Order of precedence itch!

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...

brophya2007

charlie_says wrote: »

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

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 [latex]\frac{12}{\frac{6}{2}}[/latex].

If we take the top division first, we have

[latex]\frac{\left(\frac{12}{6}\right)}{2}=\frac{2}{2}=1 [/latex]

whereas if we take the second division first, we have

[latex]\frac{12}{\left(\frac{6}{2}\right)} = \frac{12}{3} = 4.[/latex]

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

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

brophya2007 wrote: »

Use BIDMAS

Brackets
Indices
Division
Multiplication
Addition
Subtraction

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

DropTables

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

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

charlie_says

Thanks ladies and gentlemen.

MathsManiac

waraf wrote: »

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

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

Clinker, mathsmaniac & RoundTower have the jist of it