For example, 14{\displaystyle {\frac {1}{4}}}, 12{\displaystyle {\frac {1}{2}}}, 1100{\displaystyle {\frac {1}{100}}}, and 167{\displaystyle {\frac {1}{67}}} are all simplified, because they have 1 as the numerator.
For example, 26{\displaystyle {\frac {2}{6}}} is not simplified, because 6 is a multiple of 2. The numerator and denominator can still be divided by a common factor of 2, simplifying the fraction to 13{\displaystyle {\frac {1}{3}}}. The fraction 25{\displaystyle {\frac {2}{5}}} is simplified, because 5 is not a multiple of 2.
For example, 1523{\displaystyle {\frac {15}{23}}} is simplified, because 23 is a prime number. The only factors of 23 are 23 and 1, so it is impossible to find a greatest common factor you can use to simplify the numerator and denominator. (If the numerator were 1, it would be a unit fraction and thus already simplified. If the numerator were 23, the fraction would equal 1. )
For example, you know that 78{\displaystyle {\frac {7}{8}}} is simplified, because 8−7=1{\displaystyle 8-7=1}
For example, if you are reducing 515{\displaystyle {\frac {5}{15}}}, divide the numerator and denominator by 5. This will give you 13{\displaystyle {\frac {1}{3}}}, which you know cannot be reduced further because it is a unit fraction.
The fractions 15{\displaystyle {\frac {1}{5}}} and 110{\displaystyle {\frac {1}{10}}} are in their reduced, or simplified, form, because each is a unit fraction, with 1 as the numerator. You should know that 510{\displaystyle {\frac {5}{10}}} is not simplified, because 10 is a multiple of 5.
Since 109 is a prime number, you can tell that the fraction is simplified. 109 is only divisible by 109 and 1, so it shares no common factors with 12.
Since 5−4=1{\displaystyle 5-4=1}, you know that 45{\displaystyle {\frac {4}{5}}} is simplified. Since 7 is a prime number, you know that 47{\displaystyle {\frac {4}{7}}} is simplified. Since 8 is a multiple of 4, you know that 48{\displaystyle {\frac {4}{8}}} is NOT simplified.
