10 Fun Math Projects for All Grade Levels

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10 Fun Math Projects for All Grade Levels

10 Fun Math Projects for All Grade Levels

Math projects are fun inquiry-based activities that give students a chance to extend their understanding of math skills and concepts to real-world problems in a hands-on way. There are many types of math projects, and they often involve creative thinking, collaboration, and meaningful applications of math including modeling real-world scenarios, working with hands-on materials, and analyzing data.

Math projects are great for mixing up your instruction and for giving students opportunities to apply their math skills in real-world applications.

Anthony Persico

by Anthony Persico

Founder & Head Educator, Mashup Math
With a background in elementary and secondary math education and special education, Anthony has taught thousands of K-12 students across the United States.

Learn more about the author →

Last Updated: May 2025

If you are looking for a few fun math project ideas for mixing up your instruction or for keeping your students interested and engaged for any reason, then you will love this collection of fun math projects for students in grades 1-8. Having students work on fun math projects (and math art projects) is a great way to keep their attention and break up the monotony of the normal classroom routine.

The following math project ideas for elementary school, middle school, and high school students can all be modified to appropriately challenge and engage your math students based on their interests and skill/ability levels. We highly recommend that you differentiate whatever math project you choose to best meet the needs of your students.

Table of Contents (Jump To):

  1. The Ultimate Paper Airplane Competition (Grades 3-6)

  2. Dream Home Design Project (Grades 5-8)

  3. Turn Your Classroom into a Math Escape Room (Grades 4-8)

  4. Data Journalism - Class Survey (Grades 1-8)

  5. Dream Vacation Budget Project (Grades 4-8)

  6. Build a Fraction Kit (Grades 4-8)

  7. Research a Famous Mathematician (Grades 1-8)

  8. Create Your Own Math Board Game

  9. Stock Market Project

  10. Tessellation Shape Art Project

Now, are you ready to learn about some fun math projects that you can use to engage your students this school year?

(Do you want free K-8 math resources and activities in your inbox every week? Click here to sign up for our free math education email newsletter)


1.) The Ultimate Paper Airplane Competition

Suggested Grade Levels: Grades 3-6

Materials/Supplies: Printer Paper, Card Stock, Measuring Tape, Masking Tape, Stopwatch or Phone Timer

 

The Ultimate Paper Airplane Competition is a fun math project involving data collection and analysis. (Image: Mashup Math g)

 

Description: This math project focuses on data collection and analysis in the context of flying paper airplanes. Students can start by building their own paper airplanes and then flying them in an open area such as a hallway, a gymnasium, or outdoors. By working in small groups, students can take turns throwing their paper airplanes from a fixed starting point. They can collect data related to things like air time, distance flown, and target accuracy. After three to five test flights, they can use their collected data to calculate data such as:

  • The mean flight air time and/or distance of their plane.

  • The range between the longest and shortest flights.

  • The median and mode of the data points (if applicable).

Students can also collaborate with other groups to track the data of other paper airplanes in relation to their own. Finally, a large group data-driven discussion can be had to determine which group had the highest performing paper airplane and why.

Advanced Application: If you want to modify this activity to be more challenging, include a graphing component where students have to compare two data points such as distance vs air time, or distance vs. wingspan.

Click here to learn more about the Ultimate Paper Airplane Competition Project


2.) Dream Home Design Project

Suggested Grade Levels: Grades 5-8

Materials/Supplies: Graph Paper, Rulers and Protractors, Colored Pencils or Markers, Clipboards

 

Are your students ready to design their dream home blueprints?

 

Description: For this fun math art project, students are tasked with designing the floor plans for their dream homes and backyards by applying math skills including measurement, defining dimensions, scale, area, and perimeter. Students can use graph paper and markers or digital tools like Google Sketchup to create their home’s blueprints, calculate the cost of building materials and furniture, and design the layout of their house’s interior and exterior.

Students can also be given the opportunity to present their dream home blueprint to their classmates.

Advanced Application: You can make this math project more challenging by incorporating a research phase and including a budget constraint, so students have to maximize their total living space under a budget.


3.) Turn Your Classroom into an Escape Room

Suggested Grade Levels: 4-8

Materials/Supplies: Envelopes or plastic “lock boxes,” printable clue cards, timers or stopwatches, UV pens and black-lights (if using invisible clues), Clipboards

 

Math Projects for Middle School Students: Puzzles, Riddles, and Brain Teasers (Image Source: Jackson Academy)

 

Description: Can your students escape before the bell rings? The escape room project has students working in groups of 3-5 to “escape” your classroom before the bell rings by solving a sequence of math problems and puzzles. Every time the group solves a problem, they earn a keyword or a clue that will help them with the next step.

You can use the math escape room project for a variety of topics including working with fractions, solving equations, identifying shapes and figures, etc.

This math project will take some time to plan and implement, but it’s an activity that you can reuse year after year.


4.) Data Journalism - Class Survey

Suggested Grade Levels: 1-8

Materials/Supplies: Clipboards, Tally Charts, Data Entry Charts, Graph Paper, Rulers, Colored Pencils

 

Have your students collect responses from their classmates, analyze the data, and write a blog post highlighting their results. (Image: Mashup Math FP)

 

Description: The data journalism activity is a highly-flexible math project idea that works with any topic or grade level. For this project, students must design a survey that collects data by asking 5 or more questions such as What is your favorite lunch type of candy? or How many minutes, on average, do you spend working on homework on a school night? Once students have created their surveys, they can collect responses from their classmates (aim to have each student collect responses from at least 25 people). Next, students can track data using tally marks, frequency tables, and/or charts and graphs. Using the collected data, students can compute and analyze a variety of statistics ranging from simple frequency comparisons to central tendency to standard deviation.

