Decomposing fractions
Decomposing-fractions 256
Exercise Name: Decomposing fractions
Math Missions: 4th grade (U.S.) Math Mission, Arithmetic essentials Math Mission, Pre-algebra Math Mission, Mathematics I Math Mission
Types of Problems: 4

The Decomposing fractions exercise appears under the 4th grade (U.S.) Math Mission, Arithmetic essentials Math Mission, Pre-algebra Math Mission and Mathematics I Math Mission. This exercise concentrates on breaking fractions down with common denominators, effectively concentrating on the numerator as number and denominator as size, or denomination.

Types of Problems

There are four types of problems in this exercise:

  1. Use the dots to compare: This problem has several sums of fractions aligned on the left. The user selects the dots to compare the sums to a given fraction.

    Use the dots to compare

  2. Make the sum: This problem has a list of fraction. The user selects the fractions from the list which, when added together, become a given number.

    Make the sum

  3. Select those that work: This problem gives a fraction and asks the user to select all of the sums that will work to add to become that fraction.

    Select those that work

  4. Fill in blank: This problem asks the user to fill in a missing fraction to make a statement true. The statement involves distinct ways to sum fractions so that one gets the same result.

    Fill in blank


This exercise is easy to get accuracy badges because users can concentrate on the numerators and effectively view the denominators as units. Speed badges are medium difficulty at this time because selecting multiple dots and solutions does not always go quickly.

  1. If the answer to Fill in the blank is a fraction, an acceptable answer list will appear.
  2. All denominators are the same, therefore the problem can be viewed as work with the numerators. This can make it feel like integers, and might be faster to do.

Real-life Applications

  1. Fractions, decimals, and percents are used in many sports such as basketball to determine how many field goals the player has made over how many they missed.

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