4.5 comparing fractions updated
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4.5 comparing fractions updated 4.5 comparing fractions updated Presentation Transcript

    • Before the bell rings...
      • Have your covered textbook with you.
      • Solve. 0.073 + 10.1909 =
      • Compute. -350 x -7 =
    • Before the bell rings...
      • Have your covered textbook with you.
      • Solve. 0.073 + 10.1909 =
      • Compute. -350 x -7 =
    10.2639 2,450
  • Essential Questions
    • What is the value of studying fractions?
    • What is the relationship between good number sense and working with fractions?
    View slide
  • Comparing Fractions & Mixed Numbers Section 4.5 P. 198 - 201 View slide
    • In this section you will be using LCM (LCD) to compare fractions. (also a review)
    • You will be working with fractions less than one and fractions greater than one (improper fractions and mixed numbers)
    • This will test your understanding of the value of fractions.
    • The least common multiple is the smallest non-zero common multiple (when comparing two or more numbers)
    • List the multiples of 3
    • List the multiples of 7
    • Common multiples include:
    • LCM is 21
    3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51, . . 7,14,21,28,35,42,,49, . . . 21, 42, 63, ???
    • The least common multiple is the smallest non-zero common multiple (when comparing two or more numbers)
    • List the multiples of 3
    • List the multiples of 7
    • Common multiples include:
    • LCM is 21
    • The LCM of any two prime numbers can be found by . . _______________________________
    • Find the LCM for 11 and 7
    • 7 x 11=
    • Find the LCM for 5 and 13
    • 5 x 13 =
    multiplying the two numbers together
    • The LCM of any two prime numbers can be found by . . _______________________________
    • Find the LCM for 11 and 7
    • 7 x 11=
      • 77
    • Find the LCM for 5 and 13
    • 5 x 13 =
      • 65
    multiplying the two numbers together
    • This is also true for numbers that are relatively prime.
    • Find the LCM for 8 and 9
      • 8 x 9 =
    • Find the LCM for 4 and 15
      • 4 x 15
    • This is also true for numbers that are relatively prime.
    • Find the LCM for 8 and 9
      • 8 x 9 =
        • 72
    • Find the LCM for 4 and 15
      • 4 x 15
        • 60
    • The division box is probably the easiest method to find LCM.
    • Find the LCM for 45 and 50
      • LCM: 450
    • Remember, divide common factors until the top numbers are relatively prime. (no common factors other than one)
    • Use your divisibility rules to help you.
  • EXAMPLE 1 Comparing Fractions Using the LCD STEP 3 Compare the numerators: Find the least common denominator of the fractions. The LCM of 8 and 12 is 24 , so the least common denominator is 24 . STEP 1 STEP 2 Use the least common denominator to write equivalent fractions. 3 8 9 24 = 5 12 = 10 24 Compare and . 3 8 5 12 = 3 3 3 8 = 5 2 12 2 9 < 10, so 9 24 < 10 24 ANSWER 3 8 < 5 12
  • GUIDED PRACTICE for Examples 1 Copy and complete the statement with < , > or = 1 . 2 3 5 8 ? Find the least common denominator of the fractions. The LCM of 3 and 8 is 24 , so the least common denominator is 24 . STEP 1 STEP 2 Use the least common denominator to write equivalent fractions. 2 3 16 24 = 5 8 = 15 24 = 5 3 8 3 = 2 8 3 8 STEP 3 Compare the numerators: 16 > 15, so 16 24 > 15 24 > ANSWER 2 3 5 8
  • GUIDED PRACTICE for Examples 1 Copy and complete the statement with < , > or = 2 . 2 4 15 20 ? Find the least common denominator of the fractions. The LCM of 4 and 20 is 20 , so the least common denominator is 20 . STEP 1 STEP 2 Use the least common denominator to write equivalent fractions. 2 4 15 20 = 2 5 4 5 10 20 = STEP 3 Compare the numerators: 10 < 15, so 10 20 < 15 20 ANSWER 2 4 < 15 20
  • GUIDED PRACTICE for Examples 1 Copy and complete the statement with < , > or = SOLUTION 3 . 3 10 2 4 ? . Find the least common denominator of the fractions. The LCM of 10 and 4 is 20 , so the least common denominator is 20 . STEP 1 STEP 2 Use the least common denominator to write equivalent fractions. 3 10 6 20 = 2 4 = 3 2 10 5 = 2 5 4 5 = 10 20
  • GUIDED PRACTICE Comparing Fractions Using the LCD Copy and complete the statement with < , > or = SOLUTION 3. 3 10 2 4 ? . 6 < 10, so 6 20 < 10 20 Because , you can write ANSWER 6 20 10 20 < 3 10 < 2 4 STEP 3 Compare the numerators:
  • EXAMPLE 3 Comparing Mixed Numbers Write equivalent fractions using the LCD, 35 . STEP 1 Orangutans A female orangutan is about 3 7 3 is about 2 5 3 feet tall. Which of the two orangutans is taller? feet tall. A male 3 3 7 = 24 7 = 24 5 7 5 = 120 35 3 2 5 = 17 5 = 17 7 5 7 = 119 35 STEP 2 Compare the fractions: 120 35 > 119 35 ,so 3 7 > 3 2 5 3 The female orangutan is taller. ANSWER
  • GUIDED PRACTICE for Examples 2 and 3 Copy and complete the statement with < , > , or = . 5 . 16 5 1 3 ? . 3 Find the least common denominator of the fractions. The LCM of 5 , and 3 is 15 , so the LCD is 15 . STEP 1 Use the least common denominator to write equivalent fractions STEP 2 = 10 5 3 5 3 1 3 = 3 3 + 1 3 = 50 15 STEP 3 Compare the numerators: 48 < 50, so 48 15 < 50 15 ANSWER 16 5 < . 3 1 3 16 5 48 15 = = 16 3 5 3
  • GUIDED PRACTICE for Examples 2 and 3 87 < 99, 99 < 100 8 . Order the numbers , and from least to greatest . 2 7 9 2 5 12 11 4 Find the least common denominator of the fractions. The LCM of 9,12 and 4 is 36, so the LCD is 36. STEP 1 Use the least common denominator to write equivalent fractions STEP 2 2 7 9 = 25 • 4 9 • 4 2 • 9 + 7 9 = 100 36 = 29 • 3 12 • 3 = 2 5 12 2 • 12+5 12 = = 87 36 11 4 = 11 • 9 4 • 9 = 99 36 Compare the numerators: STEP 3 ANSWER 2 5 12 11 4 , and 2 7 9
    • Classzone Activity
    • on ordering mixed and improper fractions
    • Check it out!
  • Homework
    • P.200 #7-18 all