ADD, SUBTRACT, MULTIPLY, AND DIVIDE FRACTIONS
Get an exact result and follow every step.
Enter the two fractions, choose the operation and you get the result already reduced, with its steps: 3/4 − 1/6 gives 7/12. For three or more values, or a calculation with parentheses, switch modes; the table below tells you which.
Enter two fractions to begin.
(1/2) + (1/3) = 5/6
To reuse this answer, its numerator and denominator must each have at most 100 digits.
Decimals and mixed numbers appear as exact fractions. Edit fields and operators; the written expression updates when you apply, calculate or close. The keyboard edits the selected field. You can scroll long expressions within the editor.
Enter two fractions to begin.
Multiply with 2(1/3) or (1/2)(3/4). Multiplication and division are evaluated from left to right. Use × or grouping for decimals and mixed numbers.
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Adding fractions with unlike denominators
To add fractions, the parts must be the same size. One half becomes three sixths and one third becomes two sixths.
1/2 + 1/3 = 3/6 + 2/6 = 5/6
3 parts + 2 parts = 5 of 6 parts
Beyond one whole
Nine quarters fill two whole units and leave one quarter. The improper fraction 9/4 and the mixed number 2 1/4 have exactly the same value.
9/4 = 4/4 + 4/4 + 1/4 = 2 1/4
4/4 + 4/4 + 1/4 = 9/4 = 2 1/4
A real measurement
Combine 3/4 cup of flour with another 1/8 cup of the same flour. The total is 7/8 cup. Enter only the numbers in the calculator, then put the unit back on the result.
3/4 + 1/8 = 6/8 + 1/8 = 7/8
The numerator counts the blue parts; the denominator counts all equal parts. Multiply both terms of 1/2 by 2 to get 2/4. Divide both terms of 3/6 by 3 to get 1/2. The whole and its blue half stay the same.
1/2 = 2/4 = 3/6
CALCULATION GUIDE
This fraction calculator adds, subtracts, multiplies, and divides rational numbers. Enter two fractions in the simple form, choose “Mixed numbers and decimals” for a list of up to twenty operands using one operation, or choose “Expression” to combine operations in a single field. The result is reduced exactly, and the steps show how it was obtained.
For a calculation with two fractions, enter each numerator above its denominator, choose the operation, and select “Calculate.” The numerator tells you how many parts you take; the denominator tells you how many equal parts make up one whole. In 3/4, each part is one quarter of the whole and you take three parts.
“Mixed numbers and decimals” provides complete-value fields. Enter 1/2, -3, 0.25, or -1 1/2 in one field; the sign of a mixed number applies to the whole value. Add fields up to a maximum of twenty operands. For example, 1/2 + 1/3 + 1/6 equals 1 when you select addition. These fields repeat one operation, and subtraction and division proceed from left to right.
To combine operations, choose “Expression” and enter the calculation in the single field. Powers are evaluated first, then multiplication and division from left to right, and finally addition and subtraction; parentheses change the grouping. For example, 1/2 + 1/3 × 3/4 = 3/4, while (1/2 + 1/3) × 3/4 = 5/8. The ^ symbol accepts integer exponents from −100 to 100; 0^0 is undefined. For a guided explanation and more examples, see the fraction expressions calculator. For the most common mistakes, read the guide to common fraction mistakes.
Links to fraction simplification, conversion, and comparison open dedicated tools. In this calculator, “Use result” places the exact fraction in the first field for the next operation; enter the second value before calculating. If the result exceeds the 100-digit input limit, the button explains why it cannot be reused.
Open “Percentage, rounding and history” to change how the result is displayed. A percentage expresses a value out of one hundred: 1/2 is 50%. “Decimal places” rounds only the display and keeps the exact fraction. For example, 1/3 displays as 0.33 to two decimal places; the exact difference is 1/300. If the next digit is 5 with no remaining difference, rounding moves away from zero: 0.125 becomes 0.13 and −0.125 becomes −0.13.
