7.3 - additions of fractions in the numerator and or...

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9/29/2008 1 7.3 Fractions from Heck We can “un - fractionize” a fraction by multiplying it by its denominator The result will just be its numerator Any multiple of the denominator will serve. But we have to justify the multiplication Justifying multiplication We can multiply both sides of an equation by the same number. We can multiply both numerator and denominator of a fraction by the same thing . (then we are really just multiplying by “1”.) We can multiply both sides of an inequality by a positive number. (Or a negative number if we “turn the inequality around.”) Adding fractions Sometimes as a part of the process of simplifying a complex fraction, we need to add two (or more) fractions. We can only add two fractions when they have the same denominator . We can easily make a fraction have any denominator which is a multiple of its original denominator. Two approaches Convert to the form fraction over fraction. Then invert and multiply. To do the conversion, you may need to do
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Unformatted text preview: additions of fractions in the numerator and or denominator. • First , un-fractionize by multiplying both numerator and denominator by the least common multiple of all the denominators in the whole wretched mess. Finally, clean up • When you get done reducing the mess to a single fraction, there may be an opportunity to simplify. • We often call this simplification process crossing out common factors . • It works because “something over itself” is just a weird way of writing the number 1, and multiplying by 1 is a “don’t change operation”. Recognizing patterns is great, but… • When you see “the same thing” in both numerator and denominator, there is a great temptation to “cross it out”. • You can only “ cancel” factors , never terms – A factor is something that is “multiplied in” – A term is something that is “added in” ) ( 119 118 2 1 2 7 1 1 1 7 1 1 2 117 1 117 it try...
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