Advanced Application: In addition to collection data and analyzing it, students can draw conclusions and share them via writing their own blog post or news story (with a catchy headline, of course). For example, a student could write a bombshell article titled “Are Teachers Giving Us Too Much Homework? 70% of Students Spend 2+ Hours Per Night on HW!”



Do you more FREE K-8 math resources and activity ideas in your inbox every week?


5.) Budgeting Your Dream Vacation

Suggested Grade Levels: 4-8

Materials/Supplies: Maps, Travel Brochures, Graph Paper, Laptops with Internet Access

 

Are your students ready to plan and budget their dream vacation?

 

Description: For this math project, choose an appropriate budget for your students to spend on planning a dream vacation for themselves and a friend. Students must research the cost of travel, including transportation, lodging, meals, activities and experiences, and shopping for a 7 day vacation at the destination of their choice. Students can track their spending in a variety of ways, including simple budget tables and spreadsheets. Students can also use graphic tools like bar graphs and pie charts to visualize spending categories.

Advanced Application: You can make this math project more challenging by requiring students to choose a foreign country destination that requires them to make currency conversions and to research travel requirements such as passports, visas, vaccinations, and travel insurance.


6.) Build a Fraction Kit

Suggested Grade Levels: 4-8

Materials/Supplies: Construction Paper, Scissors, Markers, Rulers

 

Image via www.mashupmath.com

 

Description: Building a fraction kit using colored construction paper is one of the best ways to help your students to understand math concepts related to fractions, including simplifying fractions, equivalent fractions, comparing fractions, and adding and subtracting fractions.

Students can keep their completed fraction kits in their math notebooks to use a reference guide whenever they need help with things like comparing fractions, simplifying fractions, or adding/subtracting fractions.

Click here for step-by-step instructions on building a fraction kit

 
 

7.) Research a Famous Mathematician

Grade Levels: 1-8

Materials/Supplies: Laptops with Internet Access, List of Research Questions

 

Math Projects: Research a Famous Mathematician or Civilization

 

Description: For this math project, students will research a famous individual or civilization and their contributions to the field of mathematics and create a profile that they will present to their classmates.

Students will start by selecting a mathematician or civilization and then researching key facts and details such as biographical details, historical context, and major contributions. Students can then create a presentation that profiles their mathematician that includes an image or portrait, key information, and fun facts.

Here are a few great resources for inspiring students to learn about some lesser-known mathematicians and their amazing contributions to mathematics:


8.) Create Your Own Math Board Game

Grade Levels: 1-8

Materials/Supplies: Poster board, scissors, colored pens or markers, 6-sided dice, spinners

 

Having your students create their own math board game is a fun and creative math project idea.

 

Description: For this math project, students are tasked with creating their own math-related board games based on an assigned topic/skill or one of their choosing. To complete this project, students must choose a concept, plan their game, create a game board, design the game pieces, uses spinners or dice to determine how players will navigate the board, test and revise the game, and present their final product to the class.

Students can also be given time to rotate around the classroom in groups to attempt to play each other’s board games.


9.) Stock Market Project

Grade Levels: 6-8

Materials/Supplies: Laptops or Desktop Computers or Tablets (with Internet Access), Spreadsheet Software (Excel or Google Sheets)

 

The stock market math project teaches students about investing.

 

Description: Are your students ready to learn about investing? The stock market math project has students start with a simulated $10,000 investment budget that they must invest into ten publicly traded companies such as Nike, Microsoft, Tesla, McDonald’s, etc. Students must complete a spreadsheet or chart that includes their ten stocks (and each stock’s ticker symbol), the purchase price, the number of shares purchased, and the total cost invested into each position. Students can then track the performance of their portfolios over time by updating the performance every month or so.

We recommend showing this short TED-Ed Video How Does the Stock Market Work and using Google to research companies, find stock symbols, and see corresponding graphs and charts during the research phase.


10.) Tessellation Art Project

Grade Levels: 4-8

Materials/Supplies: Construction Paper, Scissors, Rulers, Colored Pencils or Markers, Poster Board

 

Examples of Tessellations (Image Source: artwithmrsnguyen)

 

Description: This final math project idea combines geometry and art, where students have to create an Escher Tile from a regular polygon (a square, a hexagon, or an equilateral triangle).

The video below teaches you how to create your own Escher tile. Once students have a few shapes, they can pick one that resembles something recognizable such as an animal or a fruit.

Then, they can use their tile to make a pattern image that they can then color in and display on the walls of your classroom.

 
 

Are Your Students Ready to Play Math Jeopardy?

In addition to working on fun math projects, you can also mix up your instruction by giving your students the opportunity to play our interactive Math Jeopardy Games for grades 3-6.

Click on any of the links below to play Math Jeopardy.


More Math Education Insights You Will Love:


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How to Divide Fractions in 3 Easy Steps

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How to Divide Fractions in 3 Easy Steps

How to Divide Fractions in 3 Easy Steps

In math, dividing fractions is the process of figuring out how many times one fraction fits into another. You can multiply fractions using the “keep-change-flip” method, where you multiply the first fraction by the reciprocal of the second fraction, and then simplify the result (if possible) to find the quotient.

 

How to Divide Fractions: You can easily divide fractions by fractions and fractions by whole numbers by using the keep-change-flip method.

 
Anthony Persico

by Anthony Persico

Founder & Head Educator, Mashup Math
With a background in elementary and secondary math education and special education, Anthony has taught thousands of K-12 students across the United States.

Learn more about the author →

Last Updated: May 2025

Performing operations on fractions can be challenging. Once you have mastered how to add fractions and how to subtract fractions, the next step is learning how to multiply and how to divide fractions.

