?Earlier you were introduced to the technique of cross-multiplying in the context of solving for a variable in an equation that involved fractions. Now look at another use of cross-multiplication:
Which fraction is greater, ?
The traditional technique used to compare fractions involves finding a common denominator, multiplying, and comparing the two fractions. The common denominator of 9 and 5 is 45.
Thus,
. Because 35 < 36, you can see that
is slightly bigger than
.
However, there is a shortcut to comparing fractions called (you guessed it): cross-multiplication. This process involves multiplying the numerator of one fraction with the denominator of the other fraction, and vice-versa. Again, this maneuver is legal because you’re just secretly and efficiently multiplying each side by the common denominator. Here’s how the procedure works:
 
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Set up the fractions next to each other. |
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Cross-multiply the fractions and put each answer by the corresponding numerator. (Not the denominator!) |
| 35 < 36 | Because 35 is less than 36, the first fraction must be less than the second one. |
Which fraction is greater?
Which fraction is smaller?
