# fractions witin fractions

• Jul 18th 2012, 11:35 AM
ReginaldCuthbert
fractions witin fractions
i wasn't paying attention in class. i'm guessing for this one problem correct me if i'm wrong.

3/5/7 = 21/5

that may be confussing so in word form it's 3 over 5 over 7. to solve the the problem i multiplied the whole thing by 7 to cancel out the 7 on the bottom. that's the right answer right?

right?
• Jul 18th 2012, 11:48 AM
Plato
Re: fractions witin fractions
Quote:

Originally Posted by ReginaldCuthbert
i wasn't paying attention in class. i'm guessing for this one problem correct me if i'm wrong.
3/5/7 = 21/5

$\displaystyle \frac{{\left( {\frac{3}{5}} \right)}}{7}\text{ or }\frac{3}{{\left( {\frac{5}{7}} \right)}}~?$

Using usual order order of operations, which would it be?

Look at this.
• Jul 18th 2012, 11:57 AM
skeeter
Re: fractions witin fractions
$\displaystyle 3 \div \frac{5}{7} = 3 \cdot \frac{7}{5} = \frac{21}{5}$
• Jul 18th 2012, 12:10 PM
HallsofIvy
Re: fractions witin fractions
But $\displaystyle \frac{\frac{3}{5}}{7}= \frac{3}{5}\frac{1}{7}= \frac{3}{35}$
As Plato said, "3/5/7" is bad notation as it is ambiguous. It could mean (3/5)/7 or 3/(5/7) and those are different.

(The basic arithmetic operations are defined on two numbers at a time. When we write "3+ 5+ 7" or "3*5*7" we could mean "(3+ 5)+7" or "3+(5+7)", "(3*5)*7" or "3*(5*7)". In the case of addition or products, those are the same so it doesn't matter. For the "inverse" operations, "3-5-7" or "3/5/7" that is not true. (3- 5)- 7 and 3- (5-7) are NOT the same, (3/5)/7 and 3/(5/7) are NOT the same.

(Technically, we say that addition and multiplication are "associative". Subtraction and division are not associative operations.)