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.
Continue ReadingTake, 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.
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