EZ Calculators

Fraction Calculator

Use this fraction calculator to add, subtract, multiply, divide or compare two fractions, or simplify one. Enter a whole number, numerator and denominator for each value and you'll get the answer in lowest terms, as a mixed number, a decimal and a percentage, with the steps shown.

Calculation and content reviewed by EZ Calculators Editorial Team on .

Enter values

Enter proper fractions, improper fractions, whole numbers, or mixed numbers. Choose arithmetic, exact comparison, or one-value simplification.

Build the scenario below, then calculate for a complete result report.

Runs in your browser
Operation

Choose exact fraction work

Add and subtract use a least common denominator. Multiplication combines numerators and denominators, division uses the reciprocal of a nonzero second value, comparison uses exact cross-products, and simplify reduces one value to lowest terms.
Choose an operation, comparison, or one-value simplification.

First value

Optional signed whole-number part.

Second value

Optional signed whole-number part.
Decimal and percent precisionExact fractions never change
Controls decimal and percent display only; fraction arithmetic stays exact.
Exact integer arithmeticKeep denominators positive and place a mixed-number sign on the whole part.
For a negative mixed number, place the minus sign on the whole part, such as -2 and 1/3. When the whole part is zero, the numerator may be negative. Division by a zero fraction is undefined.

How do you add fractions with different denominators?

Rewrite both fractions over a common denominator, add the numerators, then simplify. The least common denominator is the smallest number both denominators divide into. For 2/3 + 5/8, that's 24, so 2/3 becomes 16/24 and 5/8 becomes 15/24. Adding gives 31/24, which is 1 7/24 as a mixed number.

How to use the fraction calculator

Pick what you want to do first: add, subtract, multiply, divide, compare, or simplify and convert. Each value has three boxes, Whole, Numerator and Denominator. For a plain fraction like 3/5, leave Whole at 0. For a mixed number like 2 3/4, type 2, 3 and 4.

Simplify mode uses only the first value, so the second one is hidden. The decimal precision menu changes how many places the decimal and percent show. The fraction itself is always exact. This fraction calculator works alongside an AI math solver to help students solve math problems and understand the steps.

  1. Choose Add, Subtract, Multiply, Divide, Compare or Simplify and convert first value.
  2. Enter the whole number (or 0), numerator and denominator for the first value.
  3. Enter the second value if the operation needs one.
  4. Pick how many decimal places you want in the decimal and percent.
  5. Press Calculate fractions and read the simplified answer, then the work table below it.

Mixed numbers and improper fractions

A mixed number like 2 3/4 is a whole number plus a proper fraction. An improper fraction like 11/4 has a top number at least as big as the bottom one. They're two ways to write the same value. This tool works as a mixed fraction calculator and an improper fraction calculator at once. Type either form and every answer comes back in both.

Behind the scenes, mixed numbers become improper fractions before any math happens. Multiply the whole number by the denominator and add the numerator: 2 3/4 is (2 x 4 + 3)/4 = 11/4. To go back, divide: 11 / 4 is 2 with 3 left over, so 2 3/4.

For a negative mixed number, put the minus sign on the whole number and keep the numerator positive. Typing -2, 1 and 3 means -2 1/3, which is -7/3. It doesn't mean -2 + 1/3.

Formula guide
  • Mixed number to improper fraction: w n/d = (w x d + n) / d
  • Improper fraction to mixed number: whole part = numerator / denominator (drop the remainder); new numerator = the remainder

Adding fractions with unlike denominators

You can only add pieces of the same size. Thirds and eighths aren't the same size, so you first rewrite both fractions as 24ths, the smallest number that 3 and 8 both divide into. Then add the tops and keep the bottom.

Subtraction works the same way. For 3/4 - 1/3, the common denominator is 12: 9/12 - 4/12 = 5/12. Never add or subtract the denominators themselves. 1/2 + 1/3 isn't 2/5. It's 3/6 + 2/6 = 5/6.

  • Find the least common denominator (LCD) of the two denominators.
  • Multiply each numerator by whatever its denominator was multiplied by.
  • Add or subtract the numerators. Keep the LCD.
  • Simplify, and turn an improper answer into a mixed number if you need one.
Formula guide
  • a/b + c/d = (a x d + c x b) / (b x d), then simplify
  • a/b - c/d = (a x d - c x b) / (b x d), then simplify

Multiplying and dividing fractions

Multiplying is the easy one. Multiply the tops, multiply the bottoms, then simplify. No common denominator needed. With mixed numbers, convert first: 1 1/2 x 2 2/3 is 3/2 x 8/3 = 24/6 = 4.

