Simplify 8/6 - 2/3 ... What did I do wrong?

Question

I used formula a/b - c/d = (a-c)/(b+d):
8/6 - 2/3 = (8-2)/(6+3) = 6/9,
but the book says the answer is 2/3.
What did I do wrong?

Answer 1

I used formula a/b - c/d = (a-c)/(b+d):
>>that formula is wrong.

What did I do wrong?
>> use the non-existent (or non-proved) formula.

Answer 2

What you did wrong was to depend on remembering a
formula. It's wrong by the way.

Better Method One ......
8/6 is 4/3 so your expression is 4/3 minus 2/3 = 2/3.
3 is the common denominator, so you can directly
subtract the numerators. 4/3 - 2/3 is just like 4 apples
minus 2 apples, or like 4 oranges minus 2 oranges.

Better Method Two ......
Even if you don't notice that 8/6 can be reduced, you
will be heading in the right direction to remember a
principle rather than a formula. What principle? The
principle that you can't add (or subtract) apples and
oranges. 8/6 is a certain number of 6ths, where 4/3 is
a certain number of thirds. Sixths and thirds :: Apples
and oranges. So, you need to somehow come up
with a common denominator. The way we did it in
method one was to get the common denominator "3"
by reducing one of the fractions to lowest terms.
Another way is to multiply the 2nd fraction 2/3 by 2/2
(that's multiplying by 1 by the way, so nothing is changed)
to get 4/6. Now we have a common denominator "6"
so 8/6 - 4/6 = 4/6 which reduces to 2/3. Same answer.

If you insist on using a formula, don't depend on your
memory, which WILL fail you. Use your understanding of
the common denominator idea to figure it out on the spot.

To do (a/b) - (c/d) , use the facts b/b and d/d both = 1 :

(a/b) - (c/d) = (a/b)(d/d) - (c/d)(b/b) = (ad/bd) - (cb/db)

Now, because the denominators bd and db are the same,
you subtract the fractions by subtracting the numerators
and using that as the numerator, over that common
denominator. In short, that equals (ad-cb)/bd.

Use your mind, not your memory.

Answer 3

For simplifying such problems,you don't need formulas
8/6-2/3
=8/6-2/2(2/3)------Mutiplying &Dividing the 2nd term By 2(to equal the denominator),we have
=8/6-4/6
=(8-4)/6
=4/6=2/3 ans But if at all you want to use the formula ,it is a/b-c/d=(ad-bc)/bd

Answer 4

That is very strange. If we subtract 4/6 - 1/3 = (4-1)/(6+3), we get 3/9, and the book says 1/3! What is going on?

Answer 5

8/6 - 2/3 = 8/6 - 4/6 = (8-4)/6 = 2/6 = 1/3

Answer 6

You really don't need to complicate it with formulas. This isn't algebra just simple subtraction of fractions. Get both to a common denominator.
8/6 reduces to 4/3 (by dividing numerator & denominator by 2)
4/3 - 2/3 = 2/3
When subtracting fractions you get them to a common denominator (the bottom number) then subtract the numerators (the upper numbers). Addition works the same way. Don't try to make it so difficult.

Answer 7

8/6 - 2/3 =

Simplify 8/6

4/3 - 2/3
=2/3

Listen to your book :0)

The flaw in your formula:

in order to subtract (a-c), B and D must be equal.

By changing 8/6 to 4/3 (reduce), B and D are equal. So we can do

(A-C)/3

Answer 8

not really sure about that formula. simplify the first fraction with 2 and you get 4/3 - 2/3 which is indeed equal with 2/3

Answer 9

2/3 is 6/9 divided by 3/3.

So it's your answer, but reduced (simplified).
Usually, if you can reduce your answer in fraction form, you should do so. :)

Answer 10

the wrong formula in short

what you ought to ahve used was

a/b - c/d = (ad - cb)/bd

which boils down to

8/6 - 4/6 = 4/6 = 2/3

Answer 11

a/b-c/d=(ad-bc)/bd
8/6-2/3=4/3-2/3=2/3