Fraction Calculator

About this Fraction Calculator

The Fraction Calculator works with two ordinary fractions and reduces the final answer to its simplest form. It is useful for homework checks, recipe scaling, measurements and any task where fractional values are easier to understand than decimals.

Fractions are added and subtracted differently from how they are multiplied and divided, which is the single most common source of arithmetic mistakes with fractions, so this tool automatically finds a common denominator for addition and subtraction while multiplying numerators and denominators directly for multiplication.

For related tasks, try Ratio Calculator, Proportion Calculator or Average Calculator.

How the calculation works

For addition and subtraction, the tool uses a common denominator. For multiplication it multiplies numerators and denominators; division multiplies by the reciprocal. The final numerator and denominator are divided by their greatest common divisor.

How to use it

1. Enter the numerator and denominator for both fractions.
2. Choose addition, subtraction, multiplication or division.
3. Calculate to see the simplified fraction and decimal equivalent.

Practical example

For 1/2 + 1/4, the common result is 3/4, which is 0.75 as a decimal.

Adding 1/3 and 1/4 requires converting both to a common denominator of 12, giving 4/12 + 3/12 = 7/12, a step many people skip by mistake when adding fractions with different denominators directly.

Things to double-check

Always check whether the calculator has simplified (reduced) the resulting fraction to its lowest terms; an unsimplified answer like 6/8 is mathematically identical to 3/4 but is usually not accepted as a final answer in schoolwork, so compare against the simplified form shown.

How each operation works

Adding fractions needs a common denominator: 3/4 plus 5/6 becomes 9/12 plus 10/12, which is 19/12, or 1 and 7/12. Multiplying is direct: 2/3 times 9/10 is 18/30, which simplifies to 3/5. Dividing means multiplying by the reciprocal: 3/4 divided by 2/5 is 3/4 times 5/2, which is 15/8, or 1 and 7/8. Subtraction follows the same rule as addition. Understanding the steps helps you check the tool's answer and use the same method when you have no calculator.

Simplifying to lowest terms

A fraction is in lowest terms when the numerator and denominator share no factor other than 1. To simplify, divide both by their greatest common divisor. The fraction 18/30 has a divisor of 6, so it becomes 3/5. Teachers and exam boards usually expect answers in lowest terms, and it makes fractions easier to compare. If you are unsure whether a result is fully simplified, run the numerator and denominator through the GCD Calculator. Dividing by zero is not allowed, so a zero denominator is always an error.

Mixed numbers and decimals

To use a mixed number, convert it to an improper fraction: 2 and 1/3 is (2 times 3 plus 1) over 3, which is 7/3. To convert a fraction to a decimal, divide the top by the bottom: 3/8 is 0.375. Some fractions give repeating decimals, such as 1/3, which is 0.333 and so on. Converting back from a decimal works by using powers of ten, so 0.375 is 375/1000, which simplifies to 3/8. Use fractions when exactness matters and decimals when you need a measurement.

Everyday uses

Fractions appear in recipes, measurements and probability. A carpenter adding 3/8 inch and 5/16 inch converts to sixteenths: 6/16 plus 5/16 is 11/16 of an inch. A cook who needs three quarters of a recipe that calls for 2/3 cup of sugar multiplies 3/4 by 2/3 to get 1/2 cup. In probability, the chance of two independent events is found by multiplying their fractions. Practising with real examples makes the rules stick.

Comparing fractions

To decide which of two fractions is larger, cross multiply. For 5/8 and 7/11, multiply 5 by 11 to get 55 and 7 by 8 to get 56. Because 56 is larger, 7/11 is the bigger fraction, which you can confirm in decimals as 0.636 against 0.625. This works without finding a common denominator and is a quick check for recipes, measurements and test answers. If the cross products are equal, the fractions are equivalent, as with 2/3 and 4/6. When you compare many fractions, converting them all to decimals is usually faster.

Worked example: scaling a recipe

A recipe calls for 3/4 cup of sugar and you want to make 2.5 times the amount. Write 2.5 as 5/2 and multiply: 3/4 times 5/2 equals 15/8, which is 1 and 7/8 cups. If the recipe also needs 2/3 cup of milk, multiplying by 5/2 gives 10/6, which simplifies to 5/3, or 1 and 2/3 cups. Working in fractions keeps the amounts exact and avoids rounding errors. Afterward, you can convert the answers to the cup markings you have: 1 and 7/8 cups is one cup plus a half cup plus a quarter cup plus an eighth of a cup, or one cup and 14 tablespoons.

Fractions, decimals and percentages

Fractions, decimals and percentages are three ways of writing the same thing. To change a fraction to a decimal, divide the top by the bottom: 7/16 is 0.4375, which is 43.75 percent. To go from a decimal to a fraction, write it over a power of ten and simplify: 0.125 is 125/1000, or 1/8. Some fractions repeat forever as decimals, such as 2/3, which is 0.666 and so on, or 66.7 percent when rounded. Choose the form that suits the job: fractions for exact amounts, decimals for calculations with money and percentages for comparing proportions.

Fractions in measurement

Fractions are common in construction, sewing and cooking, where measurements are in eighths and sixteenths of an inch or fractions of a cup. To add 5/8 inch and 3/16 inch, convert 5/8 to 10/16 and add 3/16 to get 13/16 inch. To subtract, use the same approach. When you need a metric value, convert to a decimal first: 13/16 inch is 0.8125 inch, or about 20.6 mm. Many tape measures show markings down to 1/16 inch, so it often makes sense to round a result to the nearest sixteenth before you cut.

Common mistakes with fractions

The most common mistake is adding the denominators as well as the numerators, as in writing 1/2 plus 1/3 as 2/5. Another is forgetting to simplify, leaving a result such as 18/24 instead of 3/4. A third is forgetting that dividing by a fraction means multiplying by its reciprocal. Cross-cancelling before you multiply keeps numbers small: in 4/9 times 3/8, you can cancel a factor of 4 from 4 and 8 and a factor of 3 from 3 and 9, which leaves 1/3 times 1/2, which is 1/6. Checking your answer with decimals is a quick way to catch errors.

Key terms explained

The numerator is the top number and the denominator is the bottom. A proper fraction is less than one and an improper fraction is one or more. A mixed number combines a whole number and a fraction. Equivalent fractions have the same value, such as 1/2 and 2/4, and the simplest form has no common factor left. The reciprocal of a fraction swaps the numerator and denominator. The least common denominator is the smallest shared denominator, used to add and subtract.

Rules of thumb and quick checks

To add or subtract, find a common denominator; the formula a/b plus c/d equals (ad plus bc) over bd works, and you simplify afterward. To multiply, multiply tops and bottoms. To divide, multiply by the reciprocal. Always simplify using the greatest common divisor. Check by converting to decimals: 3/4 plus 1/8 should equal 0.875, which is 7/8. If your answer is bigger than one, convert it to a mixed number to see if it makes sense.

Frequently asked questions