Misconceptions 
Examples for Preventing or Correcting 

Some students confuse the terms numerator and denominator. 
Teach students what numerators and denominators represent. 
Some students believe that fractions must be less than 1. They believe that the numerator must be less than the denominator; otherwise, there would not be a sufficient number of pieces. 

Some students count the small dividing marks (tick marks) on a number line rather than the intervals. 
Draw thin ovals over each interval. Another method is to have students place their finger on 0, slide their finger to the right and count aloud each fractional part as they read each tick mark. 
Some students believe that fractions are equivalent only when they look identical or have the same number of selected parts. 

Some students believe that performing an operation always changes the value of the original quantity, even when multiplying or dividing by 1. 

Some students perform an operation only on the numerator when working with fractions. 
Teach students that performing an operation only on the numerator is dissimilar to applying the multiplicative identity property and results in changing the fractional value and its position on the number line. Use manipulatives as necessary. 
Some students erroneously use additive instead of multiplicative reasoning when identifying or generating equivalent fractions. For example, given , these students add 8 to both the numerator and the denominator to get , rather than multiplying both the numerator and the denominator by 8 (multiplying the whole fraction by 1) to get . 