The following free guide specifically focuses on teaching you how to divide fractions in the following scenarios:

Table of Contents (Jump to a Section):

While dividing fractions may seem challenging at first glance, you can actually easily solve all three types of problems by using a simple 3-step method for dividing fractions, which you will learn and apply to several practice problems further down in this step-by-step guide.

Together, we will learn the Keep-Change-Flip method for how to divide fractions and use it to solve a variety of practice problems.

However, before we dive into working through any examples, let’s do a quick review of some key vocabulary terms and prerequisite skills that you will need to refresh in order to be successful with this new math skill.

Before we cover how to subtract fractions and work through a few examples, let’s do a fast recap of some key characteristics and vocabulary terms related to subtracting fractions.

Are you ready to get started?

How to Divide Fractions: Key Vocabulary

Since we will be using several math vocabulary terms in this guide, it is important that you are familiar with their meanings before you start working on the practice problems.

What is the numerator of a fraction?

The numerator of a fraction is the top number of the fraction. For example, for the fraction 2/3, the numerator is 2.

What is the denominator of a fraction?

The denominator of a fraction is the bottom number of the fraction. For example, for the fraction 2/3, the numerator is 3.

Pretty simple, right? Whenever we mention the numerator of a fraction, we are talking about the top number. On the other hand, whenever we mention the denominator of a fraction, we are talking about the bottom number. Figure 01 below illustrates the relationship.

 

Figure 01: In any fraction, the numerator is the top number and the denominator is the bottom number.

 

Next, let’s make sure that you understand the difference between fractions, whole numbers, and mixed numbers (also referred to as mixed fractions).

What is a whole number?

In math, a whole number is a number that is not a fraction. For example, 7, 23, and 100 are all whole numbers.

What is a fraction?

In math, a fraction is a number that represents a part of a whole number. For example, 1/2, 2/3, and 5/8 are all fractions.

What is a mixed number?

In math, a mixed number (or a mixed fraction) is a number that consists of both a whole number and a proper fraction. For example, 3 2/5 is a mixed number that represents the sum of 3 and 2/5.

Why is it important for you to understand the key characteristics and differences between these three types of numbers? Because, in this guide, you will learn how to work with dividing each type of number using a simple 3-step method.

 

Figure 02: What is a whole number? What is a fraction? What is a mixed fraction?

 

Now that you are familiar with all of the key vocabulary related to how to divide fractions, you are ready to work through some practice problems. Let’s start with learning how to divide fractions by other fractions.


How to Divide Fractions by Fractions

How to Divide Fractions by Fractions: Example #1

Example #1: 1/4 ÷ 1/4

Our first dividing fractions example is very simple, and you may already know the answer. In this case, we are taking the fraction 1/4 (one-fourth) and dividing it by 1/4 (one-fourth). So, we are dividing the same non-zero value by itself, which we should already know will be equal to 1.

Even though we already know what the answer should be, let’s go ahead and learn our 3-step method for dividing fractions to this first practice problem to see if it works as it should.

How to Divide Fractions in 3 Easy Steps

  • Step One: Keep the first fraction as is.

  • Step Two: Change the division sign to a multiplication sign.

  • Step Three: Switch the position of the numerator and the denominator in the second fraction. Then multiply the numerators together and the denominators together and simplify if possible.

We will also be referring to this 3-step method as Keep-Change-Flip. Once you learn how to successfully follow these three simple steps, you can use them to solve any problem where you have to divide fractions!

Let’s go ahead and apply them to this first example: 1/4 ÷ 1/4

Step One: Keep the first fraction as is.

This first thing that you have to do is nothing at all. Simply leave the first fraction as is. So, 1/4 stays as 1/4.

Step Two: Change the division sign to a multiplication sign.

Next, take the division sign (÷) and change it to a multiplication sign (x) as follows:

  • 1/4 ÷ → 1/4 x

Step Three: Switch the position of the numerator and the denominator in the second fraction. Then multiply the numerators together and the denominators together and simplify if possible.

For this last step, take the second fraction and “flip” the position of the numerator and the denominator. So, 1/4 becomes 4/1 as follows:

  • 1/4 → 4/1

Now, we have used the Keep-Change-Flip method transform the original problem:

  • 1/4 ÷ 1/4 → 1/4 x 4/1

Figure 03 below illustrates how we used the keep-change-flip method to transform the original division problem into a multiplication problem.

 

Figure 03: How to Divide Fractions: Transform the original division problem into a multiplication problem using keep-change-flip.

 

Finally, we can solve this problem by multiplying these two fractions together. To do this, simply multiply the numerators together and the denominators together as follows:

  • 1/4 x 4/1 = (1x4) / (4x1) = 4/4 = 1

Final Answer: 1

When we multiply these two fractions together, we are left with (1x4) / (4x1) = 4/4 and we know that 4/4 can be reduced to 1, which we expected the answer to be when we first started this problem!

(Looking for some extra help with multiplying fractions, click here to access our free student guide).

Figure 04 below illustrates how we solved this problem after performing keep-change-flip on the original expression.

 

Figure 04: How to solve Example #1 after performing keep-change-flip on the original problem.

 

Confused? If so, that’s okay. The important thing is that you gain some experience with using keep-change-flip. Now let’s go ahead and apply it to another practice problem.


How to Divide Fractions by Fractions: Example #2

Example #2: 2/3 ÷ 4/5

For this second practice problem, we will again be using the 3-step method:

Step One: Keep the first fraction as is.

The first step, simply keep the first fraction 2/3 the same (i.e. you can just leave it as is).

Step Two: Change the division sign to a multiplication sign.

Next, take the division sign (÷) and change it to a multiplication sign (x) as follows:

  • 2/3 ÷ → 2/3 x

Step Three: Switch the position of the numerator and the denominator in the second fraction. Then multiply the numerators together and the denominators together and simplify if possible.

