SOLUTION: The quotient of two fractions is equal to the product of the first and the reciprical of the second. Why? a/b/c/d=a/bx1/c/d=a/bxd/c ?

Algebra ->  Real-numbers -> SOLUTION: The quotient of two fractions is equal to the product of the first and the reciprical of the second. Why? a/b/c/d=a/bx1/c/d=a/bxd/c ?      Log On


   

Question 34749: The quotient of two fractions is equal to the product of the first and the reciprical of the second. Why? a/b/c/d=a/bx1/c/d=a/bxd/c ?
Found 2 solutions by Earlsdon, venugopalramana:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
I would say...because multiplication is the inverse operation of division, so the quotient of two numbers (not just fractions) is the same as the product of the first and the inverse (reciprocal) of the second.
You have really done a double-inverse here so the result is the same.
a%2Fb+=+a%2A%281%2Fb%29

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
THIS FOLLOWS FROM DEFINITION OF A RECIPROCAL...
LET US SEE
LET FRACTION 1 =F1=A/B............AND
FRACTION 2 = F2 =C/D.....
QUOTIENT OF F1 TO F2 =F1/F2=(A/B)/ (C/D)=(A*D)/(B*C)=(A/B)*(D/C)
NOW RECIPROCAL OF F2 =1/F2= RF2 SAY =1/(C/D)=(D/C)
NOW PRODUCT OF F1 AND RF2 IS = (A/B)*RF2=(A/B)*(D/C)..WHICH IS SAME AS ABOVE F1/F2....