SOLUTION: write down the reciprocal of:- 1/xy, 2f-v/fv

Question 1098557: write down the reciprocal of:-
1/xy, 2f-v/fv
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!

in general, the reciprocal of a is equal to 1/a and the reciprocal of a/b is equal to b/a.

in the expression of 1 / (xy), the reciprocal is equal to (xy) / 1, which is equal to (xy).

in the expression of (2f-v) / (fv), the reciprocal is equal to (fv) / (2f-v).

you can confirm by assigning arbitrary values to the variables to see if the basic concept of a reciprocal being 1 divided by the expression holds true.

in the expression of 1 / (xy), if you let x = 2 and y = 3, the expression becomes 1 / 6.

the reciprocal should be 1 / (1/6) which is equal to 6.

x * y is the reciprocal and is equal to 2 * 3 which is equal to 6, so the concept of reciprocality holds.

in the expression of (2f-v) / (fv), if you let f = 2 and v = 3, then the expression becomes (2*2-3) / (2*3) which is equal to 1/6.

the reciprocal of 1/6 is equal to 6.

(fv) / (2f-v) is equal to (2*3) / (2*2-3) which is equal to 6/1 which is equal to 6.

the concept of reciprocality holds here as well.

the reciprocal of any expression is 1 divided by that expression.

the rest is just mathematical manipulation to get it to look like what you want.

for example, you can say that the reciprocal of (a/b) / (c/d) is equal to (c/d) / (a/b), but how did you get there?

the reciprocal of (a/b) / (c/d) is equal to 1 / ((a/b) / (c/d))

your numerator is 1 and your denominator is (a/b) / (c/d).

multiply both numerator and denominator by (c/d) and:

your numerator becomes 1 * (c/d) which is equal to (c/d).

your denominator becomes (a/b) / (c/d) * (c/d) which is equal to (a/b).

your expression becomes (c/d) / (a/b).

reciprocal of (a/b) / (c/d) is (c/d) / a/b), all derived from the fact that:

the reciprocal of (a/b) / (c/d) is equal to 1 divided by (a/b) / (c/d).

note that when you multiply the numerator of an expression and the denominator of an expression by the same amount, the value of the expression remains the same.

example:

3/6 * 5/5 = 15/30 which is the same as 3/6 which is the same as 1/2.

RELATED QUESTIONS
Write the reciprocal of... (answered by ewatrrr)

If x and the reciprocal of y are the same which of the following must be true? X=y=1... (answered by ikleyn)

Write down the equation of the line in the xy-plane with gradient 2 and y-intercept (0;... (answered by Cromlix)

I'm trying to solve a future value equation and i need to solve for t. Please i just cant (answered by Alan3354)

Write an equation in general form of the line passing through (3, -5)whose slope is the... (answered by Fombitz)

Write an equation in general form of the line passing through (3, -5) whose slope is the... (answered by Fombitz)

Find the reciprocal of 10 1/2 (answered by butterfliiizzz)

what is the reciprocal of... (answered by Edwin McCravy)

Find the reciprocal of this number.... (answered by Edwin McCravy,edjones)