Fraction Calculator
Add, subtract, multiply, and divide fractions with automatic simplification
Result
Operation Details
Operation: +
First Fraction: 0
Second Fraction: 0
Note: This calculator performs operations on fractions and automatically simplifies the result.
Understanding Fractions
Fractions show up everywhere once you start looking for them. Whether you're splitting a pizza, measuring ingredients for a recipe, or calculating discounts at a store, you're working with parts of a whole. The tricky part isn't using fractions—it's doing the math with them.
The reason fractions matter goes beyond just passing your math class. They give you precision that whole numbers can't. When you're building something, 3.5 inches might work, but 3 1/2 inches is clearer and more exact. Fractions also help you understand relationships between numbers, which comes in handy for everything from adjusting recipes to understanding financial ratios.
Types of Fractions
Proper Fractions
These are your standard fractions where the top number (numerator) is smaller than the bottom number (denominator). Think 1/2, 3/4, or 5/8. They represent less than one whole thing.
Improper Fractions
When the top number is bigger than the bottom, you've got an improper fraction like 5/4 or 7/3. These represent more than one whole, which is why they look a bit odd at first.
Mixed Numbers
A whole number plus a fraction, like 1 1/2 or 2 3/4. These are easier to visualize but need to be converted to improper fractions before you can do math with them.
Doing Math with Fractions
Here's what trips people up: each operation has its own rules. Addition and subtraction need a common denominator, but multiplication and division don't. Here's the quick version:
Adding & Subtracting
You need the same denominator to add or subtract fractions. Find a common one, convert both fractions, then add or subtract the top numbers. Don't forget to simplify at the end.
Multiplying & Dividing
Multiplication is straightforward—multiply straight across (top times top, bottom times bottom). For division, flip the second fraction and multiply. That "keep, change, flip" rule actually works.
How to Actually Get Better with Fractions
Look, fractions can be frustrating. But they're not impossible—you just need to build up your understanding step by step. Here's what actually works:
Start with what fractions mean
Before you dive into operations, make sure you really get what a fraction represents. The top number tells you how many pieces you have, the bottom tells you how many pieces make a whole. Use real things to practice—pizza slices, measuring cups, whatever helps it click.
Learn to simplify
This is huge. If you can simplify fractions quickly, everything else gets easier. Find the biggest number that divides evenly into both the top and bottom, then divide them both by it. Try it with 8/12 or 15/20 until it becomes second nature.
Get comfortable converting between forms
You'll need to switch between improper fractions (like 7/3) and mixed numbers (like 2 1/3) all the time. Same with converting to decimals. Practice going back and forth until it's automatic.
Practice the operations until they stick
Start simple: 1/2 + 1/4, then work up to harder ones like 2/3 + 5/6. Do the same with multiplying and dividing. The more you practice, the less you'll have to think about the steps.
Use them in real situations
Math makes more sense when it's connected to real life. Try doubling a recipe, figuring out how much paint you need for a room, or calculating what 1/3 off really means at a sale.
Mistakes Everyone Makes with Fractions
Adding the denominators
This is probably the most common mistake. When you see 1/2 + 1/3, it's tempting to just add across and get 2/5. But that's not how fractions work. You need to find a common denominator first (in this case, 6), convert both fractions (3/6 and 2/6), then add to get 5/6. The wrong answer isn't even close—2/5 is 0.4, while 5/6 is about 0.83.
Not simplifying your answer
You do all the work and get 6/8, but that's not really done. Simplifying to 3/4 makes it cleaner and easier to work with if you need to do more calculations. Plus, teachers will usually mark unsimplified answers as incomplete. Get in the habit of checking if both numbers share a common factor.
Dividing fractions wrong
Division trips people up because you don't actually divide—you flip the second fraction and multiply. So 1/2 ÷ 1/4 becomes 1/2 × 4/1, which equals 2. If you tried to divide normally, you'd get 1/8, which is completely wrong. The "keep, change, flip" method really does work: keep the first fraction, change ÷ to ×, flip the second fraction.
Converting mixed numbers incorrectly
When you see 2 1/3, you can't just stick the 2 and 1 together. You need to convert it properly: multiply 2 by 3 (the denominator), add 1 (the numerator), and put that over 3. So 2 1/3 becomes 7/3. If you don't convert mixed numbers before doing operations with them, your math will be off.
Where You'll Actually Use This
Fractions aren't just for math class. Once you leave school, you'll find them everywhere—some obvious, some not so much. Here are places where knowing how to work with fractions actually matters.
