# Multiplying Fractions

• Jan 12th 2011, 06:31 AM
dumluck
Multiplying Fractions
Hi All,
I'm trying to multiply the below..

$(100*50*10)/(15*10*4) = (50*25*5)/(25*10*n)$

so this would symplify to

$50/3 = 50/50n (n)$ leaving $50/3 = n$

But the answer is n = 3/10. So where did I go wrong?

.. How....?

Thanks,
• Jan 12th 2011, 07:08 AM
bjhopper
Hi dumluck,

Simplifythe equality. Both sides.Then cross multiply.You will then get the right answer

bjh
• Jan 12th 2011, 07:26 AM
dumluck
Quote:

Originally Posted by bjhopper
Hi dumluck,

Simplifythe equality. Both sides.Then cross multiply.You will then get the right answer

bjh

Hi Bjhopper,
OK let me try...

$(100*50*10)/(15*10*4) = (10*5)/(15*4) = (50)/(60)$
$(50 *25*5)/(25*10*n) = (10*5)/(5*2n) = (50)/(10n)$
Cross Multiply $(50)/(60) = (50/10n) : (50)(10n) = (50)(60) : 5n = 30 , n = 6$

Where did I go wrong// I'm trying here :) ?
• Jan 12th 2011, 07:51 AM
Soroban
Hello, dumluck!

Quote:

$\displaystyle \text{Simplify: }\;\frac{100\cdot50\cdot10}{15\cdot10\cdot4} \;=\; \frac{50\cdot25\cdot5}{25\cdot10\cdot n}$

As bjhopper suggested, reduce the fractions first.

$\displaystyle \text{The fraction on the left: }\;\frac{\rlap{///}100^{20}\cdot\rlap{//}50^5\cdot\rlap{//}10^5}{\rlap{//}15_3\cdot\rlap{//}10\cdot\rlap{/}4_2} \;=\;\frac{500}{6} \:=\:\frac{250}{3}$

$\displaystyle\text{The fraction on the right: }\:\frac{50\cdot\rlap{//}25\cdot5}{\rlap{//}25\cdot10\cdot n} \;=\;\frac{\rlap{//}50^5\cdot5}{\rlap{//}10\cdot n} \;=\;\frac{25}{n}$

So we have: . $\displaystyle \frac{250}{3} \:=\:\frac{25}{n}$

$\text{Multiply by }3n\!:\;\;250n \:=\:75 \quad\Rightarrow\quad n \;=\;\dfrac{75}{250} \;=\;\dfrac{3}{10}$

• Jan 12th 2011, 08:05 AM
dumluck
Quote:

Originally Posted by Soroban
Hello, dumluck!

[size=3]
As bjhopper suggested, reduce the fractions first.

$\displaystyle \text{The fraction on the left: }\;\frac{\rlap{///}100^{20}\cdot\rlap{//}50^5\cdot\rlap{//}10^5}{\rlap{//}15_3\cdot\rlap{//}10\cdot\rlap{/}4_2} \;=\;\frac{500}{6} \:=\:\frac{250}{3}$

Thanks Soroban,
In the above where you have seperated the symplification into three fractions (i.e you could put a line between the fractions and symplify each seperately); Is that the typical first step? As in, take each fraction and try to find a divisor, if there are no divisors look at the whole (as you have done with the '25' for the fraction on the right?). The concept I grasp, it seems to be the analysis of the problem I'm not grasping.
• Jan 12th 2011, 08:08 AM
HallsofIvy
Quote:

Originally Posted by dumluck
Hi All,
I'm trying to multiply the below..

$(100*50*10)/(15*10*4) = (50*25*5)/(25*10*n)$

so this would symplify to

$50/3 = 50/50n= (n)$ leaving $50/3 = n$

Your error is thinking that the right side is 50/50n. Canceling the "25"s in numerator and denominator leaves (50*5)(10*n). 10 divides into 50 5 times leaving (5*5)/n= 25/n, not n.

Quote:

But the answer is n = 3/10. So where did I go wrong?

.. How....?

Thanks,
• Jan 12th 2011, 08:14 AM
dumluck
I get it, thanks for that. Phew.... Think I sweated a little there...
• Jan 12th 2011, 09:07 AM
bjhopper
Hi again dumluck,
You are making mistakes in simplifing.Left side simplifies to 250/3.Right side to 25/n.

bjh