1. 10/30/14 Warm up Adding Tax to Cost How much change will you get when buying a sweater for $29.95 plus 8.5% sales tax and paying with forty dollars?

2. Adding Tax to Cost First I will change the 8.5% sales tax into a decimal. * Move the decimal 2 places to the left. =.085

3. Adding Tax to Cost Next I will use the sales tax as a decimal and multiply it by $29.95 to find out the extra cost for the tax. (I will round the product to the hundredths place) 29.95 X.085

4. Adding Tax to Cost Then I will add the tax to $29.95 to get the total cost of the sweater. $29.95 +$2.55 $32.50 Total Cost to buy sweater

5. Adding Tax to Cost Last I will subtract the total cost of the sweater by the forty dollars used to pay for the sweater, to find out how much change I would receive. $40.00 -$32.50 $7.50 Change you will receive

6. RATIO: a comparison of _____________________ Equivalent Ratios: Two ratios that name the same product. The __________ of equivalent ratios are equal You should know Ratio can be written ____ ways 1.________ 2._______ 3.________ PROPORTION: an equation which sets__________________ ________ CROSS PRODUCT: found by _________ the denominator of each ratio by the ___________ of the other. You should know….. When solving proportions, set up an equation using _____________________ _____________________ _________ EXAMPLES: 5 = x 820 6 = x 915 Eighteen roses cost $25. What is the cost of 27 roses? RATE: Compares two quantities measured in ______________. You should know….. UNIT RATE: the rate for ______ unit of a given quantity EXAMPLES: Find the unit rate $20 5 lbs 525 candy bars 15 children 324 miles 12 gallons

7. Answers Ratios and Equivalent Ratios RATIO: a comparison of two similar quantities Equivalent Ratios: Two ratios that name the same product. The cross product of equivalent ratios are equal You should know… Ratio can be written 3 ways 1. 1/2 2. 1 to 2 3. 1 :2

9. Vocabulary PROPORTION: an equation which sets two ratios equal CROSS PRODUCT: found by multiplying the denominator of each ratio by the numerator of the other You should know…. When solving proportions, set up an equation using equivalent cross products.

10. EXAMPLES: 5 = x 8 20 6 = x 9 15 Eighteen roses cost $25. What is the cost of 27 roses?

11. Vocabulary RATE: Compares two quantities measured in different labels. You should know… UNIT RATE: the rate for 1 unit of a given quantity (the second one)

12. EXAMPLES: Find the unit rate $20 5 lbs 525 candy bars 15 children 324 miles 12 gallons

13. 10/29/14 Warm up UNIT RATES 1/400 and 0.0025

14. Unit Rates

15. Rates A rate is a comparison of two different units, such as miles per hour, or two different things measured with the same unit, such as cups of concentrate per cups of water.

16. What is a unit rate? A unit rate tells the price of one item.

17. Johnny spend $75 on 15 hamburgers. At this rate, how much does 1 hamburger cost? Would it make sense for 1 hamburger to cost $75? Why? (*Hint- do not just say $75 is too much for a hamburger. ) + = $75 = ??

18. Johnny spend $75 on 15 hamburgers. At this rate, how much does 1 hamburger cost? Why wouldn’t it make sense for 1 hamburger to cost $1? =$75 = 1?? NOOO!

19. Johnny spend $75 on 15 hamburgers. At this rate, how much does 1 hamburger cost? Should you add, subtract, multiply, or divide to solve the problem in yellow? WHY?

20. Johnny spend $75 on 15 hamburgers. At this rate, how much does 1 hamburger cost? 1. Solve the problem above. Show your work. + = $75 = ?????

21. The answer… $75 ÷ 15 = $5 per every 1 hamburger That means we took all of our money ($75) and split it evenly. Each hamburger was $5.

22. If each hamburger costs $5, how much do 15 hamburgers cost? What are some different ways you can find out?

23. It takes Mary 12 minutes to play 3 songs on her piano. How many minutes long is 1 song? 2. Solve the problem in yellow. Show your work.

24. The answer…. 12 ÷ 3 = 4 minutes per every song That means we took all of the minutes she played (12 minutes) and split it evenly. Each song was 4 minutes.

25. So far you have found unit rates. A Unit Rate is the ratio of two measurements in which the second term is 1. $5_____ 4 minutes 1 burger 1 song

26. This is what we were actually solving…. $75______ = $5___ 15 burgers 1 burger How did we get from 15 to 1 on the bottom? What did we divide by? How did we get from $75 to $5 on the top? What did we divide by?

27. This is actually what we were solving…. 12 minutes = 4 minutes 3 songs 1 song How did we get from 3 to 1 on the bottom? What did we divide by? How did we get from $12 to $4 on the top? What did we divide by?

28. But…..sometimes you have to do more than just divide to find an answer.

29. For example….. Johnny spend $75 on 15 hamburgers. At this rate, how much does 20 hamburgers cost? -Just dividing will not work. -Let’s find out why…..

30. Soooo….. $75__________ = ___x_________ 15 hamburgers 20 hamburgers Look at the ratios above. The x means that we do not know what number goes there yet. Remember you have to multiply or divide to find equivalent ratios. So, I cannot add 5 on the bottom and add 5 on the top. I have to multiply or divide.

31. We know that if Johnny paid $75 for 15 hamburgers each hamburger costs $5. So how much would 20 burgers cost?

32. $75______ = $100____ 15 burgers 20 burgers Where did the $100 come from?

33. Now, let’s find out how to solve a proportion without pictures. $75______ = __x_____ 15 burgers 20 burgers The x means we are trying to find out what number goes there. We already know that $100 goes there. Let’s solve this proportion without pictures.

34. $75__________ = $5 per burger 15 hamburgers If we want to know how much 20 burgers would cost, what should we multiply?

35. We should multiply 20 burgers times $5 per burger which gives us $100 for 20 burgers. $75______ = $100____ 15 burgers 20 burgers

36. Cross multiplying is exactly what it sounds like. You multiply the numbers that are across from each other. $75______ = __x_____ 15 burgers 20 burgers $75 times 20 = 1,500 15 times x = 15x

37. $75 times 20 = 1,500 15 times x = 15x 1,500 = 15x Divide both sides by the number with the letter beside it. 1,500 divided by 15 = 15 divided by 15= So, x =

38. We still get $75______ = $100_ 15 burgers 20 burgers $75____÷ 15 = $5__ 15 burgers ÷15 1 burger $100____÷20 = $5__ 20 burgers ÷20 1 burger

39. Exit Rate? A factory can produce small wheels for the mousetrap cars at a rate of 18,000 wheels in 3 hours. What is the unit rate per hour?

40. Rate? A factory can produce small wheels for the mousetrap cars at a rate of 18,000 wheels in 3 hours. What is the unit rate per hour? 18,000 ÷ 3 = 6,000 = 6,000 wheels 3 ÷ 3 = 1 per hour