Finally, flip the positions of the numerator and the denominator of the second fraction as follows:

  • 4/5 → 5/4

Again, these 3-steps can be referred to as keep-change-flip, and they are illustrated below in Figure 05:

 

Figure 05: Transform the original problem from Example #2 using Keep-Change-Flip

 

As you can see, we have transformed the original problem using keep change flip and we can now solve it as follows:

  • 2/3 x 5/4 = (2x5) / (3x4) = 10/12 = 5/6

Final Answer: 5/6

Remember, whenever you are multiplying two fractions together, you have to multiply the numerators together and then multiply the denominators together. In this example, we are left with (2x5)/(3x4) = 10/12, and, since 10 and 12 are both divisible by 2, we can reduce and express our final answer as 5/6.

Figure 06 below shows the complete process for solving this second example.

 

Figure 06: How to Divide Fractions Using the Keep-Change-Flip Method

 

Now, let’s go ahead and work through one more example of dividing a fraction by another fraction.


How to Divide Fractions by Fractions: Example #3

Example #2: 7/8 ÷ 11/12

Step One: Keep the first fraction as is.

As always, start by keeping the first fraction (7/8 in this example) as is.

Step Two: Change the division sign to a multiplication sign.

Next, change the division sign (÷) to a multiplication sign (x):

  • 7/8 ÷ → 7/8 x

Step Three: Switch the position of the numerator and the denominator in the second fraction. Then multiply the numerators together and the denominators together and simplify if possible.

Now, flip the positions of the numerator and the denominator of the second fraction:

  • 11/12 → 12/11

The keep-change-flip process for Example #3 is shown in Figure 07 below:

 

Figure 07: How to transform a fractions division problem using keep-change-flip.

 

Now that have transformed the original problem, we can solve it as follows:

  • 7/8 x 12/11 = (7x12) / (8x11) = 84/88 = 21/22

Final Answer: 21/22

In this case, we end up with (7x12) / (8x11) = 84/88 and, since 84 and 88 are both divisible by 4, we can reduce and express our final answer as 21/22.

Figure 08 illustrates how we solved this problem.

 

Figure 08: How to Divide Fractions Using Keep-Change-Flip.

 

Next, we will learn how to divide fractions with whole numbers.


How to Divide Fractions with Whole Numbers

This next section will teach you how to divide a fraction by a whole number and how to divide a whole number by a fraction. We will again be using the keep-change-flip method to solve these kinds of problems. If you want a more in-depth review of how to use the keep-change-flip method, you can click here to revisit the previous section.

How to Divide a Fraction by a Whole Number: Example #1

Example #1: 3/7 ÷ 2

Ready for some good news? You can use the same keep-change-flip method from the previous section to solve these kinds of problems as well. However, there is one extra step involved. Whenever you want to divide a fraction by a whole number using keep-change-flip, you have to rewrite the whole number as a fraction by giving it a denominator of 1.

For this example, we can rewrite the whole number, 2, as a fraction as follows:

  • 2 → 2/1

These both mean the same thing! Now, we can say that solving the original problem is the same as solving 3/7 ÷ 2/1. And since this new problem is just dividing a fraction by another fraction, we can use the keep-change-flip method as follows:

Step One: Keep the first fraction as is.

For the first step, simply keep the first fraction, 3/7, as is.

Step Two: Change the division sign to a multiplication sign.

For the second step, change the division sign (÷) into a multiplication sign (x) as follows:

  • 3/7 ÷ → 3/7 x

Step Three: Switch the position of the numerator and the denominator in the second fraction. Then multiply the numerators together and the denominators together and simplify if possible.

Finally, flip the positions of the numerator and the denominator of the second fraction as follows:

  • 2/1 → 1/2

The keep-change-flip process effectively transforms the division problem into an equivalent multiplication problem that is much easier to solve. This entire process is illustrated in Figure 09 below.

 

Figure 09: How to Divide a Fraction by a Whole Number: Rewrite the whole number as a fraction with a denominator of 1 and use the keep-change-flip method to solve.

 

Using the keep change flip method transforms the original division problem into an equivalent multiplication problem. To multiply two fractions together, simply multiply the numerators together and then multiply the denominators together as follows:

  • 3/7 x 1/2 = (3x1) / (7x2) = 3/14

Notice that the result, 3/14, can not be reduced. Therefore:

Final Answer: 3/14

The graphic in Figure 10 below details the entire process for solving this problem.

 

Figure 10: 3/7 x 1/2 = 3/14

 

In the next example, we will use the exact same process to divide a whole number by a fraction.


How to Divide a Whole Number by a Fraction: Example #2

Example #1: 9 ÷ 3/4

If we want to use the keep-change-flip method to divide a whole number by a fraction, then we will have to rewrite the whole number (9 in this case) as a fraction as follows:

  • 9 → 9/1

Now we can rewrite the original problem 9 ÷ 3/4 as 9/1 ÷ 3/4 (remember that these expressions are equivalent—i.e. they both mean the same thing). Now that we have two fractions being divided by each other, we can use keep-change-flip to solve.

Step One: Keep the first fraction as is.

Just like before, start by keeping the first fraction, 9/1, as is.

Step Two: Change the division sign to a multiplication sign.

Next, change the division sign (÷) into a multiplication sign (x) as follows:

  • 9/1 ÷ → 9/1 x

Step Three: Switch the position of the numerator and the denominator in the second fraction. Then multiply the numerators together and the denominators together and simplify if possible.

Finally, flip the numerator and the denominator of the second fraction as follows:

  • 3/4 → 4/3

The entire process of using keep-change-flip to transform this problem is illustrated in Figure 11 below.

 

Figure 11: How to Divide a Whole Number by a Fraction: Start by rewriting the whole number as a fraction and then use keep-change-flip to solve.

