The four properties the follow are not challenging to justification algebraically, however the details will not be presented here.
You are watching: Means-extremes product property of proportions
Property 1 (Means‐Extremes Property, or Cross‐Products Property):Ifa/b=c/d, thenad =bc.Conversely, if ad = bc≠ 0, then
Example 1:Findaifa/12 = 3/4.
By residential property 1:
Example 2:Is 3 : 4 = 7 : 8 a proportion?
No. If this to be a proportion,Property 1would produce
Property 2 (Means or Extremes switching Property):Ifa/b=c/dand is a proportion, then bothd/b=c/aanda/c=b/dare proportions.
Example 3:8/10 = 4/5 is a proportion.Property 2says the if you were to switch the 8 and also 5 or move the 4 and also 10, then the brand-new statement is still a proportion.
If 8/10 = 4/5, then 5/10 = 4/8, or if 8/10 = 4/5, then 8/4 = 10/5.
Example 4:Ifx/5 =y/4, discover the ratio ofx/y.
Use the switching property of proportions and switch the means positions, the 5 and they.
Property 3 (Upside‐Down Property):Ifa/b=c/d, thenb/a=d/c.
Example 5:If 9a= 5b≠ 0, find the ratio
First, use the converse that theCross assets Propertyand obtain the following:
Next, continue in among the adhering to two ways:ApplyProperty 3to 9/5 =b/a: revolve each side upside‐down. 5/9 =a/b, ora/b= 5/9 ApplyProperty 2to 9/b= 5/a: switch the 9 and also thea. a/b= 5/9
Property 4 (Denominator Addition/Subtraction Property):Ifa/b=c/d, climate (a+b)/b= (c+d)/dor (a−b)/b= (c−d)/d.
Example 6:If 5/8 =x/y, climate 13/8 = ?
Example 7:In Figure,AB/BC= 5/8. FindAC/BC.
Figure 1 Using theSegment addition Postulate.
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Recall thatAB+BC=AC(Segment enhancement Postulate).
Example 8:A map is scaled so that 3 cm on the map is same to 5 really miles. If two cities on the map space 10 cm apart, what is the actual distance the cities space apart?