- Definitions of three types of fractions
- How to multiply fractions in three steps
- Examples of how to multiply fractions
- Common errors students make
- Engaging ways to teach multiplying fractions
What is multiplication?
Put simply, multiplication is adding the same number over and over.Good news for your students: if they can add, they can multiply!Instead of writing 1 + 1 + 1 + 1, there’s a much quicker way to write this addition problem: 1 × 4. Here are some examples: [caption id="attachment_3330" align="aligncenter" width="600"]
Defining three types of fractions
A fraction is generally composed of two parts:- Numerator -- the top number, which refers to how many parts (of a whole) you have.
- Denominator -- the bottom number, which refers to the total number of parts making up the whole.

1. Proper fractions
A proper fraction has a numerator less than the denominator.For example: ½, ⅔, ¾, ⅘, ⅚
2. Improper fractions
Though similar in structure, an improper fraction has a numerator greater than the denominator.Note: When a numerator is equal to the denominator, it’s considered “improper” because you can change it into a whole number. The same rule applies to improper fractions such as ²⁶⁄₁₃ which, if reduced, become whole (i.e., two).For example: ³⁄₂, ⁵⁄₃, ⁷⁄₆, ¹¹⁄₁₀, ⁸⁄₈
3. Mixed fractions
Unlike the first two, a mixed fraction is composed of a proper fraction and whole number.For example: 3 ½, 7 ⅔, 2 ¾, 6 ⅘, 1 ⅚
How to multiply fractions
Good things come in threes, including the three simple steps your students need to follow when learning how to multiply fractions:- Multiply the numerators (top numbers)
- Multiply the denominators (bottom numbers)
- If needed, simplify or reduce the fraction

Area models for fraction multiplication
Perfect for the visual learners in your class, the area model effectively illustrates what one fraction times (or “of”) another looks like.As you can see from the illustration below, creating an area model when multiplying fraction is easy:- Draw the fractions you’re multiplying in separate boxes, each using a different color
- Combine the drawings into one box, using a new color for the parts that overlap
- To write the product, ask yourself two questions:
- How many boxes have both colors? This will be your numerator
- How many boxes are there in total? This will be your denominator

A catchy reminder
Oh! And if your students ever forget the steps, just remind them to sing this song:Multiplying fractions? That’s no big problem. Do top times top over bottom times bottom. And before you say goodbye, don’t forget to simplify!
Multiplying fractions with whole numbers
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Solve: 2 × ⁵⁄₁₃ Rewrite whole number as a fraction: ²⁄₁ × ⁵⁄₁₃ Multiply numerators: 2 × 5 = 10 Multiply denominators: 1 × 13 = 13 New fraction: ¹⁰⁄₁₃
Note: If students struggle with whole numbers, explain that they can think of a whole number as a top number, with the bottom number always being one.Multiplying improper fractions
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Solve: ⁵⁄₃ × ⁷⁄₆ Multiply numerators: 5 × 7 = 35 Multiply denominators: 3 × 6 = 18 New fraction: ³⁵⁄₁₈
If students are familiar with mixed fractions, they can change the improper fraction to a mixed one. In this case, that mixed number would be 1 ¹⁷⁄₁₈.But you can learn more about mixed numbers below!Multiplying mixed fractions
Before teaching students how to multiply fractions with mixed numbers, there are three steps they should know:- Convert any mixed fractions into improper fractions
- Multiply the improper fractions
- Convert the final product back into a mixed number

- Find the new numerator -- Multiply the whole number with the denominator, then add the original numerator to it.
- Keep the same denominator -- The denominator remains unchanged.
Multiply Add Denominator
Step two, multiply the improper fractions as we illustrated before this section.Step three, convert that improper fraction back into a mixed number. Here’s a little rhyme to help your students remember how to do this:With an improper fraction, division is the action!
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Two major errors students make with fraction multiplication
Though some students will quickly grasp your fraction multiplication lessons, others can struggle with these new concepts.The earlier teachers catch these misconceptions, the sooner students can learn from and correct their errors.According to the What Works Clearinghouse Institute of Education Sciences practice guide, “Developing Effective Fractions Instruction for Kindergarten Through 8th Grade,” these are some of the most common misconceptions in regards to learning how to multiply fractions.
1. Believing whole numbers have the same denominator as fraction in a problem
The guide’s panel of eight experts recognized this misconception can lead students to take a problem such as 4 – ⅜ and rewrite it as ⁴⁄₈ – ⅜, for an incorrect answer of ⅛.When presented with a mixed number, students with such a misconception might add the whole number to the numerator, as in ³¹⁄₃ × ⁶⁄₇ = (³⁄₃ + ⅓) × ⁶⁄₇ = ⁴⁄₃ × ⁶⁄₇ = ²⁴⁄₂₁.Helping students understand the relation between mixed numbers and improper fractions -- and how to translate each into the other -- is crucial for working with fractions.How to help your students
Avoid the temptation to blast through foundational lessons.Take the time your students need to help them understand the relationship between improper fractions and mixed numbers, and how to convert them from one to the other. [caption id="attachment_3350" align="aligncenter" width="600"]
2. Leaving the denominator unchanged
Students can make the mistake of forgetting to multiply equal denominators. This is likely due to the fact you don’t have to touch equal denominators in fraction addition.For example, they might see ⅔ × ⅓ and incorrectly answer ⅔ instead of ²⁄₉.How to help your students
In the practice guide, expert panelists suggest “explaining the conceptual basis of fraction multiplication using unit fractions (e.g., ½ × ½ = half of a half = ¼).”In particular, teachers can show that the problem ½ × ½ is actually asking what ½ of ½ is, which implies that the product must be smaller than either fraction being multiplied.Verbalizing this misconception is helpful, but visualizing it is especially effective. Enter the fraction wall! Fraction walls are a brilliant way to help students see what, in this case, an abstract one half of one half (i.e., one quarter) looks like.Now you’re aware of many students’ pain points while learning how to multiply fractions, what’s next? Let’s explore ways to make your fraction lessons stick -- and why worksheets may not be the best strategy.Have a chat with your @rudstony4 superstar this weekend! Look at the Fractions Wall together.. ask them about our key vocabulary... NUMERATOR, DENOMINATOR, MIXED NUMBER, EQUIVALENT... how many can they explain to you?! #rudstonmaths pic.twitter.com/V02vgd9SYV
— Year 4 (@Rudstony4) February 1, 2019
The death of worksheets?