 

Now we can solve the problem by multiplying these two fractions together as follows:

  • 9/1 x 4/3 = (9x4) / (1x3) = 36/3 = 12

Notice that the result, 36/3, can be reduced. Since both the numerator and denominator are divisible by 3, we can conclude that the final answer is 12/1 or just 12.

Final Answer: 12

The graphic in Figure 12 further illustrates how we solved this problem.

 

Figure 12: How to divide a whole number by a fraction using keep-change-flip

 

Now that you know how to divide a fraction by a whole number and how to divide a whole number by a fraction, let’s move onto the final section where you will learn how to divide mixed fractions.


How to Divide Mixed Fractions

The final section of the How to Divide Fractions guide will focus on how to divide mixed fractions and how to divide fractions with mixed numbers.

Again, we can solve all of these types of problems by using the keep-change-flip method (click here to revisit the previous section).

Let’s get started with our first example!

How to Divide Fractions with Mixed Numbers: Example #1

Example #1: 5/9 ÷ 3 1/3

Whenever you have to divide fractions with mixed numbers, you can use the keep-change-flip method to find the answer. However, before you can use keep-change-flip, you will have to convert the mixed number into an improper fraction first.

In this example, we have to convert the fraction 3 1/3 into an improper fraction (a fraction whose numerator is greater than its denominator).

We can rewrite 3 1/3 as 10/3 because:

  • 3 1/3 = 3/3 + 3/3 + 3/3 + 1/3 = 10/3

If you need more help with converting mixed numbers into improper fractions, we highly recommend checking out this free guide before moving forward.

Now, we can rewrite the original problem as follows:

  • 5/9 ÷ 3 1/3 → 5/9 ÷ 10/3

Both of these expressions are equivalent to each other. The key difference here is that the new expression allows us to use the keep-change-flip method to solve it as follows:

Step One: Keep the first fraction as is.

As always, simply keep the first fraction, 5/9, as is.

Step Two: Change the division sign to a multiplication sign.

Next, change the division sign (÷) to a multiplication sign (x) as follows:

  • 5/9 ÷ → 5/9 x

Step Three: Switch the position of the numerator and the denominator in the second fraction. Then multiply the numerators together and the denominators together and simplify if possible.

Lastly, flip the positions of the numerator and the denominator of the second fraction as follows:

  • 10/3 → 3/10

Why are we doing this? Remember that the keep-change-flip method allows us to transform the original division problem into an equivalent multiplication problem that will be much easier to solve. This process is highlighted in Figure 13 below.

 

Figure 13: How to Divide Fractions with Mixed Numbers: Rewrite the mixed number as an improper fraction and then use keep-change-flip to solve.

 

From here, we can solve by multiplying these two fractions together as follows:

  • 5/9 x 3/10 = (5x3) / (9x10) = 15/90 = 1/6

Final Answer: 1/6

Figure 14 below illustrates how we were able to divide fractions with mixed numbers and solve this problem.

 

Figure 14: How to Divide Fractions with Mixed Numbers Explained

 

Now, let’s work through the final example of this guide where you will learn how to divide mixed fractions.


How to Divide Mixed Fractions: Example #2

Example #1: 6 1/2 ÷ 2 1/4

Just like the previous example, we can use the keep-change-flip method to solve this problem, but first we have to convert the mixed fractions in this problem into improper fractions.

In this case:

  • 6 1/2 = 2/2 + 2/2 + 2/2 + 2/2 + 2/2 + 2/2 + 1/2 = 13/2

  • 2 1/4 = 4/4 + 4/4 + 1/4 = 9/4

So, we can rewrite the original problem as:

  • 6 1/2 ÷ 2 1/4 → 13/2 ÷ 9/4

 

Figure 14: How to Divide Mixed Fractions: Start by rewriting any mixed fractions as improper fractions.

 

Again, if you need to review how to convert a mixed numbers into an improper fraction, we highly recommend checking out this free step-by-step guide.

Now, we have a new, yet equivalent, expression to be solved using keep-change-flip:

  • 13/2 ÷ 9/4

Step One: Keep the first fraction as is.

First, keep the first fraction, 13/2, as is.

Step Two: Change the division sign to a multiplication sign.

Second, change the division sign (÷) to a multiplication sign (x) as follows:

  • 13/2 ÷ → 13/2 x

Step Three: Switch the position of the numerator and the denominator in the second fraction. Then multiply the numerators together and the denominators together and simplify if possible.

And finally, flip the numerator and the denominator positions of the second fraction:

  • 9/4 → 4/9

 

Figure 15: How to Divide Mixed Fractions Explained

 

The last thing we have to do to solve this problem is multiply these two improper fractions together as follows:

  • 13/2 x 4/9 = (13x4) / (2x9) = 26/9 or 2 8/9

For this example, we are left we the improper fraction 26/9, which can not be reduced any further. You can also convert 26/9 into a mixed number, which would be 2 8/9. Both of these answers are equivalent.

Final Answer: 26/9 or 2 8/9

Figure 16 below shows how we found this final answer.

 

Figure 16: You will likely have to convert your final answer into a mixed number.

 

Dividing Fractions Video Tutorial

If you want to take a deeper dive into learning how to divide fractions, check out our popular How to Divide Fractions Video Tutorial on YouTube.

This animated tutorial will walk you through several examples of how to divide fractions by other fractions and how to divide fractions and whole numbers (both using the keep-change-flip method).

Try: Dividing Fractions Quiz

Now that you are familiar with how to divide fractions using the Keep-Change-Flip method, you are ready to try a few practice problems on your own.

Go ahead and try the 5-question Dividing Fractions interactive quiz below and see how many problems you can solve. After you submit your answer, you will see what the correct answer is and why.

