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A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 2 , − 8 5 , −8 5 , and 8 −5 .
The first method authorizes Congress, "whenever two-thirds of both houses shall deem it necessary", [a] to propose constitutional amendments. The second method requires Congress, "on the application of the legislatures of two-thirds of the several states" (34 as of 1959), to "call a convention for proposing amendments". [6]
The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial. This quadratic polynomial has two roots, and. The golden ratio is also closely related to the polynomial. which has roots and As the root of a quadratic polynomial, the golden ratio is a constructible number.
Cross-multiplication. In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable. The method is also occasionally known as the "cross your heart" method because lines resembling ...
Hawke v. Smith, 253 U.S. 221 (1920): "[Article V] makes provision for the proposal of amendments either by two-thirds of both houses of Congress or on application of the legislatures of two-thirds of the states, thus securing deliberation and consideration before any change can be proposed. The proposed change can only become effective by the ...
Constitutional amendment. A constitutional amendment is a modification of the constitution of a polity, organization or other type of entity. Amendments are often interwoven into the relevant sections of an existing constitution, directly altering the text. Conversely, they can be appended to the constitution as supplemental additions (codicils ...
The Rhind Mathematical Papyrus. An Egyptian fraction is a finite 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 value of an expression of this type is a positive rational number ; for ...
With the exceptions of 1, 8 and 144 (F 1 = F 2, F 6 and F 12) every Fibonacci number has a prime factor that is not a factor of any smaller Fibonacci number (Carmichael's theorem). [56] As a result, 8 and 144 ( F 6 and F 12 ) are the only Fibonacci numbers that are the product of other Fibonacci numbers.