Solving Proportions Using Cross Multiplication
| Let’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 “cross†and we obtain the
previous result:
|
ad |
= bc |
This process is often called cross multiplication.
Definition —
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 · 182
= 35 |
We leave the check to you.
|
