# Download e-book for kindle: Algebra DeMYSTiFieD (2nd Edition) by Rhonda Huettenmueller By Rhonda Huettenmueller

ISBN-10: 0071743626

ISBN-13: 9780071743624

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Extra info for Algebra DeMYSTiFieD (2nd Edition)

Sample text

Still struggling When you see a plus or minus sign in a fraction, be very careful when simplifying. For example, we cannot remove x from the numerator and denominator in the expression 2 + x ; x cannot be canceled. the only quantities that can be x divided are factors. Many students mistakenly “cancel” the x and conclude that 2 + x = 2 + 1 = 3. x 1 to see why we cannot “cancel” x, let us consider a similar fraction that does not contain a variable. 7 4 + 3 4 + 3 1 4 + 1 5 = = = = 6 6 62 2 2 “Canceling” 3 from the numerator and denominator leaves us with the false equation 7 = 5 .

The LCD for these denominators (which is 582) occurs 97th on the list of multiples of 6. We can use the prime factors of the denominators to find the LCD more efficiently. The LCD consists of every prime factor in each denominator (at its most frequent occurrence). To find the LCD for 121 and 149 , we factor 12 and 14 into their prime factorizations: 12 = 2 ⋅ 2 ⋅ 3 and 14 = 2 ⋅ 7. There are two 2’s and one 3 in the prime factorization of 12, so the LCD will have two 2’s and one 3. There is one 2 in the prime factorization of 14, but this 2 is covered by the 2’s from 12.

For example in 1 + 1 , we could compute 1 + 1 = 1 ⋅ 6 + 1 ⋅ 3 = 6 + 3 = 9 = 1 . 3 6 3 6 3 6 6 3 18 18 18 2 1 1 1 1 2 1 But we really only need to rewrite : + = ⋅ + = 2 + 1 = 3 = 1 . 3 3 6 3 2 6 6 6 6 2 While 18 is a common denominator in the above example, 6 is the smallest common denominator. When denominators get more complicated, either by ( )( ) ( ) 15 DeMYstiFieD / algebra DeMYstiFieD / Gibilisco / 000-0 / Chapter 1 16 a lG e b r a De mys tifieD being large or by having variables in them, it usually easier to use the LCD to add or subtract fractions.