Fraction Calculator

Written by the StepSolvers Team  │  Reviewed by Sarah Mitchell, Math Educator  │  Last updated July 2026

A fraction calculator adds, subtracts, multiplies, or divides two fractions and shows the full step-by-step working — including how the common denominator is found, how the result is simplified, and how to convert the answer to a decimal or mixed number.

This free fractions calculator supports proper fractions, improper fractions, mixed numbers, and whole numbers. It also converts between fractions, decimals, and percentages — all with step-by-step explanations. No signup required.

Input mode:

Step-by-Step Solution

    Final Answer:

    What Is a Fraction?

    A fraction represents a part of a whole — one number written over another, separated by a fraction bar. The top number is the numerator (how many parts you have) and the bottom is the denominator (total equal parts in the whole). For a visual introduction to how fractions work, Math is Fun covers the basics of fractions clearly.

    Numerator ← the top number (how many parts you have) ──────────── Denominator ← the bottom number (total parts in the whole) Example: 3/4 means 3 out of 4 equal parts

    Types of Fractions

    Fraction typeDefinition and example
    Proper fractionNumerator is smaller than denominator. Value is less than 1. Example: 3/4, 2/7, 5/9
    Improper fractionNumerator is equal to or greater than denominator. Value is 1 or more. Example: 7/4, 9/3, 11/5
    Mixed numberA whole number combined with a proper fraction. Example: 2¾ (means 2 + 3/4 = 11/4)
    Equivalent fractionsDifferent fractions that represent the same value. Example: 1/2 = 2/4 = 4/8 = 50/100
    Proper decimal fractionA fraction whose denominator is a power of 10. Example: 3/10 = 0.3, 45/100 = 0.45

    How to Use This Fraction Calculator

    1. Select your operation tab: Addition (+), Subtraction (−), Multiplication (×), or Division (÷).
    2. Enter the numerator and denominator for each fraction. Use the Mixed Number toggle to add a whole number in front of either fraction — the calculator converts it automatically.
    3. