Math Background

Dividing Fractions and Mixed Numbers: When Students Ask

  • Why do I need to know how to multiply and divide fractions?
    The ability to multiply and divide fractions is required in many facets of life. Chefs, retailers, bankers, pharmacists, doctors, and statisticians need to know how to multiply and divide fractions, but so do many other people, in many kinds of jobs. The best way to convince students that they need to master these skills is to create situations that relate specifically to their own life experiences. Below are a few examples. Ask students if they would be at a disadvantage in each situation if they did not know how to multiply or divide fractions.

    Example A
    An item you want is half-price. The original price is $30. The clerk charges you $17. (Yes; the clerk should charge you $15: one-halfx $30 = $15.)

    Example B
    Your dad promises that your new allowance will be 1one-fourth times your old allowance of $5 per week. Your dad now gives you $6 per week. (Yes; your dad should give you $6.25: 1one-fourth x $5 = $6.25.)

    Example C
    You are doing some yard work for your neighbor. He agrees to give you a collectible trading card for every three-fourths of an hour of work. You work for 6 hours. Your neighbor gives you 7 cards. (Yes; your neighbor should give you 8 cards: 6 ÷ three-fourths = 8.)

    Example D
    The rules state that the championship will be awarded to the team that won more than four-fifths of its games. Your rival school won 16 out of 20 games. Your school won 13 out of 15 games. The championship was awarded to your rival school. (Yes: you won more than four-fifths of your games; four-fifths x 20 = 12.)

  • What's the difference between a mixed number and an improper fraction?
    A mixed number is a number written as a whole number and a fraction. An improper fraction is a fraction in which the numerator is greater than or equal to the denominator.
  • What is a reciprocal?
    The reciprocal of a fraction is the fraction inverted. When a fraction and its reciprocal are multiplied, the product is 1.
  • Why are reciprocals used in dividing fractions?
    Reciprocals are a way of simplifying a division expression.
    One-half divided by one-fourth can be written as one-half over one-fourth

    To simplify this expression, multiply the denominator by four over one so the resulting product is 1. To maintain the value of the expression, the numerator must also be multiplied by four over one.

    division expression

Houghton Mifflin Math Grade 5