Question 560295: what does it mean to equate the cross product?
hat size head circumference head circumference
7 7/8 24 61
7 1/2
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! THE PROBLEM
The hat size, head circumference in inches, and head circumference in centimeters are in direct proportion.
They tell you that a hat size of 7 7/8 will fit a head circumference of 24 inches or 61 centimeters.
You want to know the head circumference in inches (x), and in centimeters (y) corresponding to a hat size of 7 1/2.
WHAT IS MEANT BY CROSS PRODUCTS
To find the head circumference in inches (x) corresponding to a hat size of 7 1/2 you would write the proportion
 =
To get to an equivalent equation without denominators, you would multiply both sides of the equal sign by the denominators
By doing that, and simplifying, you would get a simpler equation with one product equated (stated as equal) to another product:
The equated products involve numbers that were placed crisscross from each other in the original equation. That's why they are called "cross products".
When you are solving the problem, you can just say that the cross products are equal, and save yourself any further explanations and intermediate steps.
THE SOLUTION
For the circumference in centimeters (x), we write
=
Equating cross products we get
We write the mixed numbers as improper fractions to get
 ---> 
Multiplying both sides by  we get
 ---> 
which could be expressed as the mixed number 
or it could be approximated as the decimal 
However, since it's a circumference measurement in inches, a more appropriate answer would be 23 inches.
For the circumference in centimeters (x), we write
 =
Equating cross products we get
 or 
So  or  which simplifies to
 , and calculates to approximately 58 centimeters.
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