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| In [[mathematics]] and [[computer programming]], the '''order of operations''' (sometimes called '''operator precedence''') is a rule used to clarify which procedures should be performed first in a given [[Expression (mathematics)|mathematical expression]].
| | BMI is short for "body mass index". It's calculated from a person's weight inside kilograms plus height inside meters. The simplest method to determine BMI is to use an online calculator where you connect your fat plus height. A normal BMI is between 18.5 plus 24.9, while 25 to 29.9 is considered to be obese. When we hit a BMI of 30, you're overweight. On the additional hand, these values are less accurate inside athletic persons whom have more lean body mass plus folks that have big frames.<br><br>To calculate the waist-to-hip ratio (to keep an acronym it's called the WTHR), measure both a waist plus hips, and divide the waist size by the cool size. And yes, this indicator realizes the difference between guys and women, unlike the BMI. For females, the ratio could be no over 0.8. In different words, your waist ought to be smaller than your hips. And for guys, it should be 1.0 or less. That means that a man's waist must be the same measuring because his hips or smaller. The beer-and-pizza stomach has to go!<br><br>In 1972, Ancel Keys gave the concept its more familiar name, Body Mass Index, or BMI. In the 1980s, JS Garrow plus JD Webster suggested arbitrary zones for the BMI--including "overweight" and "obese". And the rest is history.<br><br>First, you want to determine an BMI for a child. What is a BMI? BMI stands for body mass index that is a amount that takes into account a child's height-to-weight ratio. There is a rather complex formula for calculating BMI, nevertheless this is completed fast and conveniently at a variety of online sites that provide a [http://safedietplansforwomen.com/bmi-calculator bmi calculator]. You simply connect the child's fat plus height plus the system will calculate your child's BMI. Finding a bmi calculator may be because simple because doing a Google look for which phrase.<br><br>In order to know where you fall found on the body fat charts, you will need to calculate the body fat. There are several ways to do this, from a do it oneself skin fold test, to online calculators. The skin fold test is not (omit) because correct because different techniques. Basically, you're pinching several skin at different body locations, that is measured. This can show the changes in body composition over time, whether or not it's not a totally correct method of calculating body fat.<br><br>Another limitation is that age is not considered when calculating BMI. So for elderly people, whether or not the BMI indication is normal, the truth remains which most muscles have been lost considering of age.<br><br>There are 3 leading places inside California where you can get California Medical Weight Management program. San Ramon, Watsonville plus Santa Clara are 3 leading places. Get an appointment fixed with the doctor from some of the clinic plus fill the free consultation shape online. Losing weight is fun plus simple for sure from here. It is the fact is the last time to lose weight if you follow it correctly. Moreover, it provides more benefits that you are able to get when you join it. You will truly feel a life changed. Hurry up plus join the fat reduction system today. |
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| For example, in mathematics and most computer languages multiplication is done before addition; in the expression 2 + 3 × 4, the answer is 14. Brackets, "( and ), { and }, or [ and ]", which have their own rules, may be used to avoid confusion, thus the preceding expression may also be rendered 2 + (3 × 4), but the brackets are unnecessary as multiplication still has precedence without them.
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| Since the introduction of modern algebraic notation, multiplication has taken precedence over addition.<ref>{{Cite web|url=http://mathforum.org/library/drmath/view/52582.html |title=Ask Dr. Math |publisher=Math Forum |date=22 November 2000 |accessdate=5 March 2012}}</ref> Thus 3 + 4 × 5 = 4 × 5 + 3 = 23. When exponents were first introduced in the 16th and 17th centuries, exponents took precedence over both addition and multiplication and could be placed only as a superscript to the right of their base. Thus 3 + 5<sup>2</sup> = 28 and 3 × 5<sup>2</sup> = 75. To change the order of operations, originally a [[vinculum (symbol)|vinculum]] (an overline or underline) was used. Today, [[bracket (mathematics)|parentheses or brackets]] are used to explicitly denote precedence by grouping parts of an expression that should be evaluated first. Thus, to force addition to precede multiplication, we write (2 + 3) × 4 = 20, and to force addition to precede exponentiation, we write (3 + 5)<sup>2</sup> = 64.
