Four Operations Using Fractions
Students are required to be fluent adding, subtracting, multiplying and dividing fractions. This resource list supports the teaching and learning of the use of the four operations, including efficient written methods, applied to simple fractions; proper, improper and mixed numbers.
Visit the secondary mathematics webpage to access all lists.
Links and Resources
This resource contains packs of games, investigations, worksheets and practical activities ideal for use as starter activities.
Fractions packs one and two contain activities designed to explore the concept of fractions.
Fractions pack three contains an activity 'Adding Fractions' which requires students to be familiar with finding strings of equivalent fractions. The activity 'Unit fraction patterns' is an activity requiring students to find patterns when adding unit fractions.
This resource contains two videos. The videos can be paused to allow students to attempt the calculation and then compare their method with the one shown on the video. Students could be asked to make their own video showing alternate methods or giving alternate explanations as to how to complete the calculation.
Adding and subtracting fractions with the same denominator – This video begins by showing the common mistake of adding the numerator and adding the denominator and explaining why this cannot be correct. The correct method is used with a pictorial representation to aid understanding. The video continues with a series of simple addition and subtraction examples.
Adding and subtracting fractions with different denominators – This demonstration begins again by explaining that only the numerators are added. There follows a brief recap of equivalent fractions before moving on to show a simple example of how to add fractions with different denominators.
This resource is designed to improve confidence in mathematics and was developed particularly for primary teachers and those non-specialists who teach mathematics in the lower secondary years. The resource contains a good commentary on how to teach fractions along with a number of examples and exercises suitable for use in the classroom.
Fractions part A covers addition and subtraction of fractions including some very useful worded questions, ideal for testing whether students can determine what is the correct calculation to use to solve the problem.
The next section considers how to teach the principles involved in performing multiplication and division of fractions.
Arithmetic: Fractions contains a variety of questions, including worded questions requiring students to add fractions, subtract fractions, multiply fractions and divide fractions. Examples using mixed numbers are included.
There are two useful activities. Human Multiplication is a practical activity investigating the multiplication of fractions.
Adding and Subtracting Fractions is a puzzle requiring students to add and subtract fractions.
This resource uses diagrams to illustrate division by a fraction and, to clarify the common misconception identified with this task, prompts students to rethink the statement, divide three by one quarter, as the number of quarters that fit into three.
Practice of dividing by fractions is provided by some follow-up exercises.
This resource contains three excel files dealing with various aspects of fractions:
Fractions of X (mental arithmetic) - to find fractions of amounts
Fractions: Add, Subtract, Multiply, Divide -apply the four rules to fractions and mixed numbers
Fractions: Mixed, Top-heavy, Equivalent- convert between mixed numbers and improper fractions. and find sets of equivalent fractions
Each letter of the alphabet is represented by a fraction; students add, subtract, multiply and divide fractions to reveal coded messages.
In this resource daddy bear, mummy bear and baby bear share some porridge. Several different problems can be given to students, each solution involves adding fractions with different denominators and the use reciprocals.
In this activity students are asked to generate six fractions by using three integers that sum to zero (e.g. -8, 3 and 5). They are then asked to sum these fractions as well as finding their product, with surprising results.
Proving the result algebraically involves addition and multiplication of fractions, simplification, and equating variables.