How Do You Compare Fractions?
The answer to that question depends on whether you are comparing fractions with the same denominators or if you are comparing fractions with different denominators.
Comparing Fractions with Same Denominators
Comparing fractions with the same denominators (bottom number) is easy. All you do is compare the numerators to see which fraction is greater, like this:
Comparing Fractions with Different Denominators
Comparing fractions with different denominators requires a little more work (unless you use the compare fractions calculator on this page), because in order to compare the fractions you must first turn their different denominators into the same denominators. You do that by finding the least common multiple (LCM) of the denominators.
To illustrate how you use LCM to turn different denominators into same denominators, let's suppose you want to compare the fraction 2/3 to the fraction 3/4 to see which is greater.
The first step is to find the lowest number that both 3 and 4 will divide into evenly (the LCM). According to my calculations, the LCM of the two denominators (3 & 4) is 12.
Once we have found the LCM for the two denominators, the next step is to multiply the top and bottom of each fraction by the number of times each fraction's denominator goes into the LCM.
Since 3 goes into 12 a total of 4 times, you would multiply the top and bottom of 2/3 by 4, which results in 8/12.
Next, since 4 goes into 12 a total of 3 times, you would multiply the top and bottom of 3/4 by 3, which results in 9/12.
Finally, since both denominators are now the same, you compare the numerators (8 and 9) to determine which fraction is greater. Since 9 is greater than 8, 9/12 is greater than 8/12 -- therefore 3/4 is greater than 2/3. Here is how our example of comparing fractions with different denominators might appear on paper:
|Step #1:||2x 4||Vs||3x 3||=||8||Vs||9|
|3x 4||4x 3||12||12|
So for like denominators you simply compare the numerators and for unlike denominators you multiply the top and bottom by the least common multiple of each denominator, and then compare the numerators.