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Lecture Comments (1)

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Post by Christopher Trusty on February 28, 2013

Hi professor, so the LCD with the factor tree take one set of the same and then the rest that is left over and multiply them.

And for the GCD we take only one set of the matching number multiply them and leave the rest.

so the factor tree works differently for the LCD and the GCD?

Comparing and Ordering Rational Numbers

  • To compare fractions, first make the denominators the same by finding the least common multiple. Then compare the numerators. You can also change the fractions to decimals by dividing the numerator by the denominator.
  • You can always find a common denominator for two fractions by multiplying the two denominators, but the result may not be the least common denominator.
  • To compare a list of rational numbers, change all numbers to decimals or change all numbers to fractions with common denominators.

Comparing and Ordering Rational Numbers

Which number is larger, [5/6] or [3/4]?
  • [(5 ×4)/(6 ×4)] = [20/24]
  • [(3 ×6)/(4 ×6)] = [18/24]
[5/6]
Which number is larger, [2/3] or [5/8]?
  • [(2 ×8)/(3 ×8)] = [16/24]
  • [(5 ×3)/(8 ×3)] = [15/24]
[2/3]
Which number is larger, [4/13] or [6/15]?
  • [(4 ×15)/(13 ×15)] = [60/195]
  • [(6 ×13)/(15 ×13)] = [78/195]
[6/15]
Which number is smaller, [8/3] or [9/5]?
  • [(8 ×5)/(3 ×5)] = [40/15]
  • [(9 ×3)/(5 ×3)] = [27/15]
[9/5]
Which number is smaller, [4/6] or [7/10]?
  • [(4 ×10)/(6 ×10)] = [40/60]
  • [(7 ×6)/(10 ×6)] = [42/60]
[4/6]
Which number is smaller, [5/12] or [3/5]?
  • [(5 ×5)/(12 ×5)] = [25/60]
  • [(3 ×12)/(5 ×12)] = [36/60]
[5/12]
Order these numbers from least to greatest by writing them as decimals: 0.4, [1/4], 1.2, 0.7, 1[3/8]
  • [1/4] = 4|  1.00   = 0.25
  • 1[3/8] = 1 + 8|  3.000   = 1.375
  • 0.25 < 0.4 < 0.7 < 1.2 < 1.375
[1/4], 0.4, 0.7, 1.2, 1[3/8]
Order these numbers from greatest to least by writing them as fractions: 0.6, 1[3/5], 1.4, [5/6].
  • 0.6 = [6/10]
  • 1.4 = 1[4/10]
  • Which is greater, 1[3/5] or 1[4/10]?
  • 1[(3 ×2)/(5 ×2)] = 1[6/10], so 1[3/5] is greater than 1[4/10]
  • Which is greater, [6/10] or [5/6]?
  • [(6 ×6)/(10 ×6)] = [36/60]
  • [(5 ×10)/(6 ×10)] = [50/60], so [5/6] is greater than [6/10]
  • 1[3/5] > 1[4/10] > [5/6] > [6/10]
1[3/5], 1.4, [5/6], 0.6
Write the numbers from least to greatest: [1/3], [2/5], [4/15].
  • Find the LCM of 3, 5, and 15.
  • 3: 3, 6, 9, 12, 15, 18, 21
    5: 5, 10, 15, 20, 25
    15: 15, 30
    LCM: 15
  • [(1 ×5)/(3 ×5)] = [5/15]
  • [2/5] = [6/15]
[4/15], [1/3], [2/5]
Two boxes of cereal have the same price. Box A has 15[5/8] ounces of cereal, while Box B has 15[7/12] ounces of cereal. Which cereal is the better buy?
  • Find the LCM of 8 and 12.
  • 8: 8, 16, 32, 40, 48, 56
    12: 12, 24, 36, 48, 60, 72
    LCM: 48
  • Box A: 15[(5 ×6)/(8 ×6)] = 15[30/48]
  • Box B: 15[(7 ×4)/(12 ×4)] = 15[28/48]
Box A is the better buy.

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Comparing and Ordering Rational Numbers

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • What You'll Learn and Why 0:07
    • Topics Overview
  • Vocabulary 0:29
    • Least Common Multiple (LCM)
    • Least Common Denominator (LCD)
  • Ordering Rational Numbers 2:45
    • Numbers as Decimals
    • Numbers as Fractions
  • Compare Each Pair of Numbers 8:10
    • Compare 3/4 and 4/5
    • Compare 3/11 and 1/6
  • Comparing rational Numbers in Word Problems 9:19
    • Cookies or French Fries?
  • Extra Example 1: Least to Greatest (Decimals) 11:32
  • Extra Example 2: Least to Greatest (Fractions) 13:35
  • Extra Example 3: Music Notes 15:54
  • Extra Example 4: Chocolate or Fruit 17:16