Math Background

Dividing Fractions and Mixed Numbers: Tips and Tricks

  • For conceptual understanding of multiplication and division of fractions, use models first. Then teach the algorithm.
  • Students know that the product of two counting numbers is equal to or greater than the greater factor. Explain that multiplying n (a whole number, mixed number, or another fraction) by a fraction will result in a product that is less than n. Inserting the word of in place of the multiplication sign will help students understand this concept.
  • Remind students that when multiplying fractions, they first multiply the numerators and then multiply the denominators. Common denominators are not needed for the multiplication or division of fractions.
  • Explain that simplifying can be done before or after computation, but it is usually more efficient to simplify before computation.
  • Once students understand the concept of canceling factors to simplify, show students that simplifying can be done by dividing any numerator and denominator by their greatest common factor (GCF).
    multiplication of fractions

    Explain that since both a numerator and a denominator are being divided by the same number, the value of the expression is not changed. (Since n over n = 1, any number multiplied or divided by 1 equals that same number.)

  • Explain the algorithm for dividing fractions. Define reciprocals and explain that dividing by a fraction is the same as multiplying by its reciprocal.
  • When using reciprocals to divide fractions, students often forget which fraction to invert. Emphasize that the divisor (the second fraction in the expression) is always inverted.

Houghton Mifflin Math Grade 5