Fraction Calculator

Using the calculator is straightforward. Enter the numerator (top number) and denominator (bottom number) for each fraction, then pick the operation you want: add, subtract, multiply, or divide. Hit calculate and you'll get the result, usually already in simplified form.

A few things to keep in mind before you start:

• The denominator can never be zero. If you enter zero in the bottom field, the calculator will flag it as an error.
• For mixed numbers (like 2 ½), most calculators have a separate whole-number field. Fill that in along with the numerator and denominator.
• If you want the answer as a decimal or percentage instead of a fraction, look for a conversion toggle or a separate conversion tool on the page.

Results are shown in lowest terms by default. If you want to see the step-by-step work, expand the steps section after calculating.

Adding fractions requires a common denominator. That's the one rule that everything else hinges on.

When the denominators are already the same, just add the numerators and keep the denominator. So 2/7 + 3/7 = 5/7. Simple.

When the denominators differ, you need to find the least common denominator (LCD), convert each fraction so it uses that denominator, then add the numerators. For example, to add 1/3 + 1/4:

1. Find the LCD of 3 and 4, which is 12.
2. Convert: 1/3 becomes 4/12, and 1/4 becomes 3/12.
3. Add the numerators: 4 + 3 = 7, so the answer is 7/12.

If the result is an improper fraction (numerator larger than denominator), you can convert it to a mixed number. And always check whether the answer reduces further.

Subtraction works exactly like addition, just with a minus sign. You still need a common denominator before you can do anything with the numerators.

Same denominators? Subtract the numerators and keep the denominator. 5/8 minus 2/8 is 3/8.

Different denominators follow the same LCD process:

1. Find the least common denominator.
2. Rewrite each fraction with that denominator.
3. Subtract the numerators.
4. Simplify if possible.

One place people slip up: subtracting mixed numbers when the fraction part of the second number is larger than the first. In that case, you borrow one whole unit from the whole-number part, converting it into a fraction, before you subtract. For instance, 3 1/4 minus 1 3/4 requires borrowing so that 3 1/4 becomes 2 5/4. Then 2 5/4 minus 1 3/4 equals 1 2/4, which simplifies to 1 1/2.

Multiplication is actually easier than addition or subtraction because you don't need a common denominator. Multiply straight across: numerator times numerator, denominator times denominator.

So 2/3 × 3/5 = (2×3)/(3×5) = 6/15, which simplifies to 2/5.

A handy shortcut is cross-canceling before you multiply. If a numerator and a diagonal denominator share a common factor, divide both by that factor first. It keeps the numbers smaller and often eliminates the simplification step at the end. For 4/9 × 3/8, you can cancel the 4 and 8 (both divisible by 4) and the 3 and 9 (both divisible by 3), leaving 1/2 × 1/3 = 1/6.

Dividing fractions follows one simple rule: multiply by the reciprocal. The reciprocal of a fraction is just that fraction flipped upside down. So dividing by 3/4 is the same as multiplying by 4/3.

The process looks like this:

1. Keep the first fraction as is.
2. Change the division sign to multiplication.
3. Flip the second fraction (take its reciprocal).
4. Multiply across and simplify.

Example: 2/5 ÷ 4/7 becomes 2/5 × 7/4 = 14/20, which reduces to 7/10.

This rule works for any fractions, including whole numbers (just write the whole number as a fraction over 1) and mixed numbers once they've been converted to improper fractions.

A simplified fraction (also called a fraction in lowest terms) has no common factors between the numerator and denominator other than 1. It's the most reduced form of that fraction.

To simplify, find the greatest common factor (GCF) of the numerator and denominator, then divide both by it. If 12/18 is your fraction, the GCF of 12 and 18 is 6. Divide both by 6: 12/6 = 2 and 18/6 = 3, giving you 2/3.

You can also simplify step by step if the GCF isn't obvious. Divide both numbers by any common factor, then keep going until no common factors remain. It takes more steps, but you'll land in the same place.

Fractions, decimals, and percentages are three ways of expressing the same value. Knowing how to convert between them is genuinely useful in everyday math.