If you answer 4 or more of the problems correctly, then you likely have a strong understanding of the topic. However, if you are still struggling with the practice problems, we suggest going back and working through this guide again to ensure that you have a deep understanding of how to divide fractions.


How to Divide Fractions FAQ

How do you divide fractions?

You can divide one fraction by another fraction by using the keep-change-flip method, where you keep the first fraction the same, change the division sign to multiplication, and flip the position of the numerator and denominator of the second fraction. In other words, you can divide fractions by multiplying the first fraction by the reciprocal of the second fraction.

How do you divide a whole number by a fraction?

You can divide a whole number by a fraction (or vice versa) again by using the keep-change-flip method, where you multiply the first fraction by the reciprocal of the second fraction. However, you must express the whole number as a fraction with a numerator of 1 (e.g. 8 = 8/1).

How do you divide mixed fractions?

You can divide mixed fractions (such as 1 1/3) by using the keep-change-flip method. However, you have to rewrite the mixed fraction as an improper fraction first. For example, rewrite 1 1/2 as 3/2 before using the keep-change-flip method (i.e. take the first fraction and multiply it by the reciprocal of the second fraction).


Conclusion: How to Divide Fractions

Dividing fractions can be a conceptually challenging math task, but learning how to use the keep-change-flip method can make the process much easier.

Whether you are dividing fractions with other fractions, fractions with whole numbers, whole numbers with fractions, or fractions with mixed numbers, the keep-change-flip method provides a simple three-step process for solving these types of problems.

The keep-change-flip method for dividing fractions can be summarized as follows:

  • Step One: Keep the first fraction as is.

  • Step Two: Change the division sign to a multiplication sign.

  • Step Three: Flip the position of the numerator and the denominator in the second fraction.

After you perform keep-change-flip, you can solve the problem by multiplying and reducing the result whenever possible.


Keep Learning:

Search Tags: how to subtract fractions, subtracting fractions, how to subtract fractions with different denominators, fraction subtraction, subtracting fractions with unlike denominators, how do you subtract fractions?

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10 Super Fun Math Riddles for Kids! (with Answers)

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10 Super Fun Math Riddles for Kids! (with Answers)

10 Super Fun Math Riddles and Puzzles for Kids Ages 10+ (Answers Included!)

Some have been around for centuries, while are others are brand spanking new—but all have been selected as the most fun and engaging math riddles for those who love to challenge their problem-solving skills and have fun solving math puzzles. Enjoy!

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The Educational Value of Math Riddles:

Fun and engaging math riddles and logic puzzles are an amazing way to get students to think critically, develop problem-solving skills, and think about mathematics in a creative way!

In fact, several recent studies have shown that students who work on math puzzles—with and without teacher supervision—improve their math problem-solving skills, learning abilities, and willingness to stick with challenging problems, according to Edutopia.

And if you are looking for a collection of super fun, challenging, and sometimes silly math riddles and brain teasers for kids, then it’s time to put your brain to the test!

Note that the following math riddles are best suited for kids ages and older and they are also fun for high school students and adults!

Are YOU ready?


Free Worksheet Included!

Free Worksheet Included!

There is also a link to download a Free Printable PDF Math Riddles Worksheet and Answer Key that shares all of these riddles at the end of this post!

All of the math riddles, puzzles, and brain teasers below are from the best-selling 101 Math Riddles, Puzzles, and Kids Ages 10+! PDF workbook, which is now available!

10 Awesome Maths Riddles and Brain Teasers for Kids:

Math Riddle #1: Truth or Square?

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Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve Truth or Square?

Would you like FREE math resources in your inbox every day? Click here to sign up for my free math education email newsletter (and get a free math eBook too!)


Math Riddle #2: How Old Is Lucy?

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Keep reading the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve How Old is Lucy?


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Math Riddle #3: Triple Threat

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Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve Triple Threat!


Are you looking for more super fun Math Riddles, Puzzles, and Brain Teasers to share with your kids?

The best-selling workbook 101 Math Riddles, Puzzles, and Brain Teasers for Kids Ages 10+! is now available as a PDF download. You can get yours today by clicking here.


Math Riddle #4: Matchstick Mayhem

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Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve Matchstick Mayhem!


Math Riddle #5: The In-Between

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Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve The In-Between!


Math Riddle #6: Which Weighs More?

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Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve Which Weighs More?


Math Riddle #7: Big Spender!

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Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve Big Spender!


Math Riddle #8: Mystery Parking!

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Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve Mystery Parking!


Math Riddle #9: Cuppla’ Coins

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Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve Cuppla’ Coins!


Math Riddle #10: Pascal’s Triangle

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Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve Pascal’s Triangle!


Math Riddle #11: Bonus!

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Keep reading to the bottom of this page to see the answer key AND click here to see a detailed explanation of how to solve the Bonus Riddle!


Looking for More Fun Math Riddles?

Check out our free collection of 36 Math Riddles for Kids (with answers)!

How many riddles can your kids solve?


ANSWER KEY:

  1. 14 Total Squares (detailed explanation)

  2. Lucy is 37 (detailed explanation)

  3. 1, 2, and 3 (detailed explanation)

  4. 0+4=4 or 5+4=9 (detailed explanation)

  5. A Decimal Point (detailed explanation)

  6. Neither. They both weigh the same! (detailed explanation)

  7. The hoodie costs $125, the shoes cost $25 (detailed explanation)

  8. 87 (flip the image upside down) - (detailed explanation)

  9. One is a quarter and one is a nickel (detailed explanation)

  10. 6 (detailed explanation)

  11. 1, 5, 10, 10, 5, 1 (detailed explanation)

Worksheet.jpg

Are you looking for more super fun Math Riddles, Puzzles, and Brain Teasers to share with your kids?

