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Bodmas Problems





BODMAS was introduced by Achilles Reselfelt. It is a designed to aid the memory  for solving  mathematic equation or statement. BODMAS used  to solve the equation systematically in very step of simplification by using brackets of division, multiplication, addition, subtraction. 


For example $\frac{1}{5}$ + 2$\frac{1}{2}$ * 4

In the above example the two operations are addition and multiplication, now there is a problem is whether we should add and then do multiplication  or multiply then carry on addition .Here there is a requirement for the BODMAS operation.

BODMAS Means:

B = brackets
o = of                                    (power  and square root of the terms are carried )
d = division                            (operation carried out from left- right )
m = multiplication               (operation carried out from left- right )
a = addition
s = subtraction

How to solve BODMAS problems:

Few examples are given below to show the use of BODMAS to solve the mathematical simple expression. 
  1. $\frac{50}{5}$ - 20
   The equation consists of both division and subtraction operation.

   Step1:  First divide the term before subtraction according to  BODMAS rule.

                      = 10 - 20

  Step2:  Subtraction is carried out from left to right.
         
                      =  - 10

    2.    $\frac{4}{3}$ of $\frac{4}{5}$ + 1$\frac{3}{5}*\frac{3}{3}$
  
  According to rules of BODMAS simplify and then divide

  Step1:
 First simplify and divide the term.

 $\frac{4}{3}$ 
* $\frac{4}{5}$ + $\frac{8}{5}$ * $\frac{3}{3}$

 Step 2:  Multiply the terms

 $\frac{16}{15}$ + $\frac{24}{15}$

 Step 3:  Addition is carried out from left to right and simplify.

 $\frac{40}{15}$ = $\frac{8}{3}$

3.   ( 3 + 5 - 2) * (20 - 6) * 25 - 95

    Step1:  First simplify the term inside simple bracket by BODMAS rule (addition is carried out from left to right) 

                        ( 8 - 2 ) * ( 20 - 6 ) * 25 - 95

      
Step 2:  Subtraction is carried out.
                      
                        6 * 14 * 25 - 95

     Step 3:  Multiplication is carried out between the term.
                       84 * 25 - 95
                       2100 - 95

     Step 4:  Subtract the term.
                        2005 

Simplification of Fractions including brackets using BODMAS

Example 1: 5 x [15 + {3 (6 -2 )}]

     Step 1:  Solve the inner most simple bracket first and simplify the equation
                       
                        5 x [15 + {3 x 4}]

     Step 2:  Solve the flower bracket first and simplify the equation
                       
                        5 x [15 + 12]

     Step 3:  Solve the box bracket first and simplify the equation

                        5 x 27
                       
                        = 135

Example 2:  $\frac{1}{7}+\left [\frac{7}{9}-(\frac{3}{9}+\frac{2}{9})-\frac{2}{9}  \right ]$

       Step 1: Solve the inner most simple bracket first and simplify the equation

             $\frac{1}{7}+\left [ \frac{7}{9}-\frac{5}{9}-\frac{2}{9} \right ]$
       
Step 2:  Addition and then subtraction are carried out from left to right.

            $\frac{1}{7}$ +  [$\frac{2}{9} - \frac{2}{9}$]    
                
                  $\frac{1}{7}$ + [ 0 ]    
             
Step 3:  Simplify
                                   $\frac{1}{7}$  

Best Results From Wikipedia Yahoo Answers


From Wikipedia

Order of operations

In mathematics and computer programming, the order of operations (more formally precedence rule) is a rule used to unambiguously clarify which procedures should be performed first in a given mathematical expression.

For example, in mathematics and most computer languages multiplication is done first; in the expression 2 + 3 × 4, the algebraic answer is 14. Parentheses, which have their own rules, may be used to avoid confusion, thus the above expression may also be rendered 2 + (3 × 4).

From the introduction of modern algebraic notation, where juxtaposition indicates multiplication of variables, multiplication took precedence over addition, whichever side of a number it appeared on. 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 + 52 = 28 and 3 × 52 = 75. To change the order of operations, originally a vinculum (an overline or underline) was used. Today we use parentheses. Thus, to force addition to precede multiplication, we write (2 + 3) × 4 = 20, and to force addition to precede exponentiation, we write (3 + 5)2 = 64

The standard order of operations

The standard order of operations, or precedence, is expressed in the following chart.

terms inside brackets
exponents and roots
multiplication and division
addition and subtraction

This means that if a number or other symbol, or an expression grouped by one or more symbols of grouping, is preceded by one operator and followed by another, the operator higher on the list should be applied first. The commutative and associative laws of addition and multiplication allow the operators +, −, *, and / to be applied in any order that obeys this rule. The root symbol, √, requires either parentheses around the radicand or a bar (called vinculum) over the radicand. Stacked exponents are applied from the top down.

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 Ã· 4 = 3 â€¢ Â¼ and 3 âˆ’ 4 = 3 + (−4), that is, the sum of positive three and negative four.

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.

Examples

\sqrt{1+3}+5=\sqrt4+5=2+5=7.\,

A horizontal fractional line also acts as a symbol of grouping:

\frac{1+2}{3+4}+5=\frac37+5.

For ease in reading, other grouping symbols (such as curly braces {} or square brackets [] ) are often used along with the standard round parentheses, e.g.

[(1+2)-3]-(4-5) = [3-3]-(-1) = 1. \,

Unfortunately, there exist differing conventions concerning the unary operator − (usually read "minus"). In written or printed mathematics, the expression −32 is interpreted to mean −(32) = −9, but in some applications and programming languages, notably the application Microsoft Office Excel and 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 −32 will be interpreted as (−3)2 = 9. [http://support.microsoft.com/kb/q132686/]. In any case where there is a possibility that the notation might be misinterpreted, it is advisable to use parentheses to clarify which interpretation is intended.

