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The article by Boas analyzes two-digit cases in bases other than base 10, e.g., 32 / 13 = 2 / 1 and its inverse are the only solutions in base 4 with two digits. [2]An example of anomalous cancellation with more than two digits is 165 / 462 = 15 / 42 , and an example with different numbers of digits is 98 / 392 = 8 / 32 .
For example, a fraction is put in lowest terms by cancelling out the common factors of the numerator and the denominator. [2] As another example, if a × b = a × c , then the multiplicative term a can be canceled out if a ≠0, resulting in the equivalent expression b = c ; this is equivalent to dividing through by a .
The odd greedy algorithm cannot terminate when given a fraction with an even denominator, because these fractions do not have finite representations with odd denominators. Therefore, in this case, it produces an infinite series expansion of its input. For instance Sylvester's sequence can be viewed as generated by the odd greedy expansion of 1/2.
Moving the batch of rods representing 9 to the left one position (i.e., to the tens place) gives 9[] or 90. Shifting left again to the third position (to the hundreds place) gives 9[][] or 900. Each time one shifts a number one position to the left, it is multiplied by 10. Each time one shifts a number one position to the right, it is divided ...
The simplest fraction 3 / y with a three-term expansion is 3 / 7 . A fraction 4 / y requires four terms in its greedy expansion if and only if y ≡ 1 or 17 (mod 24), for then the numerator −y mod x of the remaining fraction is 3 and the denominator is 1 (mod 6). The simplest fraction 4 / y with a four-term ...
For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible (while keeping the numerator a whole number) is called "reducing a fraction". Rewriting a radical (or "root") expression with the smallest possible whole number under the radical symbol is called "reducing a radical".
An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered). [1]
We can reduce the fractions to lowest terms by noting that the two occurrences of b on the left-hand side cancel, as do the two occurrences of d on the right-hand side, leaving =, and we can divide both sides of the equation by any of the elements—in this case we will use d —getting =.