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# Fraction basics

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### Fraction basics

1. 1. Understanding Fractions
2. 2. Fractiono A fraction is the quotient of two rational numbers. Numerator Denominator
3. 3. Classification of Fractions Proper Fraction  Improper Fraction  Mixed Number
4. 4. Classification of Fractions A proper fraction is a fraction with the numerator less (smaller) than the denominator. An improper fraction is a fraction with the numerator great (larger) than or equal (the same) to the denominator. A mixed number has a fraction and a whole number.
5. 5. Proper Fractions3 14 2
6. 6. Improper Fractions7 95 9
7. 7. Mixed Number14
8. 8. Equivalent Fractionsequivalent fractions are fractions thathave different denominators, but are thesame size. These are equivalent fractions. 6 1 18 3
9. 9. Ordering Fractions To order fractions with like denominators:  First look at the numerators.  Place the fractions with the lowest numerator first.  Place the second lowest numerator next.  Keep doing this until there are no more fractions.
10. 10. Ordering Fractions Order the following fractions: 2 1 3 4 4 4 The answer: 1 2 3 4 4 4
11. 11. Ordering FractionsTo order fractions with unlike denominators. First, find a common denominator, which is thesmallest whole number that is divisible by each of thedenominators. You find a common denominator by finding the LeastCommon Multiple (LCM) for those numbers.
12. 12. Least Common Multiple (LCM) Method 1 List the multiples of each denominator (multiply by2, 3, 4, etc.) then look for the smallest common number ineach list. Example 1/5, 1/6, and 1/15 Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 45 Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48 Multiples of 15: 15, 30, 45
13. 13. LCM The LCM of 5, 6, and 15 is 30; so the common denominator would be 30. x6 = x6 = You continue with the other two fractions.
14. 14. Ordering Fractions Now that you have a common denominator. Youput the fractions in order from Least to Greatest. 6 5 2 2 5 6 30 30 30 30 30 30
15. 15. LCM Method 2:• Factor each of the denominators into primes.• Then count the number of times each prime number appears inthe factorizations.•For each prime number, take the largest of these counts. Writedown that prime number as many times as you counted.• The product of all the prime numbers written down is the leastcommon denominator.
16. 16. Method 2o Factor each of the numbers into primes.o Count the number of times each prime number appears in the factorizations.o For each prime number, take the largest of these counts.o Write down that prime number as many times as you counted for it in step 2.o The least common multiple is the product of all the prime numbers written down.
17. 17. Method 2 Example: Find the LCM of 5, 6, and 15• Prime factorization of 5 is 5• Prime factorization of 6 is 2 x 3• Prime factorization of 15 is 3 x 5• The LCM of 5, 6. & 15 is: 5 x 2 x 3; which = 30
18. 18. Method 2o The largest count of 2s is oneo The largest count of 3s is oneo The largest count of 5s is oneo So, we simply take 2 x 3 x 5 = 30o Therefore, 30 is the LCM of 5, 6, and 15.