1. Seminar 3 Welcome

2. Agenda Decimal/Fraction Notation Addition, Subtraction, multiplication/division with Decimals

3. Slide 2- 3 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley To add when denominators are different: a) Find the least common multiple of the denominators. That number is the least common denominator, LCD.. c) Add the numerators, keeping the same denominator. d) Simplify, if possible.

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5. === = 8/4=2 2x3=6

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9. Adding Mixed Numbers Example:

10. Subtraction of Fractions

11. More examples:

12. Examples of multiplying fractions 2 ½ X ¼ 51 24 X 5858

15. Examples of dividing fractions 5 10 9 12 KEEP SWITCH to multiply FLIP number following the division sign (Reciprocal) 5959 x 12 10

18. For Project Unit 3 A recipe for a drink calls for 2/5 quart water and 1/4 quart apple juice. How much liquid is needed?

19. 2/5 + 1/4 = 8/20 + 5/20 = 13/20 Now if the recipe is doubled?

20. 13/20 13/20 + 13/20 = 26/20 =1 6/20= 1 3/10 Or 13/20 * 2 = 13/20 *2/1 =26/20 = 1 6/20 = 1 3/10 If the recipe is halved?

21. 13/20 13/20 / 2 = 13/20 / 2/1 = 13/20 * ½= 13/40

22. 42. 3245 4 tens + 2 ones + 3 tenths + 2 hundredths + 4 thousandths + 5 ten- thousandths We read this number as “Forty-two and three thousand two hundred forty-five ten- thousandths.” The decimal point is read as “and”.

23. Write a word name for the number in this sentence: The top women’s time for the 50 yard freestyle is 22.62 seconds.

24. Twenty-two and sixty-two hundredths

25. Slide 3- 25 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley To convert from decimal to fraction notation, a) count the number of decimal places, b) move the decimal point that many places to the right, and c) write the answer over a denominator with a 1 followed by that number of zeros 4.98 2 zeros 2 places Move 2 places.

26. Slide 3- 26 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Write fraction notation for 0.924. Do not simplify. 0.924 =

27. Slide 3- 27 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Write fraction notation for 0.924. Do not simplify. Solution 0.924 3 places 3 zeros 0.924.

28. Slide 3- 28 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example D Write 17.77 as a fraction and as a mixed numeral.

29. Slide 3- 29 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example D Write 17.77 as a fraction and as a mixed numeral. Solution To write as a fraction: 17.77 2 zeros 2 places 17.77 To write as a mixed numeral, we rewrite the whole number part and express the rest in fraction form:

30. Slide 3- 30 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley To convert from fraction notation to decimal notation when the denominator is 10, 100, 1000 and so on, a) count the number of zeros, and b) move the decimal point that number of places to the left. Leave off the denominator. 8.679. Move 3 places. 3 zeros

31. Slide 3- 31 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example E Write decimal notation for

32. Slide 3- 32 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example E Write decimal notation for Solution 1 place 1 zero

33. Slide 3- 33 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Section 3.1 1. In the number 623,841, which digit tells the number of 10 thousands? a) 5 b) 8 c) 6 d) 2

34. Slide 3- 34 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Section 3.1 1. In the number 623,841, which digit tells the number of 10 thousands? a) 5 b) 8 c) 6 d) 2

35. Slide 3- 35 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Section 3.1 2. Write a word name for 8.032. a) Eight and thirty-two ten thousandths b) Eight thousand, thirty-two c) Eight and thirty-two hundredths d) Eight and thirty-two thousandths

36. Slide 3- 36 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Section 3.1 2. Write a word name for 8.032. a) Eight and thirty-two ten thousandths b) Eight thousand, thirty-two c) Eight and thirty-two hundredths d) Eight and thirty-two thousandths

37. Slide 3- 37 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Section 3.1 3. Write decimal notation for a) 4.3 b) 0.53 c) 0.053 d) 0.0053

38. Slide 3- 38 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Section 3.1 3. Write decimal notation for a) 4.3 b) 0.53 c) 0.053 d) 0.0053

39. Slide 3- 39 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Adding with decimal notation is similar to adding whole numbers. First we line up the decimal points so that we can add corresponding place-value digits. Add the digits from the right. If necessary, we can write extra zeros to the far right of the decimal point so that the number of places is the same.

40. Slide 3- 40 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example A Add: 4.31 + 0.146 + 14.2 Solution Line up the decimal points and write extra zeros.4. 3 1 0. 1 4 6 1 4. 2 0 0 65681.

41. Slide 3- 41 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example D Subtract 574 – 3.825

42. Slide 3- 42 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example D Subtract 574 – 3.825 Solution 5 7 4. 0 0 0 – 3. 8 2 5 57 170. 5 99103

43. Slide 3- 43 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Section 3.2 1. Add: 2.15 + 13.07 + 25. a) 14.47 b) 40.22 c) 59.57 d) 47.81

44. Slide 3- 44 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Section 3.2 1. Add: 2.15 + 13.07 + 25. a) 14.47 b) 40.22 c) 59.57 d) 47.81

45. Slide 3- 45 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Section 3.2 4. Subtract: 70 – 8.231. a) 61.231 b) 62.769 c) 62.231 d) 61.769

46. Slide 3- 46 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Section 3.2 4. Subtract: 70 – 8.231. a) 61.231 b) 62.769 c) 62.231 d) 61.769

47. Slide 3- 47 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley To multiply using decimals: 0.8  0.43 a) Ignore the decimal points, and multiply as though both factors were whole numbers. b) Then place the decimal point in the result. The number of decimal places in the product is the sum of the number of places in the factors. (count places from the right). 2 (2 decimal places) (1 decimal place) (3 decimal places) Ignore the decimal points for now.

48. Slide 3- 48 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley To divide by a whole number; a) place the decimal point directly above the decimal point in the dividend, and b) divide as though dividing whole numbers. Quotient Dividend Remainder Divisor

49. Mileage Molly bought gasoline when the odometer read 8,678.9. After the next filling, the odometer read 8,999.9. It took 9.8 gal to fill the tank. a) How many miles did she drive? b) How many miles per gallon (mpg) did the car get?

50. Molly bought gasoline when the odometer read 8,678.9. After the next filling, the odometer read 8,999.9. It took 9.8 gal to fill the tank. First Step Subtraction 8,999.9 -8,678.9 321.0 She drove 321 miles Next divide 321 by 9.8 = 32.7 miles to the gallon.

51. Drew filled his truck’s gas tank and noted that the odometer read 62,957.1. After the next filling, the odometer read 63,247.5. It took 17.6 gal to fill the tank. How many miles per gallon did the truck get?

52. 63247.5 -62957.1 290. 4 290.4 / 17.6 = 16.5