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The plus and minus signs (+ and −) are mathematical symbols used to represent the notions of positive and negative as well as the operations of addition and subtraction. Their use has been extended to many other meanings, more or less analogous. Plus and minus are Latin terms meaning "more" and "less", respectively.
HistoryThough the signs now seem as familiar as the alphabet or the Hindu-Arabic numerals, they are not of great antiquity. The Egyptian hieroglyphic sign for addition, for example, resembled a pair of legs walking in the direction in which the text was written (Egyptian could be written either from right to left or left to right), with the reverse sign indicating subtraction: [ citation needed ]
In Europe in the early 15th century the letters "P" and "M" were generally used. [ 1 ] The symbols (P with stroke for piu, i.e., plus, and M with stroke for meno, i.e., minus) appeared for the first time in Luca Pacioli’s mathematics compendium, Summa de arithmetica, geometria, proportioni et proportionalità, first printed and published in Venice in 1494. [ 2 ] The + is a simplification of the Latin "et" (comparable to the ampersand &). [ citation needed ] The − may be derived from a tilde written over m when used to indicate subtraction; or it may come from a shorthand version of the letter m itself. [ citation needed ] In his 1489 treatise Johannes Widmann referred to the symbols − and + as minus and mer (Modern German mehr; "more"): "das − ist, das ist minus, und das + ist das mer". [ 3 ]
A book published by Henricus Grammateus in 1518 makes another early use of + and − for addition and subtraction. [ 4 ]
Robert Recorde, the designer of the equals sign, introduced plus and minus to Britain in 1557 in The Whetstone of Witte: [ citation needed ] "There be other 2 signes in often use of which the first is made thus + and betokeneth more: the other is thus made – and betokeneth lesse."
The plus sign is a binary operator that indicates addition, as in 2 + 3 = 5. It can also serve as a unary operator that leaves its operand unchanged (+x means the same as x). This notation may be used when it is desired to emphasise the positiveness of a number, especially when contrasting with the negative (+5 versus −5).
The plus sign can also indicate many other operations, depending on the mathematical system under consideration. Many algebraic structures have some operation which is called, or equivalent to, addition. Moreover, the symbolism has been extended to very different operations. Plus can mean:
Minus signThe minus sign has three main uses in mathematics: [ 5 ]
All three uses can be referred to as "minus" in everyday speech. In modern US usage, −5 (for example) is normally pronounced "negative five" rather than "minus five". "minus" may be used by speakers born before 1950, and is still popular in some contexts, but "negative" is usually taught as the only correct reading. [ 6 ] In most other parts of the English-speaking world, "minus five" is more common. Textbooks in America encourage −x to be read as "the opposite of x" or even "the additive inverse of x" to avoid giving the impression that −x is necessarily negative. [ 7 ]
In some contexts, different glyphs are used for these meanings; for instance in the computer language APL a raised minus sign is used in negative numbers (as in 2 − 5 gives − 3), but such usage is rare.
In mathematics and most programming languages, the rules for the order of operations mean that −5 2 is equal to −25. Powers bind more strongly than multiplication or division which binds more strongly than addition or subtraction. While strictly speaking, the unary minus is not subtraction, it is given the same place as subtraction. However in some programming languages and Excel in particular, unary operators bind strongest, so in these −5^2 is 25 but 0−5^2 is −25. [ 8 ]
Use in elementary educationSome elementary teachers use raised plus and minus signs before numbers to show they are positive or negative numbers. [ 9 ] For example subtracting −5 from 3 might be read as positive three take away negative 5 and be shown as
3 − − 5 becomes 3 + 5 = 8,
+ 3 − − 5 becomes + 3 + + 5 which is + 8
Use as a qualifierIn grading systems (such as examination marks), the plus sign indicates a grade one level higher and the minus sign a grade lower. For example, B− ("B minus") is one grade lower than B. Sometimes this is extended to two plus or minus signs; for example A++ is two grades higher than A.
Positive and negative are sometimes abbreviated as +ve and −ve.
In mathematics the one-sided limit x→a + means x approaches a from the right, and x→a − means x approaches a from the left. For example, when calculating what x −1 is when x approaches 0, because x −1 →+∞ when x→0 + but x −1 → −∞ when x→0 − .
Uses in computingAs well as the normal mathematical usage plus and minus may be used for a number of other purposes in computing.
Plus and minus signs are often used in tree view on a computer screen to show if a folder is collapsed or not.
In some programming languages concatenation of strings is written: "a" + "b" = "ab", although this usage is questioned by some for violating commutativity, a property addition is expected to have.
