What-is-DMAS-rule-Where-is-it-followed-Do-we-follow-this-rule-

Question Number 2917 by Rasheed Soomro last updated on 30/Nov/15

W h a t i s D M A S r u l e ? W h e r e i s i t f o l l o w e d ?

D o w e f o l l o w t h i s r u l e ?

Answered by 123456 last updated on 30/Nov/15

if i understanded it about order of operation

like

1 + 2 \times 3 = 1 + 6 = 7

1 + 2 \times 3 \neq 3 \times 3 = 9

Division Multiplication Adition Subtration

48 \div 2 (9 + 3) = 288 or 2

however in general if you want avoid

confusion is beter to use patents, like

48 \div [2 (9 + 3)] = 2

or

(48 \div 2) (9 + 3) = 288

Commented by Rasheed Soomro last updated on 30/Nov/15

I c l a i m t h a t w e {d o n}^{'} t f o l l o w t h i s r u l e .

T h i s r u l e s u g g e s t s a d d i t i o n b e f o r e s u b t r a c t i o n,

b u t w e {d o n}^{'} t d o s o . F o r e x a m p l e

B y d m a s r u l e 12 - 2 + 3 = 12 - (2 + 3) = 12 - 5 = 7

W h e r e a s w e c o n c l u d e 13 .

I f w e {d o n}^{'} t f o l l o w t h i s r u l e t h e n w h e r e i s i t f o l l o w e d ? ? ?

Commented by Filup last updated on 30/Nov/15

When you have, addition or subtraction,

you can do it in any order if you make

all terms positive - 7 = + (- 7)

And you always work left to right

Commented by prakash jain last updated on 30/Nov/15

DM is Division or Multiplication from L to R

AS is Adition or Subtration from L to R

Rule does not give priority to addition

over subtraction . Also Same priority is

given to Multiplication and Division .

Some other acronymns

PEMDAS : Multiplication even though

it appears before division is given the same

priority . All expressions are always evaluated

from left to right .

Commented by Filup last updated on 30/Nov/15

DMAS works using parentheses laws

That means, everything is made to work

with a addititve opperator^{'} +^{'} .

e . g .

- 2 + 5 \times - 6 + 12 - 7

= + (- 2) + (5 \times (- 6)) + 12 + (- 7)

= 5 \times (- 6) + 12 + (- 7) + (- 2)

= - 30 + 12 - 7 - 2

= - 9

Commented by Rasheed Soomro last updated on 30/Nov/15

O n t h e c o m m e n t o f S i r p r a k a s h

I {c a n}^{'} t r e j e c t y o u r i n t e r p r e t a t i o n o f D M A S .

B u t s o m e w o r d s a b o u t m y i n t e r p r e t a t i o n :

S o m e t i m e a g o I h a d a c h a n c e t o s t u d y a t e x t b o o k

o f m a t h s C o u n t D o w n S e r i e s f o r c l a s s V (?) b y

O x f o r d U n i v e r s i t y P ress . T h e r e I h a d r e a d t h e

i n t e r p r e t a t i o n o f D M A S w h i c h w a s t h a t o f m i n e .

I - E a d d i t i o n b e f o r e s u b t r a c t i o n . T h e b o o k

h a d g i v e n a c l e a r e x a m p l e . S i n c e t h a t I b e g a n t o

t h i n k t h a t D M A S i s a d i f f e r e n t c o n v e n t i o n .

Commented by Filup last updated on 01/Dec/15

A l s o, R a s h e e d, in your earlier comment

you mentioned how by if you follow

dmas you do addition first making :

12 - 2 + 3 = 12 - (2 + 3) .

That is incorret . Following dmas

you obtain :

12 - 2 + 3 = 12 + (- 2 + 3)

Commented by Filup last updated on 01/Dec/15

I was always taught that dmas is :

^{'} d i v i s i o n a n d {m u l t i p l i c a t i o n}^{'} T H E N

^{'} s u b t r a c t i o n a n d {a d d i t i o n}^{'} .

You can do \times and \div in any order similar

to + and - in any order .

