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The following are single-word prepositions that take clauses as complements. Prepositions marked with an asterisk in this section can only take non-finite clauses as complements. Note that dictionaries and grammars informed by concepts from traditional grammar may categorize these conjunctive prepositions as subordinating conjunctions.
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
[2] [3] Thus, in the expression 1 + 2 × 3, the multiplication is performed before addition, and the expression has the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9. When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication and placed as a superscript to the right of ...
This example uses peasant multiplication to multiply 11 by 3 to arrive at a result of 33. Decimal: Binary: 11 3 1011 11 5 6 101 110 2 12 10 1100 1 24 1 11000 —— —————— 33 100001 Describing the steps explicitly: 11 and 3 are written at the top
A preposition that takes a noun-phrase complement is called a transitive preposition (e.g., She went up the hill), and one that does not take any complements is called an intransitive preposition (e.g., She went up). [3] Prepositions can also take the following complements: clauses (e.g., after you arrived), adjective phrases (e.g., accepted as ...
When multiplication is repeated, the resulting operation is known as exponentiation. For instance, the product of three factors of two (2×2×2) is "two raised to the third power", and is denoted by 2 3, a two with a superscript three. In this example, the number two is the base, and three is the exponent. [26]
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