Wikipedia
unit fractions : A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. A unit fraction is therefore the reciprocal of a positive integer, 1/ n. Examples are 1/1, 1/2, 1/3, 1/42 etc. Multiplying any two unit fractions results in a product that is another unit fraction: However, adding, subtracting, or dividing two unit fractions produces a result that is generally not a unit fraction: Unit fractions play an important role in modular arithmetic, as they may be used to reduce modular division to the calculation of greatest common divisors. Specifically, suppose that we wish to perform divisions by a value x, modulo y. In order for division by x to be well defined modulo y, x and y must be relatively prime. Then, by using the extended Euclidean algorithm for greatest common divisors we may find a and b such that from which it follows that or equivalently Thus, to divide by x (modulo y) we ne.... More from Wikipedia
unit fractions : An Egyptian fraction is the sum of distinct unit fractions, such as . That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The.. More from Wikipedia
A manufacturer found that there were 25 defective units out of the 180..
A manufacturer found that there were 25 defective units out of the 180 sample units. Find the decimal number which is equivalent to the fraction of the defective units to the total number of sample units. => 0.33 or 0.17 or 0.23 or 0.13..
The circle graph represents the percentage of private schools in the U..
The circle graph represents the percentage of private schools in the United States, which collect annual tuition fee. Find the fraction of the schools with an annual tuition fee of $1501 to $2500. => 3 20 or 13 20 or 1 20 or 9 20..
metric conversions - unit fraction method
Concepts covered: Denominator, Numerator, Common Fraction, and Unit Fraction. I also teach you how to draw typical fractions on a circle.
Question : what are unit fraction? for my homewrok i need to know what a unit fraction is and what it would look like
-Thanks
Answer : Unit fraction- fraction whose numerator is 1 http://en.wikipedia.org/wiki/Unit_fraction.. More from Yahoo Answers
Answer : Unit fraction- fraction whose numerator is 1 http://en.wikipedia.org/wiki/Unit_fraction.. More from Yahoo Answers
Question : Prove that every positive rational number can be written as the sum of distinct unit fractions (i.e. fractions with numerator 1).
Answer : Looks like Tychabrahe missed the "distinct" part and the other poster assumed denominators are rational numbers, although he had the general approach right. I think the question assumes that the denominators should be natural numbers. If a, b N, a/b = a(1/b) = 1/b + 1/b + ... a times Thus we need to prove that we can create 1/b in "a" different ways using distinct unit fractions. First way (1/b) As the other poster pointed out: Second way 1/b = 1/b(b+1) + 1/(b+1) Again substituting for 1/(b+1) we get: Third way 1/b = 1/b[1/(b+1)(b+2) + 1/(b+2)] + 1/(b+1)(b+2) + 1/(b+2) We can now substitute for 1/(b+2) in the previous equation and get a fourth way etc... More from Yahoo Answers
Answer : Looks like Tychabrahe missed the "distinct" part and the other poster assumed denominators are rational numbers, although he had the general approach right. I think the question assumes that the denominators should be natural numbers. If a, b N, a/b = a(1/b) = 1/b + 1/b + ... a times Thus we need to prove that we can create 1/b in "a" different ways using distinct unit fractions. First way (1/b) As the other poster pointed out: Second way 1/b = 1/b(b+1) + 1/(b+1) Again substituting for 1/(b+1) we get: Third way 1/b = 1/b[1/(b+1)(b+2) + 1/(b+2)] + 1/(b+1)(b+2) + 1/(b+2) We can now substitute for 1/(b+2) in the previous equation and get a fourth way etc... More from Yahoo Answers
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