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# 4.5 comparing fractions updated

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### 4.5 comparing fractions updated

1. 1. <ul><li>Before the bell rings... </li></ul><ul><ul><li>Have your covered textbook with you. </li></ul></ul><ul><ul><li>Solve. 0.073 + 10.1909 = </li></ul></ul><ul><ul><li>Compute. -350 x -7 = </li></ul></ul>
2. 2. <ul><li>Before the bell rings... </li></ul><ul><ul><li>Have your covered textbook with you. </li></ul></ul><ul><ul><li>Solve. 0.073 + 10.1909 = </li></ul></ul><ul><ul><li>Compute. -350 x -7 = </li></ul></ul>10.2639 2,450
3. 3. Essential Questions <ul><li>What is the value of studying fractions? </li></ul><ul><li>What is the relationship between good number sense and working with fractions? </li></ul>
4. 4. Comparing Fractions & Mixed Numbers Section 4.5 P. 198 - 201
5. 5. <ul><li>In this section you will be using LCM (LCD) to compare fractions. (also a review) </li></ul><ul><li>You will be working with fractions less than one and fractions greater than one (improper fractions and mixed numbers) </li></ul><ul><li>This will test your understanding of the value of fractions. </li></ul>
6. 6. <ul><li>The least common multiple is the smallest non-zero common multiple (when comparing two or more numbers) </li></ul><ul><li>List the multiples of 3 </li></ul><ul><li>List the multiples of 7 </li></ul><ul><li>Common multiples include: </li></ul><ul><li>LCM is 21 </li></ul>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, ???
7. 7. <ul><li>The least common multiple is the smallest non-zero common multiple (when comparing two or more numbers) </li></ul><ul><li>List the multiples of 3 </li></ul><ul><li>List the multiples of 7 </li></ul><ul><li>Common multiples include: </li></ul><ul><li>LCM is 21 </li></ul>
8. 8. <ul><li>The LCM of any two prime numbers can be found by . . _______________________________ </li></ul><ul><li>Find the LCM for 11 and 7 </li></ul><ul><li>7 x 11= </li></ul><ul><li>Find the LCM for 5 and 13 </li></ul><ul><li>5 x 13 = </li></ul>multiplying the two numbers together
9. 9. <ul><li>The LCM of any two prime numbers can be found by . . _______________________________ </li></ul><ul><li>Find the LCM for 11 and 7 </li></ul><ul><li>7 x 11= </li></ul><ul><ul><li>77 </li></ul></ul><ul><li>Find the LCM for 5 and 13 </li></ul><ul><li>5 x 13 = </li></ul><ul><ul><li>65 </li></ul></ul>multiplying the two numbers together
10. 10. <ul><li>This is also true for numbers that are relatively prime. </li></ul><ul><li>Find the LCM for 8 and 9 </li></ul><ul><ul><li>8 x 9 = </li></ul></ul><ul><li>Find the LCM for 4 and 15 </li></ul><ul><ul><li>4 x 15 </li></ul></ul>
11. 11. <ul><li>This is also true for numbers that are relatively prime. </li></ul><ul><li>Find the LCM for 8 and 9 </li></ul><ul><ul><li>8 x 9 = </li></ul></ul><ul><ul><ul><li>72 </li></ul></ul></ul><ul><li>Find the LCM for 4 and 15 </li></ul><ul><ul><li>4 x 15 </li></ul></ul><ul><ul><ul><li>60 </li></ul></ul></ul>
12. 12. <ul><li>The division box is probably the easiest method to find LCM. </li></ul>
13. 13. <ul><li>Find the LCM for 45 and 50 </li></ul><ul><ul><li>LCM: 450 </li></ul></ul><ul><li>Remember, divide common factors until the top numbers are relatively prime. (no common factors other than one) </li></ul><ul><li>Use your divisibility rules to help you. </li></ul>
14. 14. 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
15. 15. 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
16. 16. 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
17. 17. 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
18. 18. 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:
19. 19. 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
20. 20. 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
21. 21. 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
22. 22. <ul><li>Classzone Activity </li></ul><ul><li>on ordering mixed and improper fractions </li></ul><ul><li>Check it out! </li></ul>
23. 23. Homework <ul><li>P.200 #7-18 all </li></ul>