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| <!-- It is tempting to talk about PEMDAS or BEDMAS or "Please excuse my dear Aunt Sally" here, but these mnemonics are covered below and there are more choices of them than easily fit in an intro. You should at least read the discussion (linked above the article head) before adding a sentence about the mnemonics in the intro. -->
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| ==The standard order of operations==
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| The order of operations used throughout mathematics, science, technology and many computer [[programming language]]s is expressed here:<ref>{{Cite web|url=http://www.algebrahelp.com/lessons/simplifying/oops/ |title=Order of Operations Lessons |publisher=Algebra.Help |date= |accessdate=5 March 2012}}</ref>
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| : '''[[Exponentiation|exponents]]''' and '''[[Nth root|roots]]'''
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| : '''[[multiplication]]''' and '''[[Division (mathematics)|division]]'''
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| : '''[[addition]]''' and '''[[subtraction]]'''
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| This means that if a mathematical expression is preceded by one operator and followed by another, the operator higher on the list should be applied first. The [[Commutative property|commutative]] and [[Associative property|associative]] laws of addition and multiplication allow terms to be added in any order and factors to be multiplied in any order, but mixed operations must obey the standard order of operations.
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| It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse) and subtraction as addition of the opposite (additive inverse). Thus 3/4 = 3 ÷ 4 = 3 • ¼; in other words the quotient of 3 and 4 equals the product of 3 and ¼. Also 3 − 4 = 3 + (−4); in other words the difference of 3 and 4 equals the sum of positive three and negative four. With this understanding, we can think of 1 − 3 + 7 as the sum of 1, negative 3, and 7, and add in any order: (1 − 3) + 7 = −2 + 7 = 5 and in reverse order (7 − 3) + 1 = 4 + 1 = 5. The important thing is to keep the negative sign with the 3.
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| The root symbol, √, requires a symbol of grouping around the radicand. The usual symbol of grouping is a bar (called [[vinculum (symbol)|vinculum]]) over the radicand. Other functions use parentheses around the input to avoid ambiguity. The parentheses are sometimes omitted if the input is a [[monomial]]. Thus, sin x = sin(x), but sin x + y = sin(x) + y, because x + y is not a monomial. Calculators usually require parentheses around all function inputs.
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| Stacked exponents are applied from the top down, i.e., from right to left.
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| Symbols of grouping can be used to override the usual order of operations. Grouped symbols can be treated as a single expression. Symbols of grouping can be removed using the associative and distributive laws, also they can be removed if the expression inside the symbol of grouping is sufficiently simplified so no ambiguity results from their removal.
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| ===Examples===
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| : <math>\sqrt{1+3}+5=\sqrt4+5=2+5=7.\,</math>
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| A horizontal fractional line also acts as a symbol of grouping:
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| : <math>\frac{1+2}{3+4}+5=\frac37+5.</math>
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| For ease in reading, other grouping symbols such as braces, sometimes called curly braces { }, or brackets, sometimes called square brackets [ ], are often used along with parentheses ( ). For example,
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| : <math>[(1+2)-3]-(4-5) = [3-3]-(-1) = 1. \, </math>
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| ===Exceptions to the standard===
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| There exist differing conventions concerning the unary operator − (usually read "minus"). In written or printed mathematics, the expression −3<sup>2</sup> is interpreted to mean −(3<sup>2</sup>) = −9,<ref>[Allen R. Angel, Elementary Algebra for College Students 8/E; Chapter 1, Section 9, Objective 3]</ref> but in some applications and programming languages, notably the application [[Microsoft Office Excel]] and [[bc programming language|the programming language bc]], unary operators have a higher priority than binary operators, that is, the unary minus (negation) has higher precedence than exponentiation, so in those languages −3<sup>2</sup> will be interpreted as (−3)<sup>2</sup> = 9.<ref>{{Cite web|url=http://support.microsoft.com/kb/q132686/ |title=Formula Returns Unexpected Positive Value |publisher=Support.microsoft.com |date=15 August 2005 |accessdate=5 March 2012}}</ref> Note this does not apply to the binary operator −; for example while the formulas <code>=-2^2</code> and <code>=0+-2^2</code> return 4 in Microsoft Excel, the formula <code>=0-2^2</code> returns −4. In cases where there is the possibility that the notation might be misinterpreted, parentheses are usually used to clarify the intended meaning, however due to the syntax of most major programming languages, it is usually hard or impossible to be ambiguous.
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| Similarly, there can be ambiguity in the use of the [[Slash (punctuation)#Arithmetic|slash]] ('/') symbol in expressions such as 1/2''x''. If one rewrites this expression as 1 ÷ 2 × ''x'' and then interprets the division symbol as indicating multiplication by the reciprocal, this becomes
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| : <math>1 \div 2 \times x = 1 \times \tfrac{1}{2} \times x = \tfrac{1}{2}x.</math>
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| Hence, with this interpretation we have that 1/2''x'' is equal to (1/2)''x'', and not 1/(2''x''). However, there are examples, including in published literature, where implied multiplication is interpreted as having higher precedence than division, so that 1/2''x'' equals 1/(2''x''), not (1/2)''x''. For example, the manuscript submission instructions for the ''[[Physical Review]]'' journals state that multiplication is of higher precedence than division with a slash,<ref>{{Cite web|url=https://publish.aps.org/files/styleguide-pr.pdf |title=Physical Review Style and Notation Guide |publisher=[[American Physical Society]]|accessdate=5 August 2012|at=Section IV–E–2–e}}</ref> and this is also the convention observed in prominent physics textbooks such as the ''[[Course of Theoretical Physics]]'' by [[Lev Landau|Landau]] and [[Evgeny Lifshitz|Lifshitz]] and the ''[[Feynman Lectures on Physics]]''.<ref>For example, the third edition of ''Mechanics'' by Landau and Lifshitz contains expressions such as ''hP<sub>z</sub>''/2π (p. 22), and the first volume of the ''Feynman Lectures'' contains expressions such as 1/2{{sqrt|''N''}} (p. 6–8). In both books these expressions are written with the convention that the solidus is evaluated last.</ref> [[Wolfram Alpha]] changed in early 2013 to treat implied multiplication the same as explicit multiplication (formerly, implied multiplication without parentheses was assumed to bind stronger than explicit multiplication). 2''x''/2''x'', 2*''x''/2*''x'', and 2(x)/2(x) now all yield x<sup>2</sup>.<ref>{{Cite web|url=http://www.wolframalpha.com/input/?i=2x%2F2x%2C+2*x%2F2*x%2C+2%28x%29%2F2%28x%29+|title=2x/2x, 2*x/2*x, 2(x)/2(x) - Wolfram|Alpha|publisher=Wolframalpha.com |date= |accessdate=11 February 2013}}</ref> The TI 89 and TI 86 calculators also yield ''x''<sup>2</sup> in all three cases.
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| ==Mnemonics== <!-- Article [[BEDMAS]] redirects to this section. Please use the anchor template if the section name changes -->
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| {{unreferenced section|date=June 2013}}
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| [[Mnemonics]] are often used to help students remember the rules, but the rules taught by the use of acronyms can be misleading. In the United States the acronym ''PEMDAS'' is common. It stands for ''P''arentheses, ''E''xponents, ''M''ultiplication, ''D''ivision, ''A''ddition, ''S''ubtraction. PEMDAS is often expanded to "Please Excuse My Dear Aunt Sally" with the first letter of each word creating the acronym PEMDAS. Canada uses ''BEDMAS''. It stands for ''B''rackets, ''E''xponents, ''D''ivision, ''M''ultiplication, ''A''ddition, ''S''ubtraction. The UK and Australia<ref>http://syllabus.bos.nsw.edu.au/assets/global/files/maths_s3_sampleu1.doc</ref> use ''BODMAS'' or ''BIDMAS''.
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| In Canada and other English speaking countries, ''P''arentheses may be called ''B''rackets, or symbols of inclusion and ''E''xponents may be called either ''I''ndices, ''P''owers or ''O''rders, which have the same precedence as ''R''oots or ''R''adicals. Since multiplication and division are of equal precedence, ''M'' and ''D'' are often interchanged, leading to such acronyms as ''BOMDAS''. The original order of operations in most countries was ''BODMAS'' which stood for ''B''rackets, ''O''rders, ''D''ivision, ''M''ultiplication, ''A''ddition, ''S''ubtraction. This mnemonic was used until exponentials were added into the mnemonic. | |
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| These mnemonics may be misleading when written this way, especially if the user is not aware that multiplication and division are of equal precedence, as are addition and subtraction. Using any of the above rules in the order "addition first, subtraction afterward" would also give the wrong answer to the problem
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| ::<math>10 - 3 + 2 \,</math>.
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| The correct answer is 9 (and not 5, which we get when we do the addition first and then the subtraction). The best way to understand a combination of addition and subtraction is to think of the subtraction as addition of a negative number. In this case, we see the problem as the sum of positive ten, negative three, and positive two. | |
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| ::<math>10 + (-3) + 2 \,</math>
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| To emphasize that addition and subtraction have the same precedence (and multiplication and division have the same precedence) the mnemonic is sometimes written P E MD AS; or, simply as PEMA.
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| All of these acronyms conflate two different ideas, operations on the one hand and symbols of grouping on the other, which can lead to confusion.
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| ==Special cases==
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| If exponentiation is indicated by stacked symbols, the usual rule is to work from the top down, thus
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| : <math> a^{b^c} = a^{(b^c)} </math>,
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| which typically is not equal to <math>(a^b)^c</math>. However, some computer systems may resolve the ambiguous expression differently. For example, [[Microsoft Office Excel]] evaluates ''a''^''b''^''c'' as (''a''^''b'')^''c'' which is opposite of normally accepted convention of top-down order of execution for exponentiation. If a=4, p=3, and q=2, <math>a^{p^q}</math> is evaluated to be 4096 in Microsoft Excel 2013, the same as <math>(a^p)^q</math>. The expression <math> a^{(p^q)} </math>, on the other hand, results in 262144 using the same program.
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| ==Calculators==
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| {{Main|Calculator input methods}}
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| Different calculators follow different orders of operations. Most non-scientific calculators without a stack work left to right without any priority given to different operators, for example giving
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| :<math>1 + 2 \times 3 = 9, \;</math>
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| while more sophisticated calculators will use a more standard priority, for example giving
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| :<math>1 + 2 \times 3 = 7. \;</math>
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| The Microsoft ''[[Calculator (Windows)|Calculator]]'' program uses the former in its standard view and the latter in its scientific and programmer views.
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| The non-scientific calculator expects two operands and an operator. When the next operator is pressed, the expression is immediately evaluated and the answer becomes the left hand of the next operator. Advanced calculators allow entry of the whole expression, grouped as necessary, and evaluates only when the user uses the equals sign.