“Your answer: bar and number line” shows parts of a whole and locates the value relative to zero. Very large results use an explanation instead of a detailed bar. The explanation steps show the conversion, operation, and reduction relevant to your calculation.
An exact answer preserves the full rational value. For example, 2/4 and 1/2 represent the same quantity because dividing the numerator and denominator of 2/4 by 2 gives 1/2. To simplify a fraction, divide both terms by their greatest common divisor (GCD). The GCD of 2 and 4 is 2; the GCD of 1 and 2 is 1. That makes 1/2 irreducible: its terms have no common divisor greater than 1.
The calculator puts the sign in the numerator and keeps the answer’s denominator positive. Thus, 2/−4 is normalized to −1/2; the two values are equal. Zero displays as 0, whether you entered 0/7 or obtained it by subtracting 1/2 − 1/2. This normalization gives the result one consistent standard form.
A proper fraction, such as 3/4, has a numerator smaller than its denominator in absolute value. An improper fraction, such as 5/4, represents one whole or more in absolute value. When a value exceeds one whole, it can also be useful to read it as a mixed number: 5/4 equals 1 1/4. For a negative value, −5/4 equals −1 1/4. To divide by a nonzero fraction, use its reciprocal, or multiplicative inverse: the reciprocal of 2/3 is 3/2, and their product is 1. Zero has no reciprocal. The improper fraction remains the exact form for further calculations; the mixed form expresses whole units plus a remaining part.
All four operations start from the same idea: a fraction represents a quantity, and each operation transforms that quantity in a particular way. The examples below show intermediate calculations you can compare with the calculator steps.
Rule: when the denominators match, add the numerators and keep the part size. Reduce the result if possible.
3/8 + 1/8 = 4/8 = 1/2
When denominators differ, find a common denominator. The least common multiple (LCM) gives the smallest shared positive denominator; for example, 2/3 + 1/4 = 8/12 + 3/12 = 11/12. Write a whole number over 1 before adding it. Practice adding fractions.
Rule: make the denominators equal, then subtract the numerators in the order written.
3/4 − 1/2 = 3/4 − 2/4 = 1/4
The result can also be negative: 1/2 − 3/4 = −1/4. With several subtractions, keep the parentheses and order. Review a subtraction step by step.
Rule: multiply the numerators together and the denominators together, then reduce.
2/3 × 3/4 = 6/12 = 1/2
You can also cancel factors before multiplying: 2/3 × 9/10 = 18/30 = 3/5. If one factor is zero, the product is zero. Explore fraction multiplication.
Rule: invert only the divisor, provided it is not zero, and multiply.
5/6 ÷ 2/3 = 5/6 × 3/2 = 5/4
Check: 5/4 × 2/3 = 5/6. Never divide by zero, including 0/7. Practice dividing fractions.
The product 2/3 × 3/4 covers six of the twelve equal parts of a rectangular whole. First divide the whole into three columns and four rows. Select two columns to represent 2/3 and three rows to represent 3/4. The six cells where the selections overlap show the product: 6/12 = 1/2.
The diagram does not change the arithmetic rule: 2 × 3 = 6 and 3 × 4 = 12. It does clarify why, in this example, the product of two positive fractions smaller than one is also smaller than either factor. That conclusion does not apply when you multiply by 3/2, which is greater than one.
The fraction −1/4 lies to the left of 0 and to the right of −1/2. Each interval on the number line below is 1/4: from −1/2 move to −1/4, then to 0, then to 1/4, and finally to 1/2. Equal spacing lets you compare quantities without changing their signs.
The result 1/2 − 3/4 = −1/4 comes from subtracting 2/4 − 3/4. On the number line, start at 1/2 and move back three steps of size 1/4; you end one step to the left of zero. This path helps you check the sign before reading the decimal form.
