This proportionis also true. One nice thing aboutworkingwith proportionsis that thereare severalproportions
that correctlyrepresentthe samedata.
c) WhatlengthshouldLeo use on the scaledrawingfor the waterline?Let representthe scalelength.Write a proportion.If two fractionsare equal,and they havethe samedenominator, then the numeratorsmustbe equal.The scalelengthfor the waterline is inches.Notethat the scalefor this drawingcan be expressedas inch to feet, or inch to foot.
Proportionsand CrossProducts
Lookat example3b above.
is true if and only if.In the proportion, , and are calledthemeans(they’rein the middle); and are
calledtheextremes(they’reon the ends).You can see that for the proportionto be true, the productof the
means mustequalthe productof the extremes. Both productsequal.
It is easyto generalizethis means-and-extremesrule for any true proportion.
Meansand ExtremesTheoremor The CrossMultiplicationTheorem
CrossMultiplicationTheorem:Let , , , and be real numbers,with and. If then.
The proofof the crossmultiplicationtheoremis example4. The proofof the converseis in the LessonExer-
cises.
Example 4
ProveThe CrossMultiplicationTheorem:For real numbers , , , and with and If, then.