Cooking and Baking
This is the most obvious one. Recipes use fractions constantly—1/2 cup of flour, 3/4 teaspoon of salt. But it gets interesting when you need to scale recipes up or down. Doubling a recipe that calls for 2/3 cup of sugar? You'll need 4/3 cups, or 1 1/3 cups. Halving a recipe with 3/4 cup of milk means you need 3/8 cup. These aren't calculations you can easily do in your head if you don't understand fractions.
Measurements in construction use fractions because inches are divided that way. You'll see things like 2x4s that are actually 1 1/2 by 3 1/2 inches, or need to cut a board into 7/8 inch strips. Blueprints and plans use fractional scales—a drawing might be 1/4 inch equals 1 foot. If you're hanging pictures, installing shelves, or building anything, you're going to need to add, subtract, and divide fractions to figure out spacing and measurements.
Money and Investing
Stock prices used to be quoted in fractions (like 23 3/8), and while they're decimals now, fractions still show up in finance. Interest rates often involve fractions—a monthly interest rate is 1/12 of the annual rate. If you're splitting bills with roommates or figuring out what your 2/3 share of something costs, you're using fractions. Business partnerships are often expressed as fractions too—someone might own 3/5 of a company while their partner owns 2/5.
Medicine and Science
Medical dosing is full of fractions because precision matters. A medication might be prescribed at 1/2 tablet twice daily, or a dose might be calculated as 3/4 of a milligram per kilogram of body weight. In genetics, you see fractions in probability—if both parents carry a gene, there's a 1/4 chance their child will express it. Chemistry uses mole ratios that are fractions. Even half-life calculations in physics are based on fractions (half after one period, 1/4 after two periods, and so on).
Screens and Technology
Ever notice how screen sizes are described as ratios? 16:9 is really 16/9, and that fraction determines the shape of your TV or monitor. Frame rates in video work the same way—30 fps means each frame is 1/30 of a second. If you work with any kind of digital media, you're constantly dealing with aspect ratios, sampling rates, and compression ratios—all fractions.
About This Guide
This fraction calculator and guide were created to help people actually understand fractions, not just memorize rules. The explanations focus on why things work the way they do, and the examples come from real situations where you'd need to use fractions. Whether you're helping a kid with homework, adjusting a recipe, or measuring something for a project, the goal is to make fractions less intimidating and more useful.
Frequently Asked Questions
How do I add fractions with different denominators?
You need to get them to have the same denominator first. Find a number that both denominators divide into evenly (the least common denominator), convert both fractions to use that denominator, then add just the top numbers. For example, with 1/3 + 1/4, you'd use 12 as your common denominator: 4/12 + 3/12 = 7/12.
What's the difference between proper and improper fractions?
A proper fraction like 3/4 has a smaller number on top, so it's less than 1. An improper fraction like 5/4 has a bigger number on top, so it's more than 1. You can convert improper fractions to mixed numbers (like 1 1/4) if that's easier to picture.
How do I turn a fraction into a decimal?
Just divide the top number by the bottom number. So 1/2 = 0.5 and 3/4 = 0.75. Some fractions give you repeating decimals, like 1/3 = 0.333... which keeps going forever.
What's a reciprocal and why do I need it?
A reciprocal is just a fraction flipped upside down. The reciprocal of 2/3 is 3/2. You need this for division—instead of dividing by a fraction, you multiply by its reciprocal. So 1/2 ÷ 1/4 becomes 1/2 × 4/1 = 2.
How do I know which fraction is bigger?
The easiest way is usually to convert both to decimals and compare. Or you can find a common denominator and see which numerator is larger. There's also a cross-multiply trick: multiply the first numerator by the second denominator, and compare that to the second numerator times the first denominator. Whichever gives you a bigger number is the bigger fraction.
How do I simplify fractions?
Find the biggest number that divides evenly into both the top and bottom, then divide them both by it. For 24/36, both are divisible by 12, so you get 2/3. Keep going until there's no common factor bigger than 1.
How do I multiply fractions?
This one's actually easier than addition. Just multiply straight across—top times top, bottom times bottom. So 2/3 × 4/5 = 8/15. Then simplify if you can.
How do I convert between mixed numbers and improper fractions?
To go from a mixed number like 2 1/3 to an improper fraction: multiply the whole number by the denominator (2 × 3 = 6), add the numerator (6 + 1 = 7), and put that over the original denominator to get 7/3. Going the other way, just divide the numerator by the denominator—the quotient becomes your whole number and the remainder goes over the denominator.
When should I use fractions instead of decimals?
Fractions are better when you need exact values. 1/3 is precise, but 0.333 is just an approximation. Fractions also make more sense for things like recipes (1/2 cup, not 0.5 cups) and measurements (3/4 inch, not 0.75 inches). If you're working with ratios or need to show exact relationships between numbers, stick with fractions.