Similarly, care must be exercised when using the slash ('/') symbol. The string of characters "1/2x" is interpreted by the above conventions as (1/2)x. The contrary interpretation should be written explicitly as 1/(2x). Again, the use of parentheses will clarify the meaning and should be used if there is any chance of misinterpretation.

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 acronymPEMDAS or "Please Excuse My Dear Aunt Sally" is common. It stands for Parentheses, Exponentiation, Multiplication, Division, Addition, Subtraction. In other English speaking countries, Parentheses may be called Brackets, and Exponentiation may be called either Indices, Powers or Orders, and since multiplication and division are of equal precedence, M and D are often interchanged, leading to such acronyms as BEDMAS, BIDMAS, BIMDAS, BODMAS, BOMDAS, BERDMAS, PERDMAS, and BPODMAS.

These mnemonics may be misleading, 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.

10 - 3 + 2 \,

The correct answer is 9, which is best understood by thinking of the problem as the sum of positive ten, negative three, and positive two.

10 + (-3) + 2 \,

There is a new mnemonic featured in Danica McKellar's books Math Doesn't Suck and Kiss My Math that does address this very issue: "Pandas Eat: Mustard on Dumplings, and Apples with Spice." The intention being that Mustard and Dumplings is a "dinner course" and that Apples and Spice is a "dessert course." Then it becomes not a linear string of operations to do one after the other, but rather the "dinner course" operations are considered together and performed left to right, and then addition and subtraction are considered together, again performed again left to right.

In college mathematics, the rules of priority are (usually) taught correctly, and students are taught the commutative law, associative law, and distributive law, which replace the grade school "rules". The "left to right" rule is not a law of mathematics.

For example,

17 \times 24 / 12 \,

is much easier whe


From Yahoo Answers

Question:I think there is something called binary operations in order to help do work out an algebra problem in which order to work when there are parenthese and brackets and operators? BODMAS? Can someone provide how you work an equation showing these?

Answers:PEMDAS is what you're thinking of. Parentheses (work left to right from innermost brackets outward) Exponents Multiplication Division Addition Subtraction

Question:I'm actually in Algebra 2, but this is the problem. 1/x+4 = 0 That's one divided by X+4. I need to solve for X. How do you do it, and what is the answer? What I usually do is multiply both sides by X+4 to eliminate the denominator on the left side of the equation. But when you do that, the X is gone! It then says 1 = 0, which makes no sense to me! HELPPPPP! My entire homework is based off of problems like these. Ughh, all three of you said different things! Which one is right!?

Answers:1/x+4 = 0 That's one divided by X+4 Ah, but it isn't. Divide takes precedence over addition (remember BODMAS http://www.mathsisfun.com/operation-order-bodmas.html ) so this means (1/x) + 4 = 0 which you can solve (1/x) + 4 = 0 (1/x) = -4 x= 1/-4 = -1/4 PS Those who don't believe me and want to mark this down because it's an unpopular answer, try it with http://www.myalgebra.com, an online algebra solver, or any mathematics package such as Maple or Mathematica. You'll get -1/4. PPS Re "Ughh, all three of you said different things!" - a lot of answers are forgetting (and those remembering not explaining) BODMAS; the standard order of operations for arithmetic and algebra. D (for division) is done before A (for addition). So if you saw 1/5+4, that means (1/5) + 4, not 1/(5+4). Likewise, 1/x+4 means (1/x) + 4, not 1/(x+4). PPPS Heather S - noooooo! 1/x=-4 1 = -4x .... i.e. multiply both sides by x 1/-4 = x ... i.e. divide both sides by -4 x = -1/4 ... simplify

Question:I am tutoring a boy for an entrance test in 5th grade in the DPS STS School. Being a student of 6th grade, I don't feel very confident about it.... Their entrance test syllabus is: English: Children are expected to read an unfamiliar text in English at a reasonable speed with a fairly good comprehension Expected to answer questions using grammatically correct and complete sentences based on unseen passage Expected to give meanings of words in a context and provide antonyms or synonyms as asked Expected to have the ability to write grammatically correct sentences and to be able to express themselves clearly in English Should be able to describe objects and narrate experiences Punctuation Story Writing Maths: Expected to find fractions, factor and multiples, percentage, sum, difference and product and quotient of bigger number. Must know the basics of geometry and should be able to identify figures like circles, cuboids, cones, cylinders and spheres etc Subtraction Division Fractions and multiples Measurement- capacity conversion (l-ml) (gm-Kg) (m-Km) Multiplication- multiplying 3 digit X 2 digit Time- calculation duration in hours and minutes BODMAS Data Handling- Range, Mode, Median, Mean Probability Number Properties Divisibility by 3,4,6,8 Multiples I don't know where to start and what to do. Can you recommend some worksheet and exercises I can do to teach him? I need urgent help! His test is on Friday!

Answers:It would probably be easiest to start with some simple flash cards to gauge what he already knows (unless you already know him). You might could even make some math word problems to hit both English and math at once.

Question:I am in 8th grade and needed to research the four rules of multiplying, dividing, subtracting and adding integers. By rules i mean ways to do problems like (-8)(-5)= x. So yea i dont remember how to do those so it would really help for somone to post a question and give me four examples of how to +, -, *, and / integers.

Answers:this short form do helps me 2 remember, that is BODMAS B = Bracket { [ ( ) ] } O = of D = Division / M = Multiplication x A = Addition + S = Subtraction - (-8)(-5)= x -8 x -5 = x -40 = x x = -40 (if am not wrong)