The simple fields separate numerator and denominator and accept signed integers. Advanced mode takes each value in a single field, so you can enter fractions, integers, terminating decimals, or mixed numbers. The format 0.25 represents one quarter. Use a period for decimals; commas may only group thousands, so 1,000.5 is accepted and 0,25 is not.
| Value | Simple fields | Advanced mode |
|---|---|---|
| Three quarters | 3 on top and 4 on the bottom | 3/4 |
| Negative integer −2 | −2 on top and 1 on the bottom | −2 |
| Decimal 0.25 | 1 on top and 4 on the bottom | 0.25 |
| Negative mixed number −1 1/2 | −3 on top and 2 on the bottom | −1 1/2 |
The input −1 1/2 equals −3/2: the minus sign applies to both the whole unit and the half. It does not equal −1 + 1/2, which is −1/2. Entering the mixed number in one advanced-mode field prevents its parts from being separated incorrectly.
Advanced mode accepts two to twenty operands and limits each numeric token to 100 digits. In expression mode, the field accepts up to 1,024 characters, and the result numerator or denominator can have up to 10,000 digits; a very complex expression may also require fewer operations or nested parentheses. No denominator may be zero, and a divisor may not have a value of zero.
Open “Show steps” to see what changed in each operation. In addition, check the common denominator and equivalent numerators; in multiplication, follow the product and reduction; in division, look for the divisor’s reciprocal. After each step, cross-multiply equivalent fractions if you need to confirm that they have the same value.
The fraction result is the exact reference. A terminating decimal, such as 1/4 = 0.25, is also exact. A repeating decimal, such as 1/3 = 0.(3), repeats the digits inside the parentheses forever. When the display shows “≈” and a finite number of decimal places, those digits are a rounded approximation, not a new exact equality.
For example, 1/7 has a longer repeating expansion than 1/3. If the decimal display reaches its digit limit, keep 1/7 for further calculations; using a rounded approximation as a new input can accumulate error. The calculator uses integer numerators and denominators, so 0.1 + 0.2 equals exactly 3/10.
To change how a value is written, you can convert a fraction to a decimal.
1/3 + 1/3 + 1/3 = 1
0.33 + 0.33 + 0.33 = 0.99
0.01 (1%) is missing to complete the whole.
Calculate with the exact fraction and round when you present the result.
A student calculates 1/2 − 1/3 and wants to know why the answer is 1/6. Convert 1/2 to 3/6 and 1/3 to 2/6; then subtract 3/6 − 2/6 = 1/6. The incorrect calculation (1 − 1)/(2 − 3) does not keep equal-sized parts and also introduces a negative denominator without explaining the operation.
A teacher can ask the class to explain why 4/8 and 1/2 represent the same quantity. Dividing the numerator and denominator by 4 shows the reduction; the calculator lets students check the result while connecting four eighths to one half.
If a recipe uses 3/4 cup of an ingredient and 1/8 cup of the same ingredient, the total is 6/8 + 1/8 = 7/8 cup. Keep the unit “cup” out of the number fields and add it back when you read the result. Adding different ingredients can help you count total volume, but it does not replace a recipe instruction for each ingredient.
In a workshop, 3/4 metre is cut from a piece that is 2 1/2 metres long. Convert 2 1/2 to 5/2 = 10/4; then subtract 10/4 − 3/4 = 7/4 = 1 3/4 metres. In advanced mode, enter “2 1/2” and “3/4.” The exact value 7/4 preserves the full measurement; include “metres” when reading the answer so the unit is not lost.
The parentheses mark the digits that repeat forever: 0.(3) is 0.333… and equals exactly 1/3. The symbol “≈” marks a rounded decimal: with two digits, 1/3 shows as ≈ 0.33 and the exact difference is 1/300. Later calculations use the fraction, not the rounded decimal.
First work out what is inside the parentheses, then the rest. In (1/10 + 2/5) ÷ 1/4, the parentheses give 1/2, and 1/2 ÷ 1/4 equals 2. If there is a multiplication or division outside, that operation is done before any addition that is not in parentheses.
Put the base in parentheses and use ^ with a whole-number exponent: (2/5)^2 gives 4/25 and (−2/5)^3 gives −8/125. A negative exponent flips the fraction, so (2/5)^−1 is 5/2.
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