My best-selling workbook 101 Math Riddles, Puzzles, and Brain Teasers for Kids Ages 10+! is now available as a PDF download. You can get yours today by clicking here.


Did I miss your favorite math riddle for kids? Share your thoughts, questions, and suggestions in the comments section below!

(Never miss a Mashup Math blog--click here to get our weekly newsletter!)

By Anthony Persico

Anthony is the content crafter and head educator for YouTube's MashUp Math and an advisor to Amazon Education's 'With Math I Can' Campaign. You can often find me happily developing animated math lessons to share on my YouTube channel . Or spending way too much time at the gym or playing on my phone.

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How to Turn a Percent into a Fraction in 3 Steps

How to Turn a Percent into a Fraction in 3 Steps

How to Turn a Percent into a Fraction

Step-by-Step Guide: How to Convert Percent to Fraction in 3 Easy Steps

 

Free Step-by-Step Guide: Percent to Fraction in 3 Steps

 

Are you ready to learn how to turn a percent into a fraction? If so, this free guide on how to convert percent to fraction will teach you everything you need to know about this important math skill. Understanding how to turn a percent into a fraction will help you with solving a variety of math problems related to topics including conversions, discounts, unit rates, and more.

Beyond the classroom, knowing how to make percent to fraction conversions will help you with real-world scenarios including sales tax, data and statistics, and shopping. So, whether you are a math student or just someone who wants to strength their overall number sense, this guide will teach you and important and useful skill.

You can use the quick links below to jump to any section of this guide, or you can work through each section in order (recommended). Let’s get started!

Table of Contents (Jump To):

 

Figure 01: What is the percent to fraction relationship?

 

Review: Percent to Fraction Key Concepts

Before we learn how to turn a percent into a fraction, let’s complete a short view of some key concepts and vocabulary terms related to percents and fractions.

For starters, percents and fractions share a relationship in that they are two different ways of expressing the same thing: a part related to a whole.

In terms of parts and wholes, a fraction, like 1/2, includes a numerator (top number that represents the part) and a denominator (bottom number that represents the whole.). So, 1/2 means that a whole is divided into two equal parts, and you have one of those parts.

On the other hand, a percent, like 50%, means represents a fraction where the denominator, or whole, is always equal to 100.

A fraction and a percent are two different ways of expressing the same thing.

For example, if we wanted to convert the fraction 1/2 to a percent, we could do that as follows:

  • 1/2 x 100 = 100/2 = 50 = 50%

So, 1/2 is equivalent to 50% (as shown in Figure 01 above).

But what if we are given a percent and had to turn it into a fraction?

Below, you will learn a simple 3-step strategy for how to turn a percent into a fraction that you can use to convert any percent to a fraction quickly and accurately.

 

Figure 02: Percent to Fraction: Why does 25% equal 1/4?

 

How to Turn a Percent into a Fraction in 3 Easy Steps

Now that you understand the relationship between percents and fractions, you are ready to learn how to turn a percent into a fraction in 3 simple steps:

How to Turn Percent to Fraction

  • Step One: Rewrite the given percent as a number without the % sign

  • Step Two: Rewrite the result as a fraction with a denominator of 100.

  • Step Three: Simplify the fraction (if possible).

Let’s say that we wanted to convert 25% to a fraction, we could use these three steps to solve the problem as follows:

Step One: Rewrite the number without a % sign:

  • 25% → 25

Step Two: Rewrite the result as a fraction with a denominator of 100:

  • 25 → 25/100

Step Three: Simplify (if possible):

You can simplify a fraction by seeing if you can find a common factor shared by both the numerator and the denominator. If they share more than one common factor, you must choose the greatest common factor.

Since 25 and 100 are both divisible by 25, we can simplify 25/100 as follows:

  • 25/100 → (25÷25) / (100÷25) = 1/4

Final Answer: 25% = 1/4

So, 25% is equivalent to the fraction 1/4.

The entire step-by-step process for showing that 25% equals 1/4 is shown in Figure 03 below.

 

Figure 03: How to convert percent to fraction in 3 steps.

 

Percent to Fraction: Example #1

Problem: Convert 75% to a fraction.

Now we are ready to use the 3-step method for converting percent to fraction to solve a few practice problems.

Step One: Rewrite without the percent sign:

  • 75% → 75

Step Two: Rewrite the result from Step One as a fraction with a denominator of 100:

  • 75 → 75/100

Step Three: Simplify (if possible):

To complete this final step, we have to see if 75/100 can be simplified (i.e. reduced). Since 75 and 100 are both divisible by 25, we can simplify the fraction as follows:

  • 75/100 → (75÷25) / (100÷25) = 3/4

Final Answer: 75% = 3/4

Figure 04 below shows how we solved this first example of how to turn a percent into a fraction.

 

Figure 04: How to convert percent to fraction.

 

Percent to Fraction: Example #2

Problem: Convert 12% to a fraction.

For our next example, we can again use our 3-step strategy to convert it to fraction as follows:

Step One: Rewrite without the %:

  • 12% → 12

Step Two: Rewrite the result from as a fraction over 100

  • 12 → 12/100

Step Three: Simplify (if possible):

After completing the second step, we are left with the fraction 12/100. Since both 12 and 100 are divisible by 4, we can simplify the fraction as follows:

  • 12/100 → (12÷4) / (100÷4) = 3/25

Final Answer: 12% = 3/25

Figure 05 below illustrates how we showed that 12% equals 3/25 in 3 steps.

 

Figure 05: How to turn a percent into a fraction example #2 solved.

 

Fraction to Percent: Example #3

Problem: Convert 150% to a fraction.