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| Calculators may associate exponents to the left or to the right depending on the model. For example, the expression a ^ b ^ c on the TI-92, the TI-30XII and the TI-30XS MultiView (all Texas Instruments calculators) associate two different ways:
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| The TI-92 and the TI-30XS MultiView in "MathPrint Mode" associate to the right, that is
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| ::a ^ b ^ c = a ^ (b ^ c) = <math> a^{(b^c)} = a^{b^c}</math>
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| whereas, the TI-30XII and the TI-30XS MultiView in "Classic Mode" associate to the left, that is
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| ::a ^ b ^ c = (a ^ b) ^ c = <math> (a^b)^c.</math>
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| An expression like 1/2''x'' is interpreted as 1/(2''x'') by TI-82, but as (1/2)''x'' by TI-83.<ref>{{cite web
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| | title = Implied Multiplication Versus Explicit Multiplication on TI Graphing Calculators
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| | publisher = Texas Instruments Incorporated
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| | date = 16 January 2011
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| | url = http://epsstore.ti.com/OA_HTML/csksxvm.jsp?nSetId=103110
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| | accessdate = 29 April 2011}}{{citation not found}}</ref>
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| <ref>{{cite web
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| | title = Google cache for: Implied Multiplication Versus Explicit Multiplication on TI Graphing Calculators
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| | publisher = Texas Instruments Incorporated
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| | date = 23 Apr 2013
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| | url = http://archive.is/20130204120803/http://epsstore.ti.com/OA_HTML/csksxvm.jsp?nSetId=103110
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| | accessdate = 10 May 2013}}</ref> While the first interpretation may be expected by some users, only the latter is in agreement with the standard rule that multiplication and division are of equal precedence,{{citation needed|date=May 2013}} so 1/2''x'' is read one divided by two and the answer multiplied by ''x''.
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| When the user is unsure how a calculator will interpret an expression, it is a good idea to use parentheses so there is no ambiguity.
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| Calculators that utilize reverse Polish notation, also known as '''postfix notation,''' use [[Stack (data structure)|stack]] to enter formulas without the need for parentheses.
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| ==Programming languages==
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| Many [[programming languages]] use precedence levels that conform to the order commonly used in mathematics, though some, such as [[APL (programming language)|APL]] and [[Smalltalk]], have no [[Operator (programming)|operator]] precedence rules (in APL, evaluation is strictly right to left; in [[Smalltalk]], it's strictly left to right).
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| The [[logical bitwise operator]]s in [[C (programming language)|C]] (and all programming languages that borrowed precedence rules from C, for example, [[C++]], [[Perl]] and [[PHP]]) have a precedence level that the creator of the C language considered to be unsatisfactory.<ref>[[Dennis M. Ritchie]]: [http://cm.bell-labs.com/who/dmr/chist.html The Development of the C Language]. In History of Programming Languages, 2nd ed., ACM Press 1996.</ref> However, many programmers have become accustomed to this order. The relative precedence levels of [[Operator (programming)|operators]] found in many C-style languages are as follows:
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| {| class="wikitable"
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| |1 || () [] -> . :: || Grouping, scope, array/member access
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| |-
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| |2 || ! ~ - + * & sizeof ''type cast'' ++x --x || (most) unary operations, sizeof and type casts
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| |-
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| |3 || * / % || Multiplication, division, [[modular arithmetic|modulo]]
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| |-
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| |4 || + - || Addition and subtraction
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| |-
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| |5 || << >> || Bitwise shift left and right
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| |-
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| |6 || < <= > >= || Comparisons: less-than, ...
