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# Understanding Fractions

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### Understanding Fractions

1. 1. UnderstandingFractions<br />Ms. Taylor<br />
2. 2. Fraction<br />A fraction is the quotient of two rational numbers.<br />Numerator<br />Denominator<br />
3. 3. Classification of Fractions<br />Proper Fraction<br />Improper Fraction<br />Mixed Number<br />
4. 4. Classification of Fractions<br />A proper fraction is a fraction with the numerator less (smaller) than the denominator.<br />An improper fraction is a fraction with the numerator great (larger) than or equal (the same) to the denominator.<br />A mixed number has a fraction and a whole number.<br />
5. 5. Proper Fractions<br />3<br />4<br /> 1<br /> 2<br />
6. 6. Improper Fractions<br /> 7<br /> 5<br />9<br /> 9<br />
7. 7. Mixed Number<br />1<br /> 4<br />3<br />
8. 8. Equivalent Fractions<br /> A equivalent fraction is a fraction that names the same fraction.<br />These are equivalent fractions.<br />6 1<br /> 18 3<br />,<br />
9. 9. Order Fractions<br />To order fractions with like denominators:<br />First look at the numerator s.<br />Place the fractions with the lowest numerator first. <br />Place the second lowest numerator next.<br />Keep doing this until there are no more fractions.<br />
10. 10. Ordering Fractions<br />Order the following fractions:<br />2 1 3<br />4 4 4<br />The answer:<br /> 1 2 3<br /> 4 4 4<br />,<br />,<br />,<br />,<br />
11. 11. Ordering Fractions<br />To order fractions with unlike denominators.<br />First find a common denominator, which is smallest whole number that is divisible by each of the denominators.<br />You find a common denominator by finding the Least Common Multiple (LCM) for whole numbers.<br />
12. 12. Least Common Multiple (LCM)<br />Method 1<br />List the multiples of each denominator (multiply by 2, 3, 4, etc.) then look for the smallest number that appears in each list.<br />Example<br />1/5, 1/6, and 1/15<br />Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 45<br />Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48<br />Multiples of 15: 15, 30, 45<br />
13. 13. LCM<br /> The LCM of 5, 6, and 15 is 30; so the common denominator would be 30.<br />* 6 =<br /> * 6 =<br />You continue with the other two fractions. <br />1<br />6<br />5<br />30<br />
14. 14. Ordering Fractions<br />Now that you have a common denominator. You put the fractions in order from least to greatest!<br />6 5 2 2 5 6<br /> 30 30 30 30 30 30<br />,<br />,<br />,<br />,<br />=<br />Terrific<br />
15. 15. LCM<br />Method 2:<br />Factor each of the denominators into primes.<br />Then count the number of times each prime number appears in each of the factorizations.<br />For each prime number, take the largest of these counts. Write down that prime number as many times as you counted.<br />The product of all the prime numbers written down is the least common denominator. <br />
16. 16. Method 2<br />Factor each of the numbers into primes.<br />Count the number of times each prime number appears in each of the factorizations.<br />For each prime number, take the largest of these counts.<br />Write down that prime number as many times as you counted for it in step 2.<br />The least common multiple is the product of all the prime numbers written down.<br />
17. 17. Method 2<br />Example: Find the LCM of 5, 6, and 15.<br />Prime factorization of 5 is 5.<br />One five<br />Prime factorization of 6 is 2 x 3.<br />One 2 and one 3<br />Prime factorization of 15 is 3 x 5.<br />One 3 and one 5<br />
18. 18. Method 2<br />The largest count of 2s is one<br />The largest count of 3s is one<br />The largest count of 5s is one<br />So, we simply take 2 x 3 x 5 = 30<br />Therefore, 30 is the LCM of 5, 6, and 15.<br />Awesome job!<br />
19. 19. References<br />Help with Fractions http://www.helpwithfractions.com/least-common-denominator.html<br />