Two fractions can be compared to determine which of them is greater by cross-multiplication. In cross multiplication, the numerator of each fraction is multiplied by the denominator of the opposing fraction. Whichever value is bigger corresponds to the larger fraction.
Take, for instance, the fractions 1/2 and 1/4. If you cross-multiply this fraction, you get the numbers 4 and 2 respectively. Since 4 is a larger value than 2, this means 1/2 is a larger fraction than 1/4.
The reason this works is because this method effectively converts both fractions so that they have a common denominator and then compares their resulting numerators. For instance, 1/2 times 4/4 is 4/8 while 1/4 times 2/2 is 2/8. The numerators for each are the same values found through cross-multiplying. This method works to compare any two fractions.
You may also use the results of cross-multiplication to see how much bigger one fraction is than another. Returning to the original example, the products of cross-multiplication were 4 and 2. This simplifies to a ratio of 2 to 1. This demonstrates the fact that the fraction 1/2 is twice as big as 1/4. It could also be said that one half contains two quarters.