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| |-
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| |7 || == != || Comparisons: equal and not equal
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| |-
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| |8 || & || Bitwise AND
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| |-
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| |9 || ^ || Bitwise exclusive OR
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| |-
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| |10 || <nowiki>|</nowiki> || Bitwise inclusive (normal) OR
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| |-
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| |11 || && || Logical AND
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| |-
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| |12 || <nowiki>||</nowiki> || Logical OR
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| |-
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| |13 || ?: = += -= *= /= %= &= <nowiki>|=</nowiki> ^= <<= >>= || Conditional expression (ternary) and assignment operators
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| |-
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| |14 ||, || [[Comma operator]]
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| |}
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| Examples:
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| * <code>!A + !B</code> ≡ <code>(!A) + (!B)</code>
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| * <code>++A + !B</code> ≡ <code>(++A) + (!B)</code>
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| * <code>A + B * C</code> ≡ <code>A + (B * C)</code>
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| * <code>A || B && C</code> ≡ <code>A || (B && C)</code>
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| * <code>(A && B == C)</code> ≡ <code>(A && (B == C) )</code>
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| [[Source-to-source compiler]]s that compile to multiple languages need to explicitly deal with the issue of different order of operations across languages. [[Haxe]] for example standardizes the order and enforces it by inserting brackets where it is appropriate.<ref>[http://blog.onthewings.net/2011/05/02/six-divided-by-two-bracket-one-plus-two/ 6÷2(1+2)=?] Andy Li's Blog. 2 May 2011. Retrieved 31 December 2012.</ref>
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| The accuracy of software developer knowledge about binary operator precedence has been found to closely follow their frequency of occurrence in source code.<ref>"[http://www.knosof.co.uk/cbook/accu06.html Developer beliefs about binary operator precedence]" Derek M. Jones, CVu 18(4):14–21</ref>
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| ==See also==
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| * [[Common operator notation]] (for a more formal description)
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| * [[Operator associativity]]
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| * [[Associativity]]
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| * [[Commutativity]]
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| * [[Distributivity]]
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| * [[Operator (programming)]]
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| * [[Operator overloading]]
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| * [[C operator precedence|Operator precedence in C and C++]]
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| * [[Reverse Polish Notation]]
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| * [[Hyperoperation]]
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| ==References==
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| <references/>
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| ==External links==
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| *{{planetmath reference|id=3951|title=Order of operations}}
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| {{Use dmy dates|date=June 2011}}
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| {{DEFAULTSORT:Order Of Operations}}
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| [[Category:Abstract algebra]]
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| [[Category:Algebra]]
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| [[Category:Mnemonics]]
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| [[Category:Operators (programming)]]
| |
BMI is short for "body mass index". It's calculated from a person's weight inside kilograms plus height inside meters. The simplest method to determine BMI is to use an online calculator where you connect your fat plus height. A normal BMI is between 18.5 plus 24.9, while 25 to 29.9 is considered to be obese. When we hit a BMI of 30, you're overweight. On the additional hand, these values are less accurate inside athletic persons whom have more lean body mass plus folks that have big frames.
To calculate the waist-to-hip ratio (to keep an acronym it's called the WTHR), measure both a waist plus hips, and divide the waist size by the cool size. And yes, this indicator realizes the difference between guys and women, unlike the BMI. For females, the ratio could be no over 0.8. In different words, your waist ought to be smaller than your hips. And for guys, it should be 1.0 or less. That means that a man's waist must be the same measuring because his hips or smaller. The beer-and-pizza stomach has to go!
In 1972, Ancel Keys gave the concept its more familiar name, Body Mass Index, or BMI. In the 1980s, JS Garrow plus JD Webster suggested arbitrary zones for the BMI--including "overweight" and "obese". And the rest is history.
First, you want to determine an BMI for a child. What is a BMI? BMI stands for body mass index that is a amount that takes into account a child's height-to-weight ratio. There is a rather complex formula for calculating BMI, nevertheless this is completed fast and conveniently at a variety of online sites that provide a bmi calculator. You simply connect the child's fat plus height plus the system will calculate your child's BMI. Finding a bmi calculator may be because simple because doing a Google look for which phrase.
In order to know where you fall found on the body fat charts, you will need to calculate the body fat. There are several ways to do this, from a do it oneself skin fold test, to online calculators. The skin fold test is not (omit) because correct because different techniques. Basically, you're pinching several skin at different body locations, that is measured. This can show the changes in body composition over time, whether or not it's not a totally correct method of calculating body fat.
Another limitation is that age is not considered when calculating BMI. So for elderly people, whether or not the BMI indication is normal, the truth remains which most muscles have been lost considering of age.
There are 3 leading places inside California where you can get California Medical Weight Management program. San Ramon, Watsonville plus Santa Clara are 3 leading places. Get an appointment fixed with the doctor from some of the clinic plus fill the free consultation shape online. Losing weight is fun plus simple for sure from here. It is the fact is the last time to lose weight if you follow it correctly. Moreover, it provides more benefits that you are able to get when you join it. You will truly feel a life changed. Hurry up plus join the fat reduction system today.