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Viva Calculator

Add Fractions Calculator

Add, subtract, multiply, and divide fractions

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Method and source check

Last checked:

Automated source and implementation review, including worked examples and documented numerical limits. This review does not provide professional advice or specialist approval.

Method

Use a least common denominator to add or subtract fractions; multiply numerator by numerator and denominator by denominator for products; multiply by the reciprocal for division. Reduce by the greatest common divisor and keep the denominator positive. Division by a zero-valued second fraction is rejected.

a/b + c/d = (ad + bc)/bd

(a/b) ÷ (c/d) = ad/bc, c ≠ 0

a/b − c/d = (ad−bc)/bd

(a/b)(c/d) = ac/bd

Variables and units

a,b
first numerator and nonzero denominator
c,d
second numerator and nonzero denominator

Worked example

1/4 + 1/6 = 3/12 + 2/12 = 5/12; the displayed decimal is 0.4167.

Limitations

Fraction result is reduced; the optional decimal display is rounded to four places.

  • Inputs represent fractions with integer numerators and nonzero integer denominators.
  • Displayed decimal approximations may not represent recurring decimals exactly.
  • Inputs and intermediate integer products, sums and common-denominator conversions must stay within the safe integer range (absolute value at most 9,007,199,254,740,991). Unsupported operations are rejected rather than shown as exact fractions.
  • Zero input denominator is invalid.
  • The second fraction cannot be zero in division.
  • 9007199254740991/1 + 2/1 is rejected because the exact sum exceeds the supported integer range.

Sources

Table of Contents

How to Use

  1. Select the operation (add, subtract, multiply, or divide)
  2. Enter the numerator and denominator for the first fraction
  3. Enter the numerator and denominator for the second fraction

Add, subtract, multiply, and divide fractions

Add, subtract, multiply, and divide fractions with step-by-step solutions. Method: Use a least common denominator to add or subtract fractions; multiply numerator by numerator and denominator by denominator for products; multiply by the reciprocal for division. Reduce by the greatest common divisor and keep the denominator positive. Division by a zero-valued second fraction is rejected.

Example

In the fraction 3/4, the numerator is 3 (you have 3 parts) and the denominator is 4 (the whole is divided into 4 equal parts).

Fraction Operations

Adding and Subtracting Fractions

Step 1: Find a common denominator (usually the Least Common Multiple)

Step 2: Convert each fraction to have the common denominator

Step 3: Add or subtract the numerators, keeping the denominator the same

Step 4: Simplify the result if possible

Example: 1/4 + 1/6 = 3/12 + 2/12 = 5/12

Multiplying Fractions

Step 1: Multiply the numerators together

Step 2: Multiply the denominators together

Step 3: Simplify the result if possible

Example: 2/3 × 3/4 = 6/12 = 1/2

Dividing Fractions

Step 1: Flip the second fraction (find its reciprocal)

Step 2: Multiply the first fraction by the reciprocal

Step 3: Simplify the result if possible

Example: 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9

Simplifying Fractions

To simplify a fraction, divide both the numerator and denominator by their Greatest Common Divisor (GCD).

Example

To simplify 6/8:

1. Find the GCD of 6 and 8, which is 2

2. Divide both by 2: 6÷2 = 3, 8÷2 = 4

3. Result: 6/8 = 3/4

Worked scenario

Apply the result to the stated units and check the method limit.

Worked scenario

  • 1/4 + 1/6 = 3/12 + 2/12 = 5/12.

Method, example, rounding, and limits

Method: Use a least common denominator to add or subtract fractions; multiply numerator by numerator and denominator by denominator for products; multiply by the reciprocal for division. Reduce by the greatest common divisor and keep the denominator positive. Division by a zero-valued second fraction is rejected.

Worked example: 1/4 + 1/6 = 5/12 ≈ 0.4167.

Rounding: 4 decimal places. Displayed values are rounded as stated beside the result.

Limit: Inputs represent fractions with integer numerators and nonzero integer denominators. Inputs and intermediate integer products or sums must stay within ±9007199254740991. Operations outside this range are rejected, even if the final fraction could be reduced.

Reference: OpenStax. https://openstax.org/books/prealgebra-2e/pages/4-5-add-and-subtract-fractions-with-different-denominators

Frequently Asked Questions

Why do I need a common denominator to add fractions?
You need a common denominator because you can only add or subtract parts that are the same size. Just like you can't add 2 apples and 3 oranges to get 5 apples, you can't add halves and thirds directly. Converting to a common denominator makes the parts the same size.
How do I find the least common denominator (LCD)?
The LCD is the Least Common Multiple (LCM) of the denominators. You can find it by listing multiples of each denominator until you find the smallest one they share, or by multiplying the denominators and dividing by their GCD.
Why do we flip and multiply when dividing fractions?
Dividing by a fraction is the same as multiplying by its reciprocal. For example, dividing by 1/2 is the same as asking 'how many halves are in this number?' which is the same as multiplying by 2.
What if my result is an improper fraction?
An improper fraction (where the numerator is larger than the denominator) is still a valid answer. You can convert it to a mixed number if needed. For example, 7/4 = 1 3/4.

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