In most programming languages, subtraction and negation are indicated with the ASCII hyphen-minus character, - . In APL a raised minus sign (Unicode U+00AF) is used to denote a negative number, as in ¯3) and in J a negative number is denoted by an underscore, as in _5.
In C and some other computer programming languages, two plus signs indicate the increment operator and two minus signs a decrement. For example, x++ means "increment the value of x by one" and x-- means "decrement the value of x by one". By extension, "++" is sometimes used in computing terminology to signify an improvement, as in the name of the language C++.
There is no concept of negative zero in mathematics, but in computing −0 may have a separate representation from zero. In the IEEE floating-point standard 1/−0 is negative infinity whereas 1/0 is positive infinity.
Other usesIn chemistry, the minus sign (rather than an en dash) is used for a single covalent bond between two atoms, in skeletal formula.
Subscripted plus and minus signs are used as diacritics in the International Phonetic Alphabet to indicate advanced or retracted articulations of speech sounds.
The minus sign is also used as tone letter in the orthographies of Dan, Krumen, Karaboro, Mwan, Wan, Yaouré, Wè, Nyabwa and Godié. [ 10 ] The Unicode character used for the tone letter (U+02D7) is different from the mathematical minus sign.
Character codesThe Unicode minus sign is designed to be the same length and height as the plus and equals signs. In most fonts these are the same width as digits in order to facilitate the alignment of numbers in tables.
The hyphen-minus sign (-) is the ASCII version of the minus sign, and doubles as a hyphen. It is usually shorter in length than the plus sign and sometimes at a different height. It can be used as a substitute for the true minus sign when the character set is limited to ASCII.
There is a commercial minus sign (⁒), which looks somewhat like an obelus, at U+2052 (HTML &x2052;).
Alternative plus signA Jewish tradition that dates from at least the 19th century is to write plus using a symbol like an inverted T. This practice was adopted into Israeli schools (this practice goes back to at least the 1940s) [ 11 ] and is still commonplace today in elementary schools (including secular schools) but in fewer secondary schools. [ 12 ] It is also used occasionally in books by religious authors, but most books for adults use the international symbol "+". The usual explanation for this practice is that it avoids the writing of a symbol "+" that looks like a Christian cross. [ 12 ] Unicode has this symbol at position U+FB29 "Hebrew letter alternative plus sign" ( ﬩ ). [ 13 ]
Wikimedia Foundation . 2010 .
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Hyphen-minus — The hyphen minus is the character at position 2DHEX in ASCII and standards that derive from it. It is used as a hyphen, a minus sign and a dash. This was a compromise that made sense in the early days of fixed width typewriters and computer… … Wikipedia
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Unlike signs — Unlike Un*like , a. 1. Not like; dissimilar; diverse; having no resemblance; as, the cases are unlike. [1913 Webster] 2. Not likely; improbable; unlikely. [Obsoles.] [1913 Webster]
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Plus / Minus by D I N G Digital Album Buy Now name your price Send as Gift licenseD I N G Scarborough, UK
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ex) Two plus two is four.
ex) Two times two is four.
ex) Nine minus three is six.
ex) Six divided by three is two.
ex) Simple writing: one, two, three . . .
ex) Simple writing: ten, eleven, twelve . . .
ex) Simple writing: zero, ten, twenty . . .
le writing: ten, eleven, twelve . . .
Students practice reading numbers and decide if an addition equation is right or wrong. Combines easy classroom English with number recognition .
Worksheet 10-20: Numbers 1-10 as individual worksheets:
Activity Suggestion: Math King
A fter you have taught plus, minus, times, and divided by using the worksheets above, print off a set of addition, subtraction, multiplication, and division flashcards and play 'The Math King'. It is a very simple game to do and will get the kids using the language of math very quickly.
H ere's how you play. The whole class lines up and tries to challenge the current math king. The teacher holds up a random flashcard and the current king and the new challenger (the first person in the line) race to shout out the answer. If they shout out the answer correctly, then the teacher points to the student who shouted first and that person has to make a sentence. For example, if the flashcards is 2x2, the the teacher will point to the first student who says four. That student will then have to say, 'two times two is four.'
I f the student does this correctly then they win the match. If it is the current king who is first then he or she just remains the king and the challenger goes to the back of the line. If it is the challenger who wins, then the challenger becomes the new king and the old king goes to the back of the line. The next student in line becomes the new challenger. It's a great activity for even your youngest learners in elementary school.
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