Solving Proportions Using Cross Multiplication
Letâ€™s consider this proportion:



To clear the fractions, we multiply both
sides by bd, the LCD of the fractions.



To simplify each side, we cancel common
factors.



The result is: 
ad 
= bc 
Now look again at the original proportion.



We draw a line from a to d, and draw a
line from b to c.



The lines form a â€œcrossâ€ and we obtain the
previous result:

ad 
= bc 
This process is often called cross multiplication.
Definition â€”
Cross MultiplicationTo clear the fractions from a proportion, multiply the numerator of
each fraction by the denominator of the other fraction.
That is,
is equivalent to
ad = bc.
Example 1
Solve the proportion for x:
Solution 


Cross multiply.
Divide both sides by 26. Simplify.

26x x 
= 5 Â· 182
= 35 
We leave the check to you.
