Expert: Josh - 4/19/2011

Question
(A)find the value of f if 1/u + 1/v =1/f,u =5 and v=3.

Answer
Hi Illy,

To find the value of f, we can first plug in the values for "u" and "v" on the left hand side of the equation. When u=5 and v=3, 1/u + 1/v equals 1/5 + 1/3. I am not sure if you are comfortable with adding fractions. The usual approach is to find a common denominator between the two fractions. For instance, 1/5 is equivalent to 3/15 [we get this from multiplying (1/5) by (3/3)]. Similarly, 1/3 is equivalent to 5/15 [we get this from multiplying (1/3) by (5/5)]. So, 1/5 + 1/3 = 3/15 + 5/15 = 8/15. We refer to the number 15 (which is a product of 5 and 3) as the lowest common denominator.

Recapping on what we have done, we now know that 1/u + 1/v = 1/f, where the part "1/u + 1/v" is given by 8/15. So, the equation we started with now becomes 8/15 = 1/f.

Flipping (reciprocating) the fractions on both sides, we have 15/8 = f.