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A valid number sentence using a 'less than' symbol: 3 + 6 < 10. A valid number sentence using a 'more than' symbol: 3 + 9 > 11. An example from a lesson plan: [6] Some students will use a direct computational approach. They will carry out the addition 26 + 39 = 65, put 65 = 26 + , and then find that = 39.
In an equation =, a is the dividend, b the divisor, and c the quotient. Division by zero is considered impossible at an elementary arithmetic level. Two numbers can be divided on paper using long division. An abbreviated version of long division, short division, can be used for smaller divisors.
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.
The simplest way of viewing division is in terms of quotition and partition: from the quotition perspective, 20 / 5 means the number of 5s that must be added to get 20. In terms of partition, 20 / 5 means the size of each of 5 parts into which a set of size 20 is divided. For example, 20 apples divide into five groups of four apples, meaning ...
In algebra, synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division. It is mostly taught for division by linear monic polynomials (known as Ruffini's rule ), but the method can be generalized to division by any polynomial .
For example, the divisor 3 may be subtracted up to 6 times from the dividend 20, before the remainder becomes negative: 20 − 3 − 3 − 3 − 3 − 3 − 3 ≥ 0, while 20 − 3 − 3 − 3 − 3 − 3 − 3 − 3 < 0. In this sense, a quotient is the integer part of the ratio of two numbers. [9]
Such an interminable division-by-zero algorithm is physically exhibited by some mechanical calculators. [4] In partitive division, the dividend is imagined to be split into parts, and the quotient is the resulting size of each part. For example, imagine ten cookies are to be divided among two friends.
[2] [3] The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. [4]