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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] In other words, a fraction a / b is irreducible if and only if a and b are coprime ...
Cancelling out is a mathematical process used for removing subexpressions from a mathematical expression, when this removal does not change the meaning or the value of the expression because the subexpressions have equal and opposing effects. [1] For example, a fraction is put in lowest terms by cancelling out the common factors of the ...
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".
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, replacing $ 23.4476 with $ 23.45, the fraction 312/937 with 1/3, or the expression √2 with 1.414. Rounding is often done to obtain a value that is easier to report and communicate than the original.
Consider √ 2 √ 2; if this is rational, then take a = b = √ 2. Otherwise, take a to be the irrational number √ 2 √ 2 and b = √ 2. Then a b = (√ 2 √ 2) √ 2 = √ 2 √ 2 · √ 2 = √ 2 2 = 2, which is rational. Although the above argument does not decide between the two cases, the Gelfond–Schneider theorem shows that √ 2 ...
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [1 ...
The smallest common multiple of the two denominators 6 and 15z is 30z, so one multiplies both sides by 30z: 5 x z + 2 y = 30 z . {\displaystyle 5xz+2y=30z.\,} The result is an equation with no fractions.