# Finding an unknown value

• Nov 18th 2011, 05:09 AM
David Green
Finding an unknown value
Starting a new thread because I made a muck of the last attempt.

1 divided by u, + 1 divided by v, = 1 divided by f

I am required to find the value of V

If u = 4/5

If f = 2/3

V = !

4/5 - 2/3 = 2/15

2/15 = 3 x 2 = 6 = 2
..........3 x 5 15 5

so is my value V = 5?

I am not sure and think there must be another way to ensure the numerator is equal to 1

Thanks

David
• Nov 18th 2011, 05:33 AM
DPaine86
Re: Finding an unknown value
For this problem you need to solve the equation for v.

Start by substituting the algebraic terms with the values provided, i.e. u = \$\displaystyle {4}{5}\$ and f = \$\displaystyle {2}{3}\$.

Therefore, the equation is as follows:

\$\displaystyle {1}{4/5} + {1}{v} = {1}{2/3}\$

This becomes:

\$\displaystyle {5}{4} + {1}{v} = {3}{2}\$ - because having '1' on top of a fraction inverts the fraction.

The equation is then solved as follows:

\$\displaystyle {5v}{4v} + {4}{4v} = {3}{2}\$
\$\displaystyle {5v+4}{4v} = {3}{2}\$
\$\displaystyle 10v+8 = 12v\$
\$\displaystyle 8 = 2v\$
\$\displaystyle v = 4\$
• Nov 18th 2011, 05:37 AM
DPaine86
Re: Finding an unknown value
For this problem you need to solve the equation for v.

Start by substituting the algebraic terms with the values provided, i.e.
\$\displaystyle u = 4/5\$ and
\$\displaystyle f = 2/3\$.

Therefore, the equation is as follows:

\$\displaystyle {1}/{4}/{5} + 1/v = 1/2/3\$

This becomes:

\$\displaystyle 5/4 + 1/v = 3/2\$ - because having '1' on top of a fraction inverts the fraction.

The equation is then solved as follows:

\$\displaystyle 5v/4v + 4/4v = 3/2\$
\$\displaystyle {5v+4}/{4v} = 3/2\$
\$\displaystyle 10v+8 = 12v\$
\$\displaystyle 8 = 2v\$
\$\displaystyle v = 4\$
• Nov 18th 2011, 05:09 PM
Wilmer
Re: Finding an unknown value
Quote:

Originally Posted by David Green
1 divided by u, + 1 divided by v, = 1 divided by f

I am required to find the value of V

If u = 4/5

If f = 2/3

Your work is very "messy", David.

Equation is:
1/u + 1/v = 1/f ; isolate v term on left:
1/v = 1/f - 1/u ; substitute values:
1/v = 1/(2/3) - 1/(4/5) ; simplify
1/v = 3/2 - 5/4
1/v = 6/4 - 5/4
1/v = 1/4
v = 4