Rule of three (mathematics) | Wikipedia audio article

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00:00:24 1 Procedure
00:01:02 2 Use
00:01:27 3 Rule of Three
00:02:04 3.1 Double Rule of Three
00:02:54 4 See also
00:03:31 5 References



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"I cannot teach anybody anything, I can only make them think."
- Socrates


SUMMARY
=======
In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.
The method is also occasionally known as the "cross your heart" method because a heart can be drawn to remember which things to multiply together and the lines resemble a heart outline.
Given an equation like:






a
b


=


c
d




{\displaystyle {\frac {a}{b}}={\frac {c}{d}}}
(where b and d are not zero), one can cross-multiply to get:




a
d
=
b
c


o
r


a
=



b
c

d


.


{\displaystyle ad=bc\qquad \mathrm {or} \qquad a={\frac {bc}{d}}.}
In Euclidean geometry the same calculation can be achieved by considering the ratios as those of similar triangles.