In mathematics, subtraction is one of the four basic arithmetic operations. It is usually denoted by an infix notation minus sign. The traditional names for the terms of the subtraction :''c'' − ''b'' = ''a'' are difference (''a''), minuend (c) and subtrahend (b). ==Basic subtraction== Imagine a line segment of length ''b'' painted on the ground with the left end labeled ''a'' and the right end labeled ''c''. Starting from position ''a'', it takes you ''b'' steps to the right to reach position ''c''. This movement to the right, called addition, can be stated as: :''a'' + ''b'' = ''c'' From position ''c'', it takes you ''b'' steps to the left to get back to ''a''. This movement to the left, called subtraction, can be stated as: :''c'' − ''b'' = ''a'' Now, imagine a line labelled with the numbers 1 (number), 2 (number), and 3 (number). From position 3, it takes no steps to the left to stay at position 3, so :3 − 0 = 3 From position 3, it only takes 1 step to the left to get to position 2, so :3 − 1 = 2 From position 3, it takes you 2 steps to the left to get to position 1, so :3 − 2 = 1 What would happen if you continued the process by going 3 steps to the left of position 3? For our example, you would walk off the end of the line which is not allowed. So, for this operation to be valid, the line must be extended. For subtraction of natural numbers, the line would have every natural number (0, 1, 2, 3, 4, ...) on it. Using the natural number line, from position 3, it takes you 3 steps to the left to get to position 0, so :3 − 3 = 0 But, for natural numbers, 3 − 4 is invalid since it leaves the line. So, for this operation to be valid, the line must be extended. Using the integer number line (…, −3, −2, −1, 0, 1, 2, 3, …), from position 3, it takes you 4 steps to the left to get to position −1, so :3 − 4 = −1 == Algorithms for subtraction == *method of complements == External links == Printable Worksheets: [http://www.kwiznet.com/p/takeQuiz.php?ChapterID=1214&CurriculumID=2&Method=Worksheet&NQ=24&NQ4P=3 One Digit Subtraction], [http://www.kwiznet.com/p/takeQuiz.php?ChapterID=1202&CurriculumID=2&Method=Worksheet&NQ=24&NQ4P=3 Two Digit Subtraction], and [http://www.kwiznet.com/p/takeQuiz.php?ChapterID=1273&CurriculumID=3&Method=Worksheet&NQ=24&NQ4P=3 Four Digit Subtraction] *[http://www.cut-the-knot.org/Curriculum/Arithmetic/SubtractionGame.shtml Subtraction Game] * [http://webhome.idirect.com/~totton/abacus/pages.htm#Subtraction1 Subtraction on a Japanese abacus] selected from [http://webhome.idirect.com/~totton/abacus/ Abacus: Mystery of the Bead] == See also == *Elementary arithmetic *Decrement Arithmetic simple:Subtraction th:การลบ
Problems with the Subtraction article This article needs to be fixed. The way it's written a and c are points while b is a distance. This is not a proper geometric analogy to the way subtraction is carried out, and the original writer is subtracting two different classes of objects. Perhaps you've heard it mentioned that you can't add or subtract apples and oranges. ---- 1) Start with 3 apples 2) Take away 2 oranges from those 3 apples 3) One shouldn't expect to have 1 apple left, as subtraction in this way just doesn't make sense. ---- Points are quite different than distances, and just as in the case with apples and oranges, one should not expect to be able to subtract distances from points. Instead a, b, and c should all be distances from the origin, a point who's numerical value is zero. In this way the distance to c minus the distance to a is the distance b. Could somebody who posesses both the tools to generate decent images as well as a strong math background fix this article?
See other meanings of words starting from letter:
Words begining with Subtraction:
Subtraction
Subtraction
Subtraction
In mathematics, subtraction is one of the four basic arithmetic operations. It is usually denoted by an infix notation minus sign. The traditional names for the terms of the subtraction :''c'' − ''b'' = ''a'' are difference (''a''), minuend (c) and subtrahend (b). ==Basic subtraction== Imagine a line segment of length ''b'' painted on the ground with the left end labeled ''a'' and the right end labeled ''c''. Starting from position ''a'', it takes you ''b'' steps to the right to reach position ''c''. This movement to the right, called addition, can be stated as: :''a'' + ''b'' = ''c'' From position ''c'', it takes you ''b'' steps to the left to get back to ''a''. This movement to the left, called subtraction, can be stated as: :''c'' − ''b'' = ''a'' Now, imagine a line labelled with the numbers 1 (number), 2 (number), and 3 (number). From position 3, it takes no steps to the left to stay at position 3, so :3 − 0 = 3 From position 3, it only takes 1 step to the left to get to position 2, so :3 − 1 = 2 From position 3, it takes you 2 steps to the left to get to position 1, so :3 − 2 = 1 What would happen if you continued the process by going 3 steps to the left of position 3? For our example, you would walk off the end of the line which is not allowed. So, for this operation to be valid, the line must be extended. For subtraction of natural numbers, the line would have every natural number (0, 1, 2, 3, 4, ...) on it. Using the natural number line, from position 3, it takes you 3 steps to the left to get to position 0, so :3 − 3 = 0 But, for natural numbers, 3 − 4 is invalid since it leaves the line. So, for this operation to be valid, the line must be extended. Using the integer number line (…, −3, −2, −1, 0, 1, 2, 3, …), from position 3, it takes you 4 steps to the left to get to position −1, so :3 − 4 = −1 == Algorithms for subtraction == *method of complements == External links == Printable Worksheets: [http://www.kwiznet.com/p/takeQuiz.php?ChapterID=1214&CurriculumID=2&Method=Worksheet&NQ=24&NQ4P=3 One Digit Subtraction], [http://www.kwiznet.com/p/takeQuiz.php?ChapterID=1202&CurriculumID=2&Method=Worksheet&NQ=24&NQ4P=3 Two Digit Subtraction], and [http://www.kwiznet.com/p/takeQuiz.php?ChapterID=1273&CurriculumID=3&Method=Worksheet&NQ=24&NQ4P=3 Four Digit Subtraction] *[http://www.cut-the-knot.org/Curriculum/Arithmetic/SubtractionGame.shtml Subtraction Game] * [http://webhome.idirect.com/~totton/abacus/pages.htm#Subtraction1 Subtraction on a Japanese abacus] selected from [http://webhome.idirect.com/~totton/abacus/ Abacus: Mystery of the Bead] == See also == *Elementary arithmetic *Decrement Arithmetic simple:Subtraction th:การลบ
Subtraction
Problems with the Subtraction article This article needs to be fixed. The way it's written a and c are points while b is a distance. This is not a proper geometric analogy to the way subtraction is carried out, and the original writer is subtracting two different classes of objects. Perhaps you've heard it mentioned that you can't add or subtract apples and oranges. ---- 1) Start with 3 apples 2) Take away 2 oranges from those 3 apples 3) One shouldn't expect to have 1 apple left, as subtraction in this way just doesn't make sense. ---- Points are quite different than distances, and just as in the case with apples and oranges, one should not expect to be able to subtract distances from points. Instead a, b, and c should all be distances from the origin, a point who's numerical value is zero. In this way the distance to c minus the distance to a is the distance b. Could somebody who posesses both the tools to generate decent images as well as a strong math background fix this article?
See other meanings of words starting from letter:
S
SB | SC | SD | SE | SF | SG | SH | SI | SJ | SK | SL | SM | SN | SO | SP | SR | SS | ST | SU | SW | SX | SY | SZ |Words begining with Subtraction:
Subtraction
Subtraction
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