But the data on US achievement scores as compared to the rest of the world indicate otherwise. Ironically, as more and more worksheets are pushed in earlier and earlier grades and the more rote, boring homework is forced on developing minds, student outcomes in the US decline further.[caption id="attachment_3352" align="aligncenter" width="424"]

Only 34% of fourth graders and 27% of eighth graders were rated as proficient in math in 2011 and this declined to 33% for 4th graders and 25% for 8th graders in 2015 (the most recent year these data are available).There is no way to put a positive spin on these outcomes: Currently, more than two-thirds of fourth-graders and three in four eighth graders are not proficient in math. This ranks 38th in the world.Does this mean schools should go worksheet-free? Not necessarily.Correlation isn’t causation. In fact, many teachers and students have found success with worksheets.However, educators need to realize education is rapidly changing, from worksheets to classroom technology.So, here are a few creative ways to teach fraction multiplication -- worksheet-free!
7 Engaging examples to teach students how to multiply fractions
1. Prodigy

- Multiply a fraction by a whole number
- Multiply two fractions
- Multiply a whole number by a missing fraction
- Multiply two fractions via word problems
- And more

2. Flip-it fractions
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3. Fraction multiplication BINGO
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4. Word problems
Word problems are a wonderful way to make math lessons relevant to your students’ lives.Learning how to multiply fractions may seem foreign to them, but a simple story can change their entire perspective not just about fractions, but math as a whole.Here’s a word problem example:The fifth graders were doing a lot of great thinking today in math. ❤️They were working on their conceptual understanding of multiplying a fraction by a whole number. @svmimac @BuenaVistaWCSD pic.twitter.com/Bg7HapJc82
— Kellianne Bockser (@BVBockser) January 25, 2019
You have ½ a bag of chips in the cupboard, but ate ½ of it after dinner. How much of the whole bag did you eat? (Do not reduce your answer to lowest terms.)
Granted, it’s a simple example. But a second ago, that fraction was just a number above and below a short line. Now, however, this “everyday” word problem has made multiplying fractions applicable to real life.5. Fraction war
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6. Food fractions
Kids love food -- it’s no secret! So why not incorporate it into your lesson plan?A teacher in the Tweet above got her kids to practice how to multiply fractions by converting delicious food recipes.You can have each student choose their favorite food and multiply the ingredients to feed the entire class.An incentive might help, too! For example, once everyone has converted their favorite food, choose a safe snack the class will love.Pull up the original recipe. Now have your students work together to multiply ingredients and, if they do it properly, the whole class will get a homemade (or store-bought) baked good!It's amazing how engaged kids get when the topic is FOOD! Goal: find a favorite recipe, then calculate each ingredient to serve all 90 5th graders! They are loving this! Sneaky way to practice multiplying fractions. ;) @Falcons_BMS #FalconsInFlight pic.twitter.com/M6Rg7zaXXQ
— Emily Libbert (@EmilyLibbert) January 24, 2019
7) Multiplied fraction pennant
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- An area model illustrating the fractions they’re multiplying
- The multiplication problem itself (with space to show their work)
- A space at the bottom that reads “My product reduces to...”
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Excited to teach your students how to multiply fractions now?
We hope so!Multiplying fractions can be a daunting task -- to learn and teach.Hopefully the thorough breakdown of different types of fractions, how to multiply them, and how to make teaching them fun helps enrich you and your students’ teaching and learning experience, respectively.Read next: How to Divide Fractions in 3 Easy Steps
