3(v+5)+6(v-10)+2v=0
3v+15+6v-60+2v=0
11v-45=0
11v=45
v=45/11
v=4.09
U need to use the smaller denominator(600).then u will not get confuse.
yes, okay that's one way, but why can't IThe first thing edwintan did was multiply both sides by the "least common multiple" of the three denominators, 600. That immediately gets rid of all fractions.
take the lowest common denominator of the three
which is 600 and use it as a divider like this:
a) 200 goes into 600 3 times... so multiply first
term by 3/3
b) 100 goes into 600 6 times... so multiply 2nd
term by 6/6
c) 300 goes into 600 2 times... so multiply 3rd
item by 2/2
this should be legal as we do the same for this:
1/2 + 2/3
so,
lowest common den= 6
2 goes into 6 3 times so mul by 3/3
and 3 goes into 6 2 times so mul by 2/2
therefore:
(3/3 x 1/2) + (2/2 x 2/3)
becomes:
3/6 + 4/6 = 7/6
why can't we do this with the 600 in my initial example???
no you won't!Your example is using 60000 .U can use 60000 and try it. U will still get the same answer.
using 60000 as a common denominator:
a) 200 goes into 600 3 times... so multiply first term by 300/300
b) 100 goes into 600 6 times... so multiply 2nd term by 600/600
c) 300 goes into 600 2 times... so multiply 3rd item by 200/200
(300/300) x (v+5/200) + (600/600) x (v-10/100) + (200/200) (v/300) = 0
300(v+5/200)/60000 + 600(v-10/100)/60000 + 200v/60000 = 0
(300v + 1500 + 600v - 6000 + 200v) / 60000 = 0
(1100v +1500 - 6000) / 60000 = 0
(1100v - 4500) = 60000
1100v = 60000 + 4500
v = 64500/1100
v = 58.6 ???
*** BUT ***
why is it the using the same analogy as above it works for a similar equation like this:
1/2 + 2/3
lowest common denominator= 6
a) 2 goes into 6 3 times so multiply 1st term by 3/3
b) 3 goes into 6 2 times so multiply 2nd term by 2/2
therefore doing the exact same reasoning as the equation above we do:
(3/3 x 1/2) + (2/2 x 2/3)
becomes:
3/6 + 4/6 = 7/6
and why here it works and above it doesn't??
someone... anyone please...
thanks
(300/300) x (v+5/200) + (600/600) x (v-10/100) + (200/200) (v/300) = 0
300(v+5/200)/60000 + 600(v-10/100)/60000 + 200v/60000 = 0
(300v + 1500 + 600v - 6000 + 200v) / 60000 = 0
(1100v +1500 - 6000) / 60000 = 0
(1100v - 4500) = 60000
1100v = 60000 + 4500
v = 64500/1100
v = 58.6 ???
As per above u are using the wrong method .see below for the correction..
(1100v +1500 - 6000) / 60000 = 0
1100v-4500/60000=0/1
60000/60000 x (1100v-4500)=60000/1 x 0
therefore it become 1100v - 4500 = 0
1100v = 4500
v=4500/1100
v=45/11 = 4.09
Some of your working method is wrong..
isn't the symbol u used on the right of the equal sign the symbol for golden ratio?
Besides the point ,u can't just multiply 600/300 and 600/200 with the fractions just to get the denominators even, 'cause u would change the fraction entirely. its just like multiplying by 2 and 3, respectively.
However, multiplying to get common denominators of 60000 to solve for v works just as well:
[(v+5)/200]*(300/300) + [(v-10)/100]*(600/600) + [v/300]*(200/200) = 0
{ (v+5)/200]*(600/300) + [(v-10)/100]*(600/600) + [v/300]*(600/200) DOESNOT= 0 }
(300v+1500)/60000 + (600v-6000)/60000 + 200v/60000 = 0
300v+1500+600v-6000+200v = 0
1100v-4500 = 0
1100v = 4500
11v = 45
v = 45/11 = 4.09