When the denominators are the same, comparing fractions is easy. We simply
compare the numerators. For example, ¾ > ¼ because 3 > 1.
Comparing fractions when the denominators are different
To compare fractions that have different denominators, convert them all to a set of
fractions that have the same denominator. There are three steps to comparing
fractions when the denominators are different.
1. Find the Least Common Denominator (LCD) for the group of fractions you are
comparing.
2. Find the multiplier for each fraction. Multiply both the top and bottom of each
fraction by that multiplier. The example below will detail how this is done.
3. Compare and order the numerators of each fraction.
Determine which is larger: 10/24 or 22/45.
1. Find the LCD for the group of fractions you are comparing.
When denominators are different, you can use equivalent fractions as a tool to
create new fractions with the same denominator. This will make them easy to
compare. This new denominator is called the least common denominator (LCD).
The least common denominator is the smallest number that is a common
multiple of each of the original denominators.
Finding the LCD of a Set of Fractions:
A. Write the prime factorization for the denominator of each fraction.
B. Note all prime factors that occur. For each prime factor that occurs, determine in
which denominator it occurs the most. Write down the prime factor the number of
times it occurs in that one denominator.
C. Calculate the LCD of your fractions. To do this, multiply the factors written down
in step B.
To elaborate how these steps are done, let's find the LCD for 10/24 and 22/45:
A. Write the prime factorization for the denominator of each fraction.
• _Prime factors of 24 are: 2, 2, 2, and 3.
• _Prime factors of 45 are: 3, 3 and 5.
B. Note all prime factors that occur. For each prime factor that occurs, determine
in which denominator it occurs the most. Write down the prime factor the
number of times it occurs in that one denominator.
• _The prime factors that occur are 2, 2, 2, 3, 3, and 5.
NOTE: The prime factor 2 occurred only in 24, so we write that three
times (the number of times 2 occurs in 24 as a prime factor). The prime
factor 3 occurred in both 24 and 45 but most often in 45, so we write
that two times (the number of times 3 occurred in 45 as a prime
factor). The prime factor 5 occurred only once (in 45), so we write that