November 14

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November 14

  1. 1. November 14, 2012 Today: Warm-Up: Review Fractions & GCF Decimals: +, -, x, ÷ STAR Math Khan Academy: Nov. 10th & 17 Topics
  2. 2. Warm-Up:Khan Academy Help: Dividing Fractions Word Probs.
  3. 3. Warm-Up:3. Which Fraction is larger: 4/6 or 7/10?4. 2/5 + 7/8 = 5. 3 3/7 + 2 3/8 =6. 6/11 - 5/12 = 7. 3 2/7 - 2 1/8 =8. 8/15 • 3/11 = 9. 3 2/7 • 2 1/8 =10. 8/15 ÷ 3/11 11. 3 2/7 ÷ 2 1/8 = = 12. Find the Prime Factorization of 60 13. Simplify, using GCF: 144/150
  4. 4. Decimals: Objectives1. Read decimals 6. Add decimals2. Write decimals 7. Subtract decimals3. Compare the size of 8. Multiply decimals decimals to one 9. Divide decimals another 10. Round decimals to4. Convert fractions to nearest tenth decimals 11. Round decimals to5. Convert decimals to nearest hundredth fractions
  5. 5. Decimals: Definition A decimal is a fraction with a denominator that is a multiple of 10. The decimal (.) is used to indicate place value. Examples: 3 equals 0.3 stated as "three tenths" 10 18 equals 0.18 stated as "eighteen hundre dths" 100 Caution: each decimal expression with a value less than 1 is preceded by a leading zero to emphasize the presence of a decimal. For example, .7 is correctly written as 0.7
  6. 6. Decimals: Place values
  7. 7. Decimals: Reading Reading 1. Read the whole number on the left 2. Read the decimal point as the word “and” 3. Read the decimal fraction on the right Example: 8.3 = “eight and three tenths” 4.06 = “four and six hundredths” 0.5 = “five tenths
  8. 8. Decimals: Writing Write as follows1. The whole number (if none, then write a zero - (“0”)2. The decimal point to indicate the place of value3. The decimal fraction portion of the number Examples: “Seven and five tenths” = 7.5 “One hundred twenty-five thousandths” = 0.125
  9. 9. Decimals: Comparing Values Zeros do not change the value of the number whether added at the beginning or the end, but they are unsafe as trailers.  Ex: .7 is the same numerical value as 0.7 12.6250 is the same value as 12.625 but, 30.0 can be misinterpreted as 300! Use leading zeros; AVOID trailing zeros
  10. 10. Decimals: Comparing Values (cont’d) Zeros added within a decimal number change the value dramatically  Example: 0.375 is NOT the same as 0.0375 2.025 is NOT the same as 20.025
  11. 11. Decimals: Comparing Values (cont’d) Different whole numbers  Ifwhole numbers are present and different, whole numbers are compared to determine largest  Example: 4.8 is greater than 2.9 Same or no whole number  The number in the tenths place determines largest  Example: 0.45 is larger than 0.37
  12. 12. Decimals: Comparing Values (cont’d) Same or no whole number, and the number in the tenths place is the same The decimal with the highest number in the hundredths place is the largest  Examples: 0.67 is larger than 0.66 0.17 is larger than 0.14 0.09 is larger than 0.08
  13. 13. Decimals: Adding and Subtracting Place the numbers in the columns so the decimals are lined up. Add or subtract from left to right.  Examples: 16.4 .7 21.8 .750 .7 + 3.0 + .324 - .050 Safety Point: Zeros may be added to help line up decimals – don’t include in final answer!
  14. 14. Decimals: Multiplying Place decimal correctly! Multiply numbers; in the product (answer), count decimal places right to left equal to the total decimal places in the numbers being multiplied.  Example: 1.2 .7 x 3.2 x .050 24 36 384. = 3.84
  15. 15. Decimals: Multiplying (cont’d) Add zeros where needed to ensure correct placement of decimal in answer  Example: 0.11 x .33 0.11 .12 x 0.33 x .14 33 33 0363. = 0.0363
  16. 16. Multiplying by Decimal Movement Multiplying by 10, 100, 1,000 can be done by moving decimal to the right one space for each zero in the number by which multiplying  Example: 1.6 x 10 = 1.6 = 16 5.2 x 100 = 5.20 = 520 .7 • 10 = .8 • 100 =
  17. 17. Decimals: Dividing Same as for whole numbers Q uotient Divisor Dividend  Example: 9 27 = 27 divided by 9
  18. 18. Decimals: Dividing a Decimal To divide by a whole number, place decimal in quotient directly above decimal in dividend 3 .5 5 1 7 .5 8 22.3 - 15 25 4 35.7 - 25 0
  19. 19. Decimals: Dividing by a Decimal Move the decimal in the divisor to the right until the number is a whole number. Then move the decimal in the dividend the same number of spaces. 2 3 .2 . 3 6 9 .6 0.3 6.96 - 6 9 - 9 .8 12.1 6 -6 0
  20. 20. Class Work: Decimal Handout:Every Other ProblemGirls: Begin with First ProblemGents: Begin with SecondProblem
  21. 21. Decimals: Changing from Fractions Rewrite fraction in division format Divide the numerator by the denominator and add zeros as needed Method can be used to compare fraction size 0.4 2 1 1 5 2.0 0.333... and 0.166... 5 3 6 1 1 Therefore is larger than 3 6

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