To divide, flip the second fraction and multiply. 7/8 divided by 1/4 becomes 7/8 x 4/1 = 28/8, which simplifies to 7/2 or 3 1/2. You can't divide by a fraction that equals zero, so the calculator stops you if the second value is 0.

Formula guide
  • a/b x c/d = (a x c) / (b x d)
  • a/b divided by c/d = a/b x d/c, where c is not zero

How to simplify fractions

A fraction is in simplest form when no whole number above 1 divides both the top and the bottom. Find the greatest common factor (GCF) and divide both by it. For 18/24, the GCF is 6, so 18/24 = 3/4.

Choose Simplify and convert first value to do just this step. You'll get the lowest-terms fraction, the mixed number, the decimal, the percentage and the reciprocal, plus whether the decimal ends or repeats.

Fractions simplified by their greatest common factor
FractionGCFSimplest formDecimal
18/2463/40.75
42/56143/40.75
45/60153/40.75
28/847/2 = 3 1/23.5
15/90151/60.1666...

Fraction examples for every mode

Each row below is what you'd see after entering the values and pressing the button. The comparison row also shows the exact gap between the two fractions.

Worked fraction calculator examples
ModeInputExact answerMixed number or note
Add2/3 + 5/831/241 7/24
Add mixed numbers2 1/2 + 1 3/417/44 1/4
Subtract mixed numbers3 1/3 - 1 3/419/121 7/12
Multiply1 1/2 x 2 2/34Whole number
Divide7/8 divided by 1/47/23 1/2
Compare2/3 vs 3/52/3 > 3/5Gap of 1/15
Simplify18/243/40.75 or 75%

Comparing two fractions exactly

To see which fraction is bigger, cross multiply. For 2/3 and 3/5, compare 2 x 5 = 10 with 3 x 3 = 9. Since 10 is bigger, 2/3 is the larger fraction. Compare mode does this with whole numbers, so two decimals that look the same after rounding can't fool it.

You also get both fractions rewritten over their least common denominator (10/15 and 9/15 here) and the exact difference, 1/15.

Sources

These textbook sections cover the fraction rules used on this page.

OpenStax: Add and Subtract Fractions with Different DenominatorsExplains the least common denominator method with worked problems.OpenStax: Multiply and Divide FractionsCovers multiplying fractions and dividing by a reciprocal.OpenStax: Add and Subtract Mixed NumbersShows how to convert and combine mixed numbers step by step.Common Core State Standards for MathematicsLists the fraction skills expected at each grade level.

FAQ

How do I enter a mixed number?

Type the whole number in Whole, then the numerator and denominator. For 3 2/5, enter 3, 2 and 5. Leave Whole at 0 for an ordinary fraction like 2/5.

How do you turn an improper fraction into a mixed number?

Divide the numerator by the denominator. The whole answer is the whole number and the remainder goes over the original denominator. For 17/4, 17 divided by 4 is 4 remainder 1, so 17/4 = 4 1/4.

What is 1/2 + 1/3?

1/2 + 1/3 = 5/6. The common denominator is 6, so 1/2 becomes 3/6 and 1/3 becomes 2/6. Adding the numerators gives 5/6, which is already in simplest form.

How do I subtract a bigger fraction from a smaller one?

Do it the same way and the answer comes out negative. 1/4 - 2/3 is 3/12 - 8/12 = -5/12. The calculator keeps the minus sign on the numerator.

Can the calculator add three or more fractions?

Not in one step. It works with two values at a time. Add the first two, then enter that answer as the first value and add the third.

How do I divide a fraction by a whole number?

Write the whole number as a fraction over 1, then flip and multiply. 3/4 divided by 2 is 3/4 x 1/2 = 3/8. In the calculator, enter Whole 2, numerator 0 and denominator 1.

Are the decimal and percent answers exact?

The fraction and mixed number are always exact. The decimal and percent are rounded to the places you choose unless they end sooner, so 1/3 shows as 0.333333 at six places.

Can I use negative fractions?

Yes. For a negative mixed number, put the minus sign on the whole part. If Whole is 0, you can type a negative numerator instead, like -1 over 3. Denominators must be positive.