Order of precedence itch!

charlie_says · 19-08-2009, 18:03

Could some one please explain as it isn't in my maths book what to do with the order of precedence rules when dealing with fractions of fractions that have brackets with some of the terms, and include exponents, further divison, addition and subtraction.

Example I photo'd and uploaded (it was faster than writing it out onscreen

)

Thanks, I'm not looking for an answer to the problem in the image just the way to attack it using the precedence rules, the order confuses me with so much going on...

brophya2007 · 19-08-2009, 18:08

Quote:

Originally Posted by charlie_says

Could some one please explain as it isn't in my maths book what to do with the order of precedence rules when dealing with fractions of fractions that have brackets with some of the terms, and include exponents, further divison, addition and subtraction.

Example I photo'd and uploaded (it was faster than writing it out onscreen

)

Thanks, I'm not looking for an answer to the problem in the image just the way to attack it using the precedence rules, the order confuses me with so much going on...

Use BIDMAS

Brackets
Indices
Division
Multiplication
Addition
Subtraction

Clinker · 19-08-2009, 19:33

Order of precedence won't help you here: a triple-decker fraction is inherently ambiguous, unless brackets are provided to show which division comes first. Sometimes one of the fraction lines is heavier or longer to give some guidance.

Consider the expression $\frac{12}{\frac{6}{2}}$ .

If we take the top division first, we have

$\frac{\left(\frac{12}{6}\right)}{2}=\frac{2}{2}=1$

whereas if we take the second division first, we have

$\frac{12}{\left(\frac{6}{2}\right)} = \frac{12}{3} = 4.$

As it can produce two different values, the expression is not well-defined: in other words it's meaningless, unless brackets are provided. As the two operations are the same, order of precedence can't help you: that tells you the order in which you perform different operations.

RoundTower · 20-08-2009, 13:06

if you see a triple-decker fraction like this you can expect to see one big thick line and one skinny one. In that case the big thick one takes precedence, which means you have to do the other one first.

waraf · 20-08-2009, 13:22

Quote:

Originally Posted by brophya2007

Use BIDMAS

Brackets
Indices
Division
Multiplication
Addition
Subtraction

Shouldn't multiplication come before division as in BOMDAS (Brackets Ordinals Multiplication Division Addition Subtraction)

DropTables · 20-08-2009, 14:05

It doesn't matter
(3 * 4 )/5 = 3 * (4/5)

http://en.wikipedia.org/wiki/Order_of_operations

charlie_says · 20-08-2009, 14:23

Thanks ladies and gentlemen.

MathsManiac · 20-08-2009, 17:15

Quote:

Originally Posted by waraf

Shouldn't multiplication come before division as in BOMDAS (Brackets Ordinals Multiplication Division Addition Subtraction)

No! Multiplication and division have equal precedence, as do addition and subtraction.

Generally, operations of equal precedence are evaluated from left to right:

5 + 4 - 2 = (5+4) - 2 = 7
5 - 4 + 2 = (5-4) + 2 = 3
5 * 4 / 2 = (5*4) / 2 = 10
5 / 4 * 2 = (5/4) * 2 = 2.5

FirtY · 21-08-2009, 19:17

@waraf I think you'll find it's BODMAS

Clinker, mathsmaniac & RoundTower have the jist of it

19-08-2009, 18:03	#1
charlie_says Registered User Join Date: Aug 2003 Location: Galway Posts: 262 Adverts \| Friends	Order of precedence itch! Could some one please explain as it isn't in my maths book what to do with the order of precedence rules when dealing with fractions of fractions that have brackets with some of the terms, and include exponents, further divison, addition and subtraction. Example I photo'd and uploaded (it was faster than writing it out onscreen ) Thanks, I'm not looking for an answer to the problem in the image just the way to attack it using the precedence rules, the order confuses me with so much going on... __________________ The boy is father to the man.

20-08-2009, 14:23	#7
charlie_says Registered User Join Date: Aug 2003 Location: Galway Posts: 262 Adverts \| Friends	Thanks ladies and gentlemen. __________________ The boy is father to the man.

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19-08-2009, 19:33	#3
Clinker Registered User Join Date: Mar 2009 Location: Dun Laoghaire Posts: 126 Adverts \| Friends	Order of precedence won't help you here: a triple-decker fraction is inherently ambiguous, unless brackets are provided to show which division comes first. Sometimes one of the fraction lines is heavier or longer to give some guidance. Consider the expression $\frac{12}{\frac{6}{2}}$ . If we take the top division first, we have $\frac{\left(\frac{12}{6}\right)}{2}=\frac{2}{2}=1$ whereas if we take the second division first, we have $\frac{12}{\left(\frac{6}{2}\right)} = \frac{12}{3} = 4.$ As it can produce two different values, the expression is not well-defined: in other words it's meaningless, unless brackets are provided. As the two operations are the same, order of precedence can't help you: that tells you the order in which you perform different operations.

20-08-2009, 13:06	#4
RoundTower Registered User Join Date: Nov 2004 Location: turning AA into a bluff, preflop Posts: 5,031 Adverts \| Friends	if you see a triple-decker fraction like this you can expect to see one big thick line and one skinny one. In that case the big thick one takes precedence, which means you have to do the other one first.

20-08-2009, 14:05	#6
DropTables Registered User Join Date: Aug 2009 Location: Urth Posts: 10 Adverts \| Friends	It doesn't matter (3 * 4 )/5 = 3 * (4/5) http://en.wikipedia.org/wiki/Order_of_operations

21-08-2009, 19:17	#9
FirtY Registered User Join Date: Jul 2009 Posts: 5 Adverts \| Friends	@waraf I think you'll find it's BODMAS Clinker, mathsmaniac & RoundTower have the jist of it