Every fraction can be written in its lowest terms. When the numerator and denominator are coprime (the only positive integer that goes into both the numerator and denominator evenly is 1) the fraction is irreducible, in its simplest term or lowest terms. For example, 12/18 is not in lowest terms because the numerator (12) and the denominator (18) both can be exactly divided by 6. Dividing the numerator an denominator by 6, you can write this fraction as (12/6)/(18/6) = 2/3. Simplifying fractions means that you divide the numerator and the denominator by the biggest possible integer. Sometimes it is difficult to find this biggest possible integer. In that case you can divide the numerator and denominator several times by a positive integer, untill there is no positive integer left besides 1. For example 12/18, the numerator (12) and the denominator (18) both can be exactly divided by 2, so you can write this fraction as 6/9. Still we can find a positive integer that goes into both the numerator (6) and denominator (9) evenly: 3. Dividing numerator an denominator by 3 will result in wirting our fraction as 2/3. the fraction now is in its lowest terms, because we can not find a positive integer that goes into both the numerator and denominator besides 1.