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6 1 2 1 1 −1 4 5 9. and would be written in modern notation as 6 1 / 4 , 1 1 / 5 , and 2 − 1 / 9 (i.e., 1 8 / 9 ). The horizontal fraction bar is first attested in the work of Al-Hassār (fl. 1200), [35] a Muslim mathematician from Fez, Morocco, who specialized in Islamic inheritance jurisprudence.
The same syntactic expression 1 + 2 × 3 can have different values (mathematically 7, but also 9), depending on the order of operations implied by the context (See also Operations § Calculators). For real numbers , the product a × b × c {\displaystyle a\times b\times c} is unambiguous because ( a × b ) × c = a × ( b × c ) {\displaystyle ...
where c 1 = 1 / a 1 , c 2 = a 1 / a 2 , c 3 = a 2 / a 1 a 3 , and in general c n+1 = 1 / a n+1 c n . Second, if none of the partial denominators b i are zero we can use a similar procedure to choose another sequence {d i} to make each partial denominator a 1:
[3] Free response questions typically require little work for instructors to write, but can be difficult to grade consistently as they require subjective judgments. Free response tests are a relatively effective test of higher-level reasoning, as the format requires test-takers to provide more of their reasoning in the answer than multiple ...
For the expression of mood, English uses a number of modal auxiliaries, such as can, may, will, shall and the past tense forms could, might, would, should. There are also subjunctive and imperative moods , both based on the plain form of the verb (i.e. without the third person singular -s ), for use in subordinate clauses (e.g. subjunctive: It ...
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include: Simplification of algebraic expressions, in computer algebra; Simplification of boolean expressions i.e. logic optimization
[1] [2] [3] [better source needed]. For example, 3 x 2 − 2 x y + c {\displaystyle 3x^{2}-2xy+c} is an algebraic expression. Since taking the square root is the same as raising to the power 1 / 2 , the following is also an algebraic expression:
Simple English Wikipedia was launched on September 18, 2001. [1] [2]In 2012, Andrew Lih, a Wikipedian and author, told NBC News' Helen A.S. Popkin that the Simple English Wikipedia does not "have a high standing in the Wikipedia community", and added that it never had a clear purpose: "Is it for people under the age 14, or just a simpler version of complex articles?", wrote Popkin.