How to teach multiplication of fractions by whole numbers relying on students' present knowledge

    In this article, we'll explore effective strategies for teaching fraction multiplication, building on students' prior knowledge of fractions and multiplication concepts. We'll demonstrate how to transition from addition to multiplication of fractions and provide practical tasks for teachers to use in their lessons.

If you liked the article and want more effective small-group instruction strategies for your lessons, check out the activities and ideas provided by Happy Numbers and start a free trial (available only this week) right now! 

Multiplication by a whole number as a repeated addition

    Begin exploring multiplication of fractions by reminding students what repeated addition is. Happy Numbers suggests using a model of division into groups to visualize the concept of repeated addition. For example, adding 3 equal parts of a model divided into 4 pieces gives us the repeated addition of 14. 
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    Now you can ask students to rewrite the same equation as a multiplication problem, and show them that with fractions, just like with whole numbers, repeated addition can be written as multiplication. 
To see the full exercise, follow this link.

    That’s how easy it is to multiply unit fractions by whole numbers if you already have a solid foundation! Once students get the idea, teachers can include various practical tasks to promote fluency, just like Happy Numbers does.
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    Matching fractions with their multiplication equivalents is just one example of how teachers can diversify activities. Board games, cards, mazes, and puzzles are also great ways to practice the new skill in a fun way. 

Multiplication of fractions by whole numbers

    Next, students move to a bit more abstract level by applying their knowledge of repeated addition to solving more complex multiplication equations. 

    It’s helpful to start with an example where a given fraction is represented as a sum of its unit fractions, or, as students have just learned, as a multiplication of a single unit fraction by a whole number.

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    The next step is a bit more complex, as students have to rely on their prior knowledge of the associative property of multiplication. Help the students see that it’s much easier to multiply the whole numbers first, and then multiply the resultant number and a fraction. 
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    Once students get the final answer (an improper fraction), teachers can lead them to draw a conclusion, which will be a general rule for multiplying fractions by whole numbers. 
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    Some students will probably notice the pattern at first sight, and they’ll be right in pointing out the following: multiplication of a fraction by a whole number is nothing but the multiplication of the numerator by this whole number, without affecting the denominator. 
To see the full exercise, follow this link.

    Once again, Happy Numbers recommends as much practice as students need before moving on to the next stage. Printables or online activities will be the best choice to go with.  

Multiplication of mixed fractions by whole numbers

    Now that students feel comfortable enough multiplying fractions by whole numbers, they’re ready to move to the next step and learn how to multiply mixed fractions and whole numbers. 

    Teachers may start by reminding students what mixed numbers are. Happy Numbers, for example, gives a familiar multiplication problem and asks students to calculate the answer. If it’s greater than one, students should also rewrite the answer as a mixed number. 
To see the full exercise, follow this link.

    Moving further, students rely on their prior skills with the distributive property to learn how to multiply mixed fractions and whole numbers. Here, it’s helpful to use pictorial references, just like Happy Numbers does, to help students actually model multiplication expressions. 
To see the full exercise, follow this link.

    By dragging the necessary number of tiles, students represent the expression as repeated addition first. 
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    Then, teachers can ask students to record the whole multiplication expression and solve it by referring to the distributive property. Keep the tile models in sight to help students visualize the problem and see that in order to find the answer they just need to multiply each part of the mixed fraction by the same number and add the results. 
To see the full exercise, follow this link.

    Now that they’ve figured out the pattern, students have an expression that they can easily calculate and answer as a mixed number. 
To see the full exercise, follow this link.

    Eventually, teachers can spend a few moments summing up the idea and helping students outline the general rule. Happy Numbers reviews the main steps that students need to follow to solve similar math problems in the future. 
To see the full exercise, follow this link.

    To make sure students grasp the idea, once again, provide some practice tasks that’ll help them consolidate their knowledge and prepare them to apply it to more complex word problems. Happy Numbers suggests various activities from online games to printable exercises, where students can work through the new skill. 

Solve word problems by multiplying fractions and whole numbers

    Our final stage is teaching students how to apply the knowledge they’ve just learned in practice. Begin with the simplest examples and see how students gain more confidence and independence while solving word problems on an abstract level. 
To see the full exercise, follow this link.

We hope the ideas shared in this article will help you and your students succeed in this potentially challenging topic. If you find these tips helpful, check out what Happy Numbers offers its users by setting up your class and starting a free trial  available only this week! 

    This is how Happy Numbers teaches multiplication of fractions by whole numbers building on the foundation of students' previously mastered skills. We recommend proceeding through the whole process carefully, moving from concrete to more abstract representations, helping students establish an understanding of the new concept. It’ll guarantee successful results and effortless math growth. 

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