Show your students how to multiply fractions and mixed numbers digitally using models and the standard algorithm.
To multiply fractions, I use two strategies: visual models and the standard algorithm. To teach mixed number multiplication, I use area models in addition to the standard algorithm.
My students have always had a pretty easy time with multiplying fractions using the standard algorithm. They just multiply straight across! However, when trying to create a strong understanding of what’s actually happening to the fractions being multiplied, I find that a visual model works best.
The information below explains the various ways to solve multiplication problems using fractions and mixed numbers. The images and video use a digital resource, but all of the information below can also be taught using a printable version.
Multiplying Fractions by Whole Numbers – Video Example
When you first teach students to multiply a fraction by a whole number, they often multiply both the numerator and denominator by the whole number. This creates an equivalent fraction. With a visual model, students can better see how the pieces of the fraction duplicate, often resulting in a product that is a mixed number.
Multiplying Fractions by Fractions – Video Example
A visual model can show how two fractions less than one (2/3 and 3/5), when multiplied, will have a product that is less than the first factor, 2/3. Students will eventually learn that when a fraction is multiplied by another fraction that is <1, the product will be less than the value of the first fraction. This is because you are taking part of a part or a piece of a piece.
When you show them how to multiply the two fractions using a visual model, they see the original fraction represented either vertically or horizontally. Then the second fraction is created on top of the first fraction and shown in the opposite direction (if the first fraction was drawn vertically, draw the second fraction over it horizontally). The area where the two fractions overlap is the product.
It’s like having a baking dish with 2/3 of the brownies that were baked. Then you eat 3/5 of the remaining brownie. You’re eating 3/5 OF 2/3, which is 6/15 of the entire dish. It is multiplication as opposed to subtraction.
Multiplying Mixed Numbers – Video Example
One of the most common errors that students make when learning to multiply mixed numbers is that they multiply the whole numbers and then multiply the fractions.
Example: 3 1/5 x 4 2/3 They will multiply 3 x 4 to get 12, and then 1/5 x 2/3 to get 2/15 with an answer of 12 2/15. They are completely forgetting to multiply the 3 from 3 1/5 by the fraction in the second mixed number, 2/3. They’re also forgetting to multiply the fraction 1/5 in 3 1/5 by the whole number, 4, in 4 2/3.
An area model has you multiply all pieces of the two mixed numbers. Once each product has been found, they are added together to find the final product.
The Standard Algorithm
Once students are familiar with visual models and have a strong foundation of multiplying fractions and mixed numbers, I like to introduce the standard algorithm.
Multiplying Fractions – Video Example
The standard algorithm is fairly simple when multiplying fractions. If the fractions are less than one, multiply the numerators and then multiply the denominators. Simplify the answer if you can. If you’re multiplying a fraction by a whole number, rewrite the whole number as a fraction over 1 (5 = 5/1), and then multiply across.
Multiplying Mixed Numbers – Video Example
Mixed Numbers are a little more complicated. In order to make sure that both the whole numbers and fractions are multiplied in each factor, convert the mixed numbers to improper fractions and then multiply across. I like to cross reduce the fractions before multiplying if I can. This alleviates reducing the fraction later when the product is much larger.
While it may seem overwhelming to teach using so many strategies, remember that kids think and learn differently. Some understand fractions more conceptually and comprehend what they’re doing when using the standard algorithm. Others may need to see the fractions more concretely when performing these operations and the visual models are beneficial to them.