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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]
A ratio that has integers for both quantities and that cannot be reduced any further (using integers) is said to be in simplest form or lowest terms. Sometimes it is useful to write a ratio in the form 1:x or x:1, where x is not necessarily an integer, to enable comparisons of different ratios. For example, the ratio 4:5 can be written as 1:1 ...
Quadratic equations of the form + + = can be solved by first reducing the equation to the form + = (where = / and = /), and then aligning the index ("1") of the C scale to the value on the D scale. The cursor is then moved along the rule until a position is found where the numbers on the CI and D scales add up to p {\displaystyle p} .
Also, some fractions (such as 1 ⁄ 7, which is 0.14285714285714; to 14 significant figures) can be difficult to recognize in decimal form; as a result, many scientific calculators are able to work in vulgar fractions or mixed numbers.
The diagonal of a half square forms the basis for the geometrical construction of a golden rectangle.. The golden ratio φ is the arithmetic mean of 1 and . [4] The algebraic relationship between , the golden ratio and the conjugate of the golden ratio (Φ = − 1 / φ = 1 − φ) is expressed in the following formulae:
It has the symbols I, V, X, L, C, D, M as its basic numerals to represent the numbers 1, 5, 10, 50, 100, 500, and 1000. [33] A numeral system is positional if the position of a basic numeral in a compound expression determines its value. Positional numeral systems have a radix that acts as a multiplicand of the different positions. For each ...
A simple arithmetic calculator was first included with Windows 1.0. [5]In Windows 3.0, a scientific mode was added, which included exponents and roots, logarithms, factorial-based functions, trigonometry (supports radian, degree and gradians angles), base conversions (2, 8, 10, 16), logic operations, statistical functions such as single variable statistics and linear regression.
Note that if n 2 is the closest perfect square to the desired square x and d = x - n 2 is their difference, it is more convenient to express this approximation in the form of mixed fraction as . Thus, in the previous example, the square root of 15 is 4 − 1 8 . {\displaystyle 4{\tfrac {-1}{8}}.}