The 4 properties the follow room not an overwhelming to justification algebraically, however the details will not be presented here.

You are watching: Which of the following is the means-extremes product property of proportions?

*Property 1 (Means‐Extremes Property, or Cross‐Products Property):*If*a/b*=*c/d*, then*ad =bc*.*Conversely, if advertisement = bc*≠ 0, then

**Example 1:**Find*a*if*a*/12 = 3/4.

*By residential property 1:*

**Example 2:**Is 3 : 4 = 7 : 8 a proportion?

No. If this were a proportion,*Property 1*would produce

*Property 2 (Means or Extremes convert Property):*If*a*/*b*=*c*/*d*and is a proportion, then both*d*/*b*=*c*/*a*and*a*/*c*=*b*/*d*are proportions.

**Example 3:**8/10 = 4/5 is a proportion.*Property 2*says the if you were to switch the 8 and 5 or switch the 4 and 10, climate the brand-new statement is still a proportion.

If 8/10 = 4/5, climate 5/10 = 4/8, or if 8/10 = 4/5, then 8/4 = 10/5.

**Example 4:**If*x*/5 =*y*/4, find the ratio of*x*/*y.*

Use the switching residential property of proportions and also switch the method positions, the 5 and the*y.*

*Property 3 (Upside‐Down Property):*If*a*/*b*=*c*/*d*, then*b*/*a*=*d*/*c*.

**Example 5:**If 9*a*= 5*b*≠ 0, uncover the ratio

First, use the converse of the*Cross products Property*and attain the following:

Next, continue in one of the following two ways:

Apply*Property 3*to 9/5 =

*b*/

*a:*revolve each next upside‐down. 5/9 =

*a/b*, or

*a/b*= 5/9 Apply

*Property 2*to 9/

*b*= 5/

*a:*move the 9 and the

*a.*

*a*/

*b*= 5/9

*Property 4 (Denominator Addition/Subtraction Property):*If*a*/*b*=*c*/*d*, climate (*a*+*b*)/*b*= (*c*+*d*)/*d*or (*a*−*b*)/*b*= (*c*−*d*)/*d.*

**Example 6:**If 5/8 =*x*/*y*, then 13/8 = ?

**Example 7:**In Figure,*AB*/*BC*= 5/8. Find*AC*/*BC*.

**Figure 1 **Using the*Segment enhancement Postulate.See more: Find The Possible Value Or Values Of Y In The Quadratic Equation 4 – 4Y – Y2 = 0.*

Recall that*AB*+*BC*=*AC**(Segment enhancement Postulate).*

**Example 8:**A map is scaled so the 3 cm on the map is equal to 5 yes, really miles. If two cities on the map space 10 cm apart, what is the actual street the cities are apart?