Simplify. 3 - a/b over a/b?

Question

Simplify. 3 - a/b over a/b

Answer 1

You start with [3-(a/b)] / (a/b)

To get a/b out of the denomenator, multiply the top and bottom of the fraction by b/a:

[3-(a/b)] * (b/a) = (3b/a) - (ab/ba) = (3b/a) - 1

Now find common denomenators:

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

and there's your answer:

(3b - a) / a

Answer 2

Without parens or brackets you must perform the division first in this expression. The problem is knowing whether the 'over a/b' is for the whole expression or just the '- a/b' portion. I would do the problem like this:

3 - (a/b divided by a/b) = 3 - (a/b * b/a) = 3 - (ab/ab) = 3 - 1 = 2

Follow the rules of order of operations fist exponents, then multiplications and divisions, then additions and subtractions last.

Answer 3

(3 - (a/b) ) / ( a/b ) =
(3 / ( a/b )) - ((a/b) / (a/b) ) = (3 / (a/b )) - 1
= (3b/a) - 1

Answer 4

3-a/b
--------
a/b

=

(3-a/b) * (b/a) = (3b/a) - (ab/ba) = 3b/a - 1

Answer 5

(3-a/b)/(a/b)=(3-a/b)(b/a)
3b/a-1

Answer 6

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