What method is used to compare fractions to determine which is greater?

To determine which fraction is greater, cross-multiplication is an effective method. This technique involves multiplying the numerator of one fraction by the denominator of the other fraction. This allows for a direct comparison without the need to find a common denominator or convert the fractions to decimals.

For example, if you have two fractions, ( \frac{a}{b} ) and ( \frac{c}{d} ), you cross-multiply to get ( a \times d ) and ( c \times b ). By comparing the two products, you can clearly see which fraction is larger: if ( a \times d ) is greater than ( c \times b ), then ( \frac{a}{b} ) is greater than ( \frac{c}{d} ).

This method is particularly useful because it eliminates the complexity of finding a common denominator or dealing with decimal conversions, making it a quick and reliable way to assess the relative sizes of two fractions.