rate because the units in the numerator and denominator are different.

7. In basketball practice. Kathlene made 17 baskets in 25 attempts. She compared the number of baskets she made to the total number of attempts she made by using the ratio. A ratio is a comparison of two quantities by division. 17 25 Kathlene can write her ratio of baskets made to attempts in three different ways. 17 25 17 to 2517:25 Course 2 5-1 Ratios

8. Twenty students are asked to choose their favorite music category. Eight chose pop, seven chose hip hop, and five chose rock. Write each ratio in all three forms. Course 2 5-1 Ratios A. rock to hip hop 5757, 5 to 7, 5:7 The ratio of rock to hip hop is 5 to 7, which can be written as follows: B. hip hop to pop The ratio of hip hop to pop is 7 to 8, which can be written as follows: 7878, 7 to 8, 7:8

9. Twenty students are asked to choose their favorite music category. Eight chose pop, seven chose hip hop, and five chose rock. Write each ratio in all three forms. Course 2 5-1 Ratios C. rock to pop and hip hop The ratio of rock to pop is 5 to 8 and rock to hip hop is 5 to 7, which can be written as follows: 5 15, 5 to 15, 5:15

10. Nineteen students are asked to choose their favorite sport. Nine chose rock climbing, four chose kite surfing, and six chose snow boarding. Write each ratio in all three forms. Course 2 5-1 Ratios A. snow boarding to rock climbing 6969, 6 to 9, 6:9 The ratio of snow boarding to rock climbing is 6 to 9, which can be written as follows: B. kite surfing to snow boarding The ratio of kite surfing to snow boarding is 4 to 6, which can be written as follows: 4646, 4 to 6, 4:6

11. Course 2 5-1 Ratios C. rock climbing to kite surfing and snowboarding The ratio of rock climbing to kite surfing is 9 to 4 and rock climbing to snow boarding is 9 to 6, which can be written as follows: 9 10, 9 to 10, 9:10 Nineteen students are asked to choose their favorite sport. Nine chose rock climbing, four chose kite surfing, and six chose snow boarding. Write each ratio in all three forms.

12. On average, most people can read about 600 words in 3 minutes. Write the ratio of words to minutes in all three forms. Write your answer in simplest form. Course 2 5-1 Ratios words minute Write the ratio as a fraction. 600 ÷ 3 3 ÷ 3 = 600 3 Simplify. For every minute, there are 200 words read. words minute = words minute = 200 1 The ratio of words to minutes is 200 to 1.

13. At Casitas Middle School there are 456 microscopes for 152 students. Write the ratio of microscopes to students in all three forms. Write your answer in simplest form. Course 2 5-1 Ratios microscopes students Write the ratio as a fraction. 456 ÷ 152 152 ÷ 152 = 456 152 Simplify. For every microscope, there are 3 children. microscope students = microscope students = 3131 The ratio of microscopes to students is 3 to 1.

14. Honey-lemon cough drops come in packages of 30 drops per 10-ounce bag. Cherry cough drops come in packages of 24 drops per 6-ounce bag. Compare the ratio of drops per ounces for each bag of cough drops. Course 2 5-1 Ratios Honey-lemonCherry Drops3024 Ounces106 Honey-lemon: drops ounces = 30 10 = 3131 Cherry: drops ounces = 24 6 = 4141 Because 4 > 3 and the denominators are the same, the drops to ounces is greater in the bag of cherry cough drops. Write the ratios as fractions with common denominators.

15. Jelly beans come in small packages of 25 per 5 ounce package and large packages of 56 per 8 ounce package. Compare the ratio of jelly beans per ounce for each of the packages. Course 2 5-1 Ratios LargeSmall Jelly beans5625 Ounces85 Large: jelly beans ounces = 56 8 = 7171 Small: jelly beans ounces = 25 5 = 5151 Because 7 > 5 and the denominators are the same, jelly beans to ounces is greater in the small package. Write the ratios as fractions with common denominators.

