The Understanding dividing fractions by fractions exercise appears under the Arithmetic essentials Math Mission and Pre-algebra Math Mission. This exercise helps strengthen the idea of dividing fractions being the same as multiplying by the reciprocal.

Types of Problems

There are three types of problems in this exercise:

  1. Write an equivalent expression: This problem provides either a multiplication or division problem using fractions. The student is asked to fill in the blank with a number that will change the division problem into a multiplication problem or vice versa.

    Write an equivalent expression

  2. Compare to one: This problem provides a list of arithmetic problems involving fractions. In each row the student is asked to select whether the problem evaluates to something that is smaller than one, or bigger than or equal to one.

    Compare to one

  3. Use number line to answer and select: This problem has a visual aid of a number line and a question asking how many times a number goes into another. The student is to select the division problem that represents the situation, and to write the answer in the box.

    Use number line to answer and select


This exercise is easy to get accuracy badges as long as the student is familiar with the concept of dividing by a fraction being equivalent to multiplication by the reciprocal. The speed badges are medium because of the time involved to do one of the problems well.

  1. For the Write an equivalent expression problem it is not necessary to ready too closely. Just flip the second number, and write it in.
  2. For the Compare to one problem it can take a bit of time to figure out all answers on the initial runs. There are not too many different examples used so they recycle often. Research indicates there are about eight different versions of this problem.
  3. For Use number line to answer and select it is easier for speed if the correct division problem is selected first, and then the answer is typed it. Then it becomes possible to hit enter to submit the answer.

Real-life Applications

  1. Fractions are used in real life in many different ways, but they are most commonly used in the cooking, construction and science industries.

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