Where did the 2 come from

1. Jan 14, 2015

jim1174

I need some help with this fraction problem. 8 5/6 - 1 1/3 you Need to rewrite the problem as 8 5/6 - 1 2/3 where did the two come from ?

2. Jan 14, 2015

Stephen Tashi

Can you show the whole text of this problem and supposed solution?

3. Jan 14, 2015

jim1174

The problem is 8 5/6 - 1 1/3 the answer is 8 5/6 - 1 2/6 answer 7 1/2 I just want to know how they got the 2 in 2/6

4. Jan 15, 2015

Staff: Mentor

The expression is either 8 5/6 - 1 1/3 or 8 5/6 - 1 2/3. The two are not the same.

Since the answer is 7 1/2, the problem must have been 8 5/6 - 1 1/3. The only explanation for 8 5/6 - 1 2/3 is that it's a typo.

Edit: Jim, I didn't notice that you revised what you wrote in your later post. 1 1/3 is the same as 1 2/6.

5. Jan 15, 2015

Stephen Tashi

They changed 1/3 to 2/6 by multiplying the top and bottom of the fraction 1/3 by the number 2.

6. Jan 15, 2015

jim1174

The question is 8 5/6 - 1 1/3 you are supposed to re write the problem as 8 5/6 - 1 2/6 what I want to know is when they changed the 1/3 to 2/6 where did the two come from

7. Jan 15, 2015

Staff: Mentor

You can multiply the top of a fraction by any number so long as you multiply the bottom of that fraction by the same AND THIS DOESN'T CHANGE THE VALUE of that fraction.

So 1/3 is equivalent to 2/6 in all regards.

QUESTION: Would you prefer 1 slice of a pie after the pie was cut up into 3 equal pieces, or
would you prefer 2 slices of the same pie after it had been cut into 6 pieces?

ANS: there is no difference!

The decision to convert the denominator into a 6 was so that it matched the denominator of the first fraction in the problem.

Last edited: Jan 15, 2015
8. Jan 15, 2015

Staff: Mentor

If I may propose a different way of seeing it: any number multiplied by 1 is the same number. Therefore, you can always multiply any fraction by $n/n$ (provided $n$ is not zero!):

$$\frac{1}{3} = \frac{1}{3} \times 1 = \frac{1}{3} \times \frac{2}{2} = \frac{2}{6}$$