Inside Track: Converting Between Improper Fractions & Mixed Numbers

Teaching Video:

Key Idea:

Methods for converting between improper fractions and mixed numbers involve application of basic arithmetic. This will be most successful when students understand the meanings behind the symbols and so can understand the processes, rather than attempting to memorize the processes alone by rote.

Improper fractions and mixed numbers may be thought of in pairs; each improper fraction has an associated, equivalent mixed number.

Use physical or visual models to illustrate fraction ideas with students, then help them to understand how to convert one form into the other. For example:

Put out two apples.

Cut one apple into fourths (quarters), remove one piece.

Ask how many apples are on the plate (one and three fourths)

Ask the child to write the mixed number in the correct form

Ask how many fourths there would be if both apples were cut into fourths (seven fourths)

Ask the child to write the improper fraction

Have the child explain the connections between the two numbers

Put out another 3 apples, remove two fourths so there is a total of four and one fourth

Ask how many fourths there are altogether, what is the improper fraction and the mixed number

Extending These Activities:

Instruction about common fractions in elementary school involves simple denominators, such as halves, thirds, fourths, sixths and eighths. Extend the child’s abilities in this topic to more difficult fractions. For example: