1. ## Multiplying Fractions

Hi All,
I'm trying to multiply the below..

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

so this would symplify to

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

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

.. How....?

Thanks,

2. Hi dumluck,

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

bjh

3. 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...

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

Where did I go wrong// I'm trying here ?

4. Hello, dumluck!

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

As bjhopper suggested, reduce the fractions first.

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

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

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

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

5. Originally Posted by Soroban
Hello, dumluck!

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

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

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

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

so this would symplify to

$\displaystyle 50/3 = 50/50n= (n)$ leaving $\displaystyle 50/3 = n$
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.

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

.. How....?

Thanks,

7. I get it, thanks for that. Phew.... Think I sweated a little there...

8. Hi again dumluck,
You are making mistakes in simplifing.Left side simplifies to 250/3.Right side to 25/n.

bjh