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# Bodmas Rule

Introduction to BODMAS :

BODMAS was introduced by Achilles Reselfelt to help in solving mathematical problem involving operational signs. Whenever an operation is introduced in a sum,BODMAS rule is applicable. The BODMAS rule determines the order of operations.

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 )
s = subtraction
First do bracket then powers of next do Division and multiplication then addition and subtraction of the sum. Concerned to bracket,if expression contains all the three types of brackets, the first to be disposed of are round bracket followed by curly brackets and square brackets in turn.

Solve the Problem using BODMAS Rule:

1)   6 + 2*4

Solution:   BODMAS rule is applied here
= 6 + 2*4   multiply the number and then add the numbers
= 6 + 8
= 14

2)  (4 + 5) ÷ 3 + 5

Solution:   Using BODMAS rule
= (4 + 5) ÷ 3 + 5 Bracket is removed first
=   9 ÷ 3 + 5             Division is carried out  and then addition
=   3 + 5
= 8

3)  (4 * 2 + 3)*(10 - 6)*12

Solution:
Step 1:  First simplify the term inside simple bracket by BODMAS rule                                       (solve the bracket and then multiplication is carried out from left to right)
(8 + 3)*(10 - 6)*12

Step 2:  addition and Subtraction is carried out.
11 * 4 * 12

Step 3:  Multiplication is carried out between the term.
528

Fraction and Order of Operation:

1) 2 + $\frac{3}{2}$* 8

Solution:

Step 1: division is carried out first
2 + 3*4

Step 2: Multiply the number and then add from left to right
= 2 + 12
= 14

2)  4 + $\frac{2}{3}$ - 3 + $\frac{1}{2}$

Solution:

Step 1: Taking over  a common denominator between 3 and 2 is 6 division                                  is carried out first

$\frac{6*4}{6}$+$\frac{2*2}{6}$-$\frac{3*6}{6}$+$\frac{3}{6}$

Step 2:  Multiply the numerator

$\frac{24}{6}$+$\frac{4}{6}$-$\frac{18}{6}$+$\frac{3}{6}$

Step 3: add the fractions over a common denominator to a single fraction.

= $\frac{24+4-18+3}{6}$

Step 4: Evaluate using BODMAS (first addition then subtraction)

=  $\frac{5}{6}$

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 Ã— 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 Ã— 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&nbsp;+&nbsp;4&nbsp;&times;&nbsp;5 =&nbsp;4&nbsp;&times;&nbsp;5&nbsp;+&nbsp;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&nbsp;+&nbsp;52 = 28 and 3&nbsp;&times;&nbsp;52 =&nbsp;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&nbsp;+&nbsp;3)&nbsp;&times;&nbsp;4 =&nbsp;20, and to force addition to precede exponentiation, we write (3&nbsp;+&nbsp;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

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 +, âˆ’, *, and / to be applied in any order that obeys this rule. The root symbol, âˆš, 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 =&nbsp;3&nbsp;Ã·&nbsp;4 = 3&nbsp;â€¢&nbsp;Â¼ and 3&nbsp;âˆ’&nbsp;4 = 3&nbsp;+&nbsp;(âˆ’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 âˆ’ (usually read "minus"). In written or printed mathematics, the expression &minus;32 is interpreted to mean &minus;(32)&nbsp;=&nbsp;&minus;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 &minus;32 will be interpreted as (&minus;3)2&nbsp;=&nbsp;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&nbsp;"1/2x" is interpreted by the above conventions as&nbsp;(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

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)

Question:It's my cousin's homework. He's only a First Yr. Student. Pls help me :(

Answers:Let me teach you the B.O.D.M.A.S rule then you can teach it to your cousin. B= Bracket O= Occupations D= Division M= Multiplication A= Addition S= Subtraction Firstly, complete whats in the bracket first. Then move on to the others following the procedure from B to S.

Question:Using Numbers 1 - 10 how many sums can you make and can you list them please, you can not use the same number twice and you have to follow the rules of bodmas :) Thanks x *I meant Number Not Work Sorry (in The Question.

Answers:Do you mean like 1*2*3*5*10*(9-7)/6 ?

Question:Erik says that x+2/x-2 is is simplest form, Phil says that x+2/x-2 can be simplified to -1. Which student is correct? Use algebra terminology to defend him. What was the incorrect student's mistake?

Answers:x+2/x-2 = (x^2 - 2x + 2)/x [BODMAS rule] So Eric is correct.