16. Find the rate. A Ferris wheel revolves 35 times in 105 minutes. How many minutes does 1 revolution take? 105 minutes 35 revolutions Write a rate that compares minutes and revolutions. Simplify. Divide the numerator and denominator by 35. Course 2 5-2 Rates 105 minutes ÷ 35 35 revolutions ÷ 35 3 minutes 1 revolution The Ferris wheel revolves 1 time in 3 minutes.

17. Find the rate. Sue walks 6 yards and passes 24 security lights set along the sidewalk. How many security lights does she pass in 1 yard? 24 lights 6 yards Write a rate that compares security lights and yards. Simplify. Divide the numerator and denominator by 6. Course 2 5-2 Rates 24 lights ÷ 6 6 yards ÷ 6 4 lights 1 yard Sue passes 4 security lights in 1 yard.

18. Find the rate. A dog walks 696 steps in 12 minutes. How many steps does the dog take in 1 minute? 696 steps 12 minutes Write a rate that compares steps and minutes. Simplify. Divide the numerator and denominator by 12. Course 2 5-2 Rates 696 steps ÷ 12 12 minutes ÷ 12 58 steps 1 minute The dog walks 58 steps per minute.

19. Find the rate. To make 12 smoothies, Henry needs 30 cups of ice. How many cups of ice does he need for one smoothie? 30 cups of ice 12 smoothies Write a rate that compares cups of ice and smoothies. Simplify. Divide the numerator and denominator by 12. Course 2 5-2 Rates 30 cups of ice ÷ 12 12 smoothies ÷ 12 2.5 cups of ice 1 smoothie Henry needs 2.5 cups of ice per smoothie.

20. Danielle is cycling 68 miles as a fundraising commitment. She wants to complete her ride in 4 hours. What should be her average speed in miles per hour? 68 miles 4 hours Write the rate as a fraction. 68 miles ÷ 4 4 hours ÷ 4 = 17 miles 1 hour Divide the numerator and denominator by the denominator Danielle’s average speed should be 17 miles per hour. Course 2 5-2 Rates

21. Rhett is a pilot and needs to fly 1191 miles to the next city. He wants to complete his flight in 3 hours. What should be his average speed in miles per hour? 1191 miles 3 hours Write the rate as a fraction. 1191 miles ÷ 3 3 hours ÷ 3 = 397 miles 1 hour Divide the numerator and denominator by the denominator Rhett’s average speed should be 397 miles per hour. Course 2 5-2 Rates

22. A unit price is the price of one unit of an item. The unit used depends on how the item is sold. The table shows some examples. Course 2 5-2 Rates Type of ItemExample of Units LiquidOunces, quarts, gallons, liters SolidOunces, pounds, grams, kilograms Any itemBottle, container, carton

23. A 12-ounce sports drink costs $0.99, and a 16- ounce sports drink costs $1.19. Which size is the best buy? Consumer Math Application SizePrice 12 ounces$0.99 16 ounces$1.19 Divide the price by the number of ounces (oz) to find the unit price of each size. $0.99 12 oz ≈ $0.08 oz Since $0.07 < $0.08, the 16 oz sports drink is the best buy. Course 2 5-2 Rates $1.19 16 oz ≈ $0.07 oz

24. A 1.5 gallon container of milk costs $4.02, and a 3.5 gallon container of milk costs $8.75. Which size is the best buy? SizePrice 1.5 gal$4.02 3.5 gal$8.75 Divide the price by the number of gallons (g) to find the unit price of each size. $4.02 1.5 gal = $2.68 gal Since $2.50 < $2.68, the 3.5 gallon container is the best buy. Course 2 5-2 Rates $8.75 3.5 gal = $2.50 gal

25. TOTD A coin bank contains 16 quarters, 12 dimes, and 8 nickels. Insert Lesson Title Here Course 2 5-1&2 Ratios and Rates 1. nickels to quarters 2. On a school trip, Bus 1 has 3 teachers and 14 students. Bus 2 has 4 teachers and 28 students. Which bus has the greater ratio of teachers to students? 3. There are 220 calories in 5 crackers. Write the ratio of calories to crackers in all three forms. Write your answers in simplest form.