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Ratios and Rates

Ratios and Rates. October 30, 2013 Mrs. Ford. Warm-up. A restaurant bill will be paid equally between 4 friends. The bill totaled $25.20. How much should each friend pay?. $25.20 / 4 = $6.30. Ratios. Lesson Essential Question: What is a ratio and how is it used in the real world?

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Ratios and Rates

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  1. Ratios and Rates October 30, 2013 Mrs. Ford

  2. Warm-up A restaurant bill will be paid equally between 4 friends. The bill totaled $25.20. How much should each friend pay? $25.20 / 4 = $6.30

  3. Ratios Lesson Essential Question: • What is a ratio and how is it used in the real world? Areas of Interaction: • Approaches To Learning • Health and Social Education

  4. Opening • Ohio State Band Things to look for: • Use of Integers, angles, ratio, proportions, reflection, rotation, and scale

  5. What do you know about ratios and rates?

  6. Cellphone Rates Travel Abroad Recipes Mileage

  7. Ratios • A ratio is a comparison of two or more quantities (numbers) and can be written in several different forms. For example, if there were 4 boys and 5 girls in our class today then we could write these two quantities as a ratio, 4/5.” • We could also write this ratio as 4 to 5 or 4:5. These all mean the same thing. We are comparing two quantities, 4 to 5.

  8. Three Ways to Write A Ratio 4/5, 4 to 5, 4:5 • This is an example of a part-to-part ratio. What is the actual ratio of boys to girls in our classroom today?

  9. Would this change if I asked for the ratio of girls to boys? Yes, the numbers would be reversed 5/4

  10. If there were 4 boys and 5 girls in our class today then we could write these two quantities as a ratio, 4/5 • We could use this information to write a part-to-whole ratio, otherwise known as a fraction. • If we put the two parts together, girls and boys, we would say the total is students. • So the ratio of boys to students would be 4/9, since there are 4 boys and 4+5=9 students altogether.

  11. Rates • The third kind of ratio we will talk about in this unit is called a rate, which is a comparison of two different things (different units). • One example of a rate is a speed limit, which compares miles to hours, or miles per hour. Can anyone think of another example of a rate?” • (Examples: miles per gallon, dollars per hour, feet per mile)

  12. Rates • So the three kinds of ratios are: • Part-to-part, • Part-to-whole • Rate • Rates cannot be written as part-to-part ratios or part-to-whole ratios since they are comparing two different units.”

  13. Vocabulary • Ratio, • Part-to-part ratio, • Part-to-whole ratio, • Rate

  14. Classwork • Green Textbook • Page 317-318 – Do the activity, review Example 1, Example 2, and Example 3 • Page 319, problems 2-36 even only

  15. November 6, 2013 Math Mrs. Ford

  16. Warm Up In Mr. Romero’s auto shop class, the ratio of boys to girls is 5:2. If there are 35 students in the class, how many are boys?

  17. Warm Up • In Mr. Romero’s auto shop class, the ratio of boys to girls is 5:2. If there are 35 students in the class, how many are boys? Boys Girls Number of students divided by the number of units 7 units = 35 35/7 = 5 1 unit = 5 5 units of 5 5 x 5 = 25 In Mr. Romero’s class, there are 25 boys.

  18. A rate is a form of ratio in which the two terms are in different units. • For example: price of wheat is $2 for 3 Kgs, then the rate would be $2 for 3 Kgs and the unit of rate would be $/Kg. • Similarly if a car goes 100 miles in 1.5 hour, then the rate is 100 miles per 1.5 hour and unit is miles/hr. • Note that ratios are usually don’t have units.

  19. Unit rate is a rate in which the rate is expressed as a quantity of 1. • Rate has a denominator of 1. • For example, if a car goes 60 miles in 1 hour, then the unit rate is 60 miles per hour. • Other examples are: $5 per kg, 5 steps per second and $80 per barrel.

  20. Unit price is the rate when it is expressed in unit currency like dollar or cent. • An example is price of corn is $2 per ounce and price of petrol is $5 per gallon. Remember that the price is always the numerator and the unit is the denominator.

  21. Converting rate to unit rate/price • Rate can be converted to unit rate simply by dividing the first term by second term. Consider an example: • If a car travels 45 miles in 30 min, what is the rate at which the car is travelling? If we express the rate in miles/hr, the rate would simply be 45 miles/0.5 hr which is 90 miles per hr. If we want to express in miles/minute the rate would be 45/30 = 1.5 miles per minute. 45 ÷ 30 = 1.5

  22. Converting rate to unit rate/price • If John bought 2.5 Kgs of rice for $7.5, then what is the unit price of rice? • Solution: Here the denominator should be 2.5 Kg and numerator is the price $7.5. (7.5/2.5) • The unit price of rice would thus be 7.5 ÷ 2.5 = $3 /Kg.

  23. Rates and unit rates are used to solve many real world problems. It takes 30 minutes for a tap to fill one bucket. How much time would it take to fill 6 buckets? • The problem can be done using the concept of unit rate. The unit rate to fill the buckets would be 1 bucket/0.5 hour which is 2 buckets per hr. • Thus to fill 6 buckets, it would take 6/2 = 3 hours.

  24. Example: 240 miles in 4 hours. = 240 miles/4 hours = 60 miles / 1 hour • Example: Suppose you drove 96 miles to San Francisco in 3 hours. What would be the unit rate? = 96 miles ÷ 3 hours = 32 mph

  25. Example: Suppose you work at a coffee shop and make $9.50 an hour and work 8 hours. How much would you make? $9.50 x 8 hours = $76.00 Suppose you stayed late and worked 10 hours? $9.50 x 10 hours = $95.00 Example: An ice cream cone may be 35 calories per ounce. If the ice cream cone is 7 ounces, how many calories are in the ice cream cone. 35 calories/oz. x 7 ounces = 245 calories Suppose a different cone was 45 calories/ounce. How many calories would be in the whole cone? 45 calories/oz. x 7 ounces = 315 calories

  26. Unit rates can be used to find the better buy • What’s the better buy? A) 12 ounce can of soda for $.84 B) 16 ounce bottle for $1.20 $0.84 ÷ 12 = $0.07/oz. $1.20 ÷ 16 = $0.075/oz. What's the better deal? 16 oz. bottle or 12 oz. can • What’s the better buy? A) 4 oz. Snicker Bar for $0.80 B) 6 oz. Three Musketeers Bar for $0.90 0.80 / 4 = .20/oz Snicker 0.90 / 6 = .15/oz Three Musketeers

  27. Classwork • Blue Textbook • With your partner Investigation 1.1 – Ads That Sell Investigation 1.2 – Targeting an Audience

  28. November 7, 2013 Math Mrs. Ford

  29. Proportions • A proportion is also a way of comparing. But a proportion is a way of comparing two ratios. If the ratios are equal, then we can say that they are “in proportion” or “form a proportion.” • Put in your notebook: A proportion shows that two ratios are equal. Example: 1/6 = 2/12

  30. Proportions Two ways to tell if the ratios form a proportion 1. Cross multiply. If the cross products are equal, then the two ratios do form a proportion. 2. Reduce both ratios to their simplest forms. If they are equal in their simplest form, then they form a proportion.

  31. 3 = 9 7 21 7 x 9 = 63

  32. Activity • For this activity, we are going to do an apple juice taste test that involves ratios

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