For all you math whizzes, I need help with a Singapore problem . . .

[Jackie in AR]

[2(a-b)] - [(a/3 + b/4) + (a/6 - 3b/4)] =

 

The answer is 3/2(a-b) according to the book.

 

Will someone please show me how to work this problem correctly?

 

Thanks!

[Krista in LA]

[2(a-b)] - [(a/3 + b/4) + (a/6 - 3b/4)] =

 

The answer is 3/2(a-b) according to the book.

 

Will someone please show me how to work this problem correctly?

 

Thanks!

 

The lowest common demonitator for 3, 4, and 6 is 12 so you need to multiply each fraction to get it over 12.

 

(12/12)* [2(a-b)] - {[(4/4)(a/3) + (3/3)(b/4)] + [(2/2)(a/6) - (3/3)(3b/4)]} =

 

24(a-b)/12 - [(4a/12) + (3b/12) + 2a/12 - 9b/12)] =

(24a-24b)/12 - [(6a-6b)/12] =

(18a-18b)/12 =

18(a-b)/12 =

3(a-b)/2 = 3/2 (a-b)

[Snickerdoodle]

:)

[Kat in GA]

[2(a-b)] - [(a/3 + b/4) + (a/6 - 3b/4)] =

 

The answer is 3/2(a-b) according to the book.

 

Will someone please show me how to work this problem correctly?

 

Thanks!

 

Here is a slight variation on the other answer:

 

First get rid of the brackets:

2a - 2b - a/3 - b/4 - a/6 + 3b/4

 

Change all the a's to sixths and all the b's to fourths:

 

12a/6 - 8b/4 - 2a/6 - b/4 - a/6 + 3b/4 = 9a/6 - 6b/4

 

Then you reduce: 3a/2 - 3b/2 = 3/2 (a - b)

[JenneinCA]

[2(a-b)] - [(a/3 + b/4) + (a/6 - 3b/4)] =

 

distributing the 2 and the negative: 2a-2b -a/3 -b/4 -a/6 +3b/4 =

 

Common denominator of 12: 24a/12 -24b/12 -4a/12 -3b/12 -2a/12 +9b/12

 

Reorder to put like terms together: 24a/12 -4a/12 -2a/12 -24b/12 -3b/12 +9b/12

 

Combine like terms: (24a-4a-2a)/12 + (-24b-3b+9b)/12

 

More combining: 18a/12 + (-18b)/12

 

Simplifying: 3a/2 -3b/2

 

More simplifying: (3a-3b)/2

 

Still more: (3/2)(a-b)

[Jackie in AR]

Here is what I did wrong: I multiplied each term by 12 instead of 12/12 as I should have.

 

And when I divide the answer I came up with (18a-18b) by 12, I get 3/2 (a-b).

 

Many thanks to all of you!!