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6 Finding A Common Denominator So, for example, let’s consider adding two fractions as follows: 8/9 + 3/4 = ? We multiply the terms by 1 = 4/4 and 1 = 9/9 respectively to get: (4/4)(8/9) + (9/9)(3/4) = (4*8)/(4*9) + (9*3)/(9*4) = 32/36 + 27/36 Here we have carried out the indicated multiplications of numerator factors and of denominator factors. We postpone, for the minute, carrying out the indicated addition because that is the subject of the next LCS. In the step taken here, the first term is multiplied by 1 = l/l and the second term is multiplied by 1 = k/k . This produces the common denominator lk=kl . We also notice that the numerators have now changed to ln and km . Click me for video ^ QuickTimeª and a decompressor are needed to see this picture.
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7 Adding and Subtracting Fractions If there are more than two terms in the expression it may be necessary to find new common denominators that the 3 rd , 4 th , and other terms will share with the first two terms. Another point is that this denominator, lk , may not be the smallest common denominator of the two fractions. The smallest such denominator is called the lowest common denominator. In a subsequent lesson we shall explore this mathematical topic further. But for the purposes of adding and subtracting fractions there is no need to find the lowest common denominator; the common denominator as obtained above will be sufficient. Given the close similarity of LCS numbers 2 and 3, we have combined their presentations. Once the terms of the addition or subtraction problem are converted to have equal denominators, it is quite easy to perform the addition or subtraction simply by adding or subtracting the numerators and keeping the converted denominator. This is shown above in the LCS numbers 2 and 3. 1 2 Addition of fractions Convert to equal denominators and add numerators. n/k + m/k = ? (n + m)/k 1 3 Subtracting fractions Convert to equal denominators and subtract numerators n/k - m/k = ? (n - m)/k Saxon Lesson Learning Concept Statement Number Concept Name Description (answers what is this concept?) Question (among many) Correct Answer Click me for video > QuickTimeª and a decompressor are needed to see this picture.
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8 Proper and Improper Fractions We can continue with the example we developed for LCS 1: 32/36 + 27/36 = (32 + 27)/36 = 59/36 This is a correct answer but it is in the form of an improper fraction. We will soon address converting this to a mixed format in LCS 6, below. ________________________________________________ It should be recalled that proper fractions (fractions of value less than one) can be combined with whole numbers to form what is called a mixed number. Unlike the usual format in algebra for indicating multiplication, the mixed number places the whole number on the left next to the fraction to its right (with no symbols between) and no multiplication is indicated by this placement. In fact, it is addition of the whole number plus the fraction that is indicated by this “arrangement.” You may recall that mixed numbers can result from improper fractions. An improper fraction indicates division of a larger numerator by a smaller denominator. When we carry out that division incompletely to form a whole number
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  • Fall '09
  • WHITE
  • Fractions, Correct Answer, Elementary arithmetic, Mathematics in medieval Islam

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