For this third and final example, we have a percentage (150%) that is greater than 100. However, we can still convert this percent to a fraction by using our 3-step strategy as follows:

Step One: Rewrite 150% the percent sign:

  • 150% → 150

Step Two: Rewrite 150 as a fraction with a denominator of 100

  • 150 → 150/100

Step Three: Simplify (if possible):

Can we simplify the fraction 150/100? Since both 150 and 100 share a greatest common factor of 50, we can simplify this fraction as follows:

  • 150/100 → (150÷50) / (100÷50) = 3/2

Final Answer: 150% = 3/2

So, 150% is equivalent to the improper fraction 3/2 (as shown in Figure 06 below).

 

Figure 06: How to convert percent to fraction in 3 steps.

 

 
 

More Free Math Resources:

How to Turn a Fraction into a Percent in 2 Steps

How to Turn a Fraction into a Percent in 2 Steps

How to Turn a Fraction into a Percent

Step-by-Step Guide: How to Convert Fraction to Percent in 2 Easy Steps

 

Free Step-by-Step Guide: Fraction to Percent in 2 Easy Steps

 

Knowing how to turn a fraction into a percent is a simple math skill that can help you solve problems in the classroom as well as in the real-world. When you understand how to turn fraction to percent, you can quickly and easily solve problems and make conversions, which is an incredibly useful skill that everyone should learn at some point.

This free guide on turning fraction to percent will teach you how to turn a fraction into a percent by following a simple 2-step method that you can use to solve a variety of math problems involving fractions and percents. To help you to learn this skill, we will work through three example problems of how to make a fraction into a percent, which will give you a great amount of practice and experience with this skill.

While we recommend that you work through each section of our fraction to percent guide, you can use the Table of Contents links below to jump to any section that you choose:

Table of Contents (Jump To):

 

Figure 01: Fraction to Percent Relationship

 

Review: Fraction to Percent Relationships

Let’s start off with a quick review of the fraction to percent relationship along with some important math vocabulary related to this topic.

What is the relationship between a fraction and a percent?

In math, fractions and percents are two different ways of expressing the same concept: a part and a whole.

A fraction, like 4/5, means that there is a whole divided into 5 equal parts, and you have 4 of those parts. The part is the numerator (the value above the fraction line), and the whole is the denominator (the value below the fraction line).

A percent, like 80%, means that there is a whole represented by 100%, and you have 80 equal parts of that whole. In other words, a percent is a fraction where the denominator is always 100 (i.e. a percent is the same thing as a fraction, but it is always out of 100). So, the fraction 4/5 can be expressed as a percent by multiplying it by 100 as follows:

  • 4/5 x 100 = 400/5 = 80%

Therefore, we can say that the fraction 4/5 expressed as a percent is 80% (as shown in Figure 01 above).

Understanding the relationship between fractions and percents is key to learning how to turn a fraction into a percent will help you to make fast and accurate conversions between measurements, make comparisons involving data, and solve properties related to topics including sales, taxes, discounts, statistics, and even exam scores.

 

Figure 02: How to make a fraction into a percent in two steps.

 

How to Turn a Fraction into a Percent in 2 Easy Steps

Now that we have reviewed the relationship between fractions and percents, let’s learn a simple two-step method for how to make a fraction into a percent:

How to Turn a Fraction into a Percent

  • Step One: Divide the numerator by the denominator to convert the fraction into a decimal.

  • Step Two: Multiply the result by 100 and express as a percent using a % sign.

For example, let’s turn the fraction 1/2 into a percent by using this two-step method:

Step One: Start by dividing the numerator by the denominator and express the result as a decimal:

  • 1/2 = 1 ÷ 2 = 0.5

Step Two: Multiply by 100 and express as a percent:

  • 0.5 x 100 = 50 → 50%

So, the fraction 1/2 is equivalent to 50% (as shown in Figure 02 above).

 

Figure 03: How to convert fraction to percent in two steps.

 

Fraction to Percent: Example #1

Problem: Convert 3/4 to a percent.

Let’s gain some experience with using our two-step method for how to turn a fraction into a percent by applying it to the fraction 3/4 as follows:

Step One: First, we have to divide the numerator by the denominator to express the fraction in decimal form:

  • 3/4 = 3 ÷ 4 = 0.75

Step Two: Now, multiply the result from the first step by 100 and solve:

  • 0.75 x 100 = 75 → 75%

Final Answer: The fraction 3/4 is equivalent to 75%.

The step-by-step process for solving this first example is shown in Figure 03 above.

Now, let’s go ahead and try another practice problem on how to make a fraction into a percent.


 

Figure 04: How to turn a fraction into a percent example #2 solved.

 

Fraction to Percent: Example #2

Problem: Convert 2/5 to a percent.

We can solve this next example using the same two-step method that we used to solve Example #1 as follows:

Step One: Convert the fraction to a decimal by dividing the numerator by the denominator:

  • 2/5 = 2 ÷ 5 = 0.4

Step Two: Multiply the result by 100 and express the answer as a percent (%):

  • 0.4 x 100 = 40 → 40%

Final Answer: 2/5 = 40%

Figure 04 above illustrates how we turned this fraction into a percent in two easy steps.

Are you starting to get the hang of it? Now, let’s work through one more fraction to percent practice problem.


 

Figure 05: The fraction 7/8 is equal to 87.5%

 

Fraction to Percent: Example #3

Problem: Convert 7/8 to a percent.

For this third and final example of how to make a fraction into a percent, we want to convert the fraction 7/8 into a percent, and we can use our two-step method to do that.

Step One: Divide the numerator by the denominator and express the answer as a decimal:

  • 7/8 = 7 ÷ 8 = 0.875

Step Two: Multiply the decimal from Step One by 100 and express the answer as a percent (%):

  • 0.875 x 100 = 87.5 → 87.5%

Final Answer: 7/8 = 87.5%

Figure 05 above shows how we used our two-step method to solve Example #3.



 
 

More Free Math Resources: