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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.
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