Repeating decimals like 0.333... are just 1/3. Most fraction-to-decimal conversions either terminate (end) or repeat. Your calculator will usually show a rounded decimal for the repeating ones.

A mixed number combines a whole number and a proper fraction, like 3 2/5. An improper fraction has a numerator that's larger than or equal to its denominator, like 17/5. They represent the same value, just written differently.

Converting a mixed number to an improper fraction: multiply the whole number by the denominator, add the numerator, and put that total over the original denominator. So 3 2/5 = (3×5 + 2)/5 = 17/5.

Going the other direction: divide the numerator by the denominator. The quotient is the whole number, the remainder becomes the new numerator, and the denominator stays the same. 17 ÷ 5 = 3 remainder 2, so 17/5 = 3 2/5.

Improper fractions are often easier to work with during calculations. Mixed numbers are easier to read and interpret in a real-world context. The calculator accepts both formats and can display results in either form.

Here's a quick reference for the core fraction formulas. These apply to proper fractions, improper fractions, and (after converting) mixed numbers.

A few rules that always apply:

• The denominator can never be zero.
• A fraction equals zero only when the numerator is zero (and the denominator is not).
• Any number divided by itself equals 1, so 5/5 = 1.
• Always simplify your final answer unless the problem specifically asks for a different form.

Seeing the steps in action makes the formulas stick. Here are worked examples for each operation.

Addition: 1/2 + 2/3
LCD of 2 and 3 is 6. Convert: 3/6 + 4/6 = 7/6 = 1 1/6.

Subtraction: 5/6 − 1/4
LCD of 6 and 4 is 12. Convert: 10/12 − 3/12 = 7/12.

Multiplication: 3/5 × 10/9
Cross-cancel: 3 and 9 share a factor of 3 (giving 1 and 3); 10 and 5 share a factor of 5 (giving 2 and 1). Now: 1/1 × 2/3 = 2/3.

Division: 7/8 ÷ 7/4
Flip the second fraction and multiply: 7/8 × 4/7 = 28/56 = 1/2.

Mixed number multiplication: 1 1/2 × 2 2/3
Convert: 3/2 × 8/3. Cross-cancel the 3s: 1/2 × 8/1 = 8/2 = 4.

Each of these follows the same rules described above. The numbers change but the process doesn't.

A common denominator is any number that both denominators divide into evenly. The least common multiple (LCM) of the denominators is the smallest such number, and using it keeps your fractions as simple as possible throughout the calculation.

To find the LCM of two numbers, you have a few options:

• List multiples: Write out multiples of each number until you find one they share. Multiples of 4: 4, 8, 12, 16... Multiples of 6: 6, 12, 18... LCM = 12.
• Prime factorization: Break each number into prime factors. Take the highest power of each prime that appears. For 4 (2²) and 6 (2×3): highest powers are 2² and 3, so LCM = 4 × 3 = 12.
• Formula: LCM(a, b) = (a × b) / GCF(a, b). If GCF of 4 and 6 is 2, then LCM = 24/2 = 12.

Once you have the LCM, convert each fraction by multiplying numerator and denominator by whatever factor brings the denominator up to the LCM. Then add or subtract as usual.

Comparing fractions is easy when the denominators match: just look at the numerators. 3/7 is less than 5/7 because 3 is less than 5.

When denominators differ, you've got a couple of options. The most reliable is to convert both fractions to a common denominator and then compare numerators. To compare 2/3 and 3/5, find the LCD (15), convert to 10/15 and 9/15, and it's clear that 2/3 is larger.

Another approach: convert each fraction to a decimal by dividing numerator by denominator, then compare the decimals. It's faster for a quick check, though it can introduce rounding with repeating decimals.

To order a list of fractions from smallest to largest:

1. Convert all fractions to a common denominator (or to decimals).
2. Sort by numerator (or decimal value).
3. Rewrite the original fractions in that order.

This comes up more than you'd think, whether you're ranking measurements, scaling a recipe, or working through a math problem set. The fraction calculator can handle the conversion step for you, so ordering becomes a matter of reading the results.