2 \times 3 \div 4 = \frac{(2 \times 3)}{4} = 2 \times (\frac{3}{4})

2 - 3 + 4 = (2 - 3) + 4 = 2 + (- 3 + 4)

Commented by Rasheed Soomro last updated on 01/Dec/15

M r F i l u p

W h e n y o u w r i t e 12 - 2 + 3 a s 12 + (- 2) + 3

^{'} -^{'} r e m a i n s n o l o n g e r b i n a r y o p e r a t i o n . I n t h e

l a t t e r f o r m^{'} -^{'} i s u n a r y o p e r a t i o n a n d D M A S

r u l e i s a b o u t o r d e r o f b i n a r y o p e r a t i o n s . Y o u

s u g g e s t a n a l t e r n a t e w h e r e a s I t h i n k w h a t

t h e r u l e r e q u i r e i n a c t u a l e x p r e s s i o n .

A c t u a l l y m a t t e r {i s n}^{'} t i t h o w c o u l d w e c a l c u l a t e

a n e x p r e s s i o n . M a t t e r i s w h a t i s a n i n t e r p r e t a t i o n

o f D M A S .

O n e i n t e r p r e t a t i o n i s t h a t M r p r a k a s h h a s

m e n t i o n e d . O t h e r i n t e r p r e t a t i o n i s w h a t I h a d

r e a d s o m e t i m e a g o .

T h e i n t e r p r e t a t i o n m e n t i o n e d b y M r p r a k a s h

i s c o n s i s t e n t w i t h o u r w a y o f c a l c u l a t i o n w h e r e a s

i n t e r p r e t a t i o n m e n t i o n e d b y m e i s n o t c o m p a t i b l e .

A n y w a y D M A S i s m a t t e r o f c o n v e n t i o n a n d

m y p r o b l e m i t s a c t u a l i n t e r p r e t a t i o n . {T h a t}^{'} s a l l .

Commented by 123456 last updated on 01/Dec/15

sum is associative and comutative

so you can take it in any order

(x + y) + z = x + (y + z) = x + (z + y)

however subtraction dont is comutative in geeral

x - y \neq y - x

and dont is associative in general

x - (y - z) = x - y + z

(x - y) - z = x - y - z

x - (y - z) \neq (x - y) - z

Commented by 123456 last updated on 01/Dec/15

2 \times 3 \div 4 = 2 \times \frac{3}{4} = \frac{2 \times 3}{4} = \frac{3}{2}

however if you interchange \times with \div

the order will be important

2 \div 3 \times 4

2 \div (3 \times 4) = \frac{2}{3 \times 4} = \frac{2}{12} = \frac{1}{6}

(2 \div 3) \times 4 = \frac{2}{3} \times 4 = \frac{8}{3}

Commented by Rasheed Soomro last updated on 01/Dec/15

M a t t e r i s i n t e r p r e t a t i n g D M A S r u l e .

Commented by Filup last updated on 01/Dec/15

It is more of a matter of interperating

the parenthese laws . The dmas law

is heavily weighed onto the ability

to correctly apply parenthesise .

Commented by Rasheed Soomro last updated on 01/Dec/15

^{'} M u l t i p l i c a t i o n h a s p r i o r i t y o v e r {a d d i t i o n}^{'} . N o d o u b t i t

i s . B u t t h i s i s o n l y b y c o n v e n t i o n . I t i s o n l y t h i s

c o n v e n t i o n, f o r w h i c h w e w r i t e 5 + 6 \times 8 i n s t e a d o f

5 + (6 \times 8) . T h i s p r i o r i t y i s m a n - m a d e . I f t h e r e w e r e

a c o n v e n t i o n i n w h i c h a d d i t i o n h a d p r i o r i t y o v e r

m u l t i p l i c a t i o n t h e n w e h a d w r i t t e n 5 + 6 \times 8 i n s t e a d o f (5 + 6) \times 8

a n d 5 + 6 \times 8 w e r e c a l c u l a t e d a s u n d e r

5 + 6 \times 8 = 11 \times 8 = 88

S o p r i o r i t y i s p u r e l y m a n - m a d e .

D i c i s i o n t o p a r e n t h e c i s e o n e o p e r a t i o n a n d l e a v e o t h e r

i s p u r e l y m a n - m a d e .

O n e e x a m p l e o f p r i o r i t y t o b e m a n - m a d e i s a s u n d e r :

- 3^{2} i s c o n s i d e r d a s - (3^{2}) i n o u r c o n v e n t i o n, b u t i n s o m e

c o m p u t e r p r o g r a m s i t i s t r e a t e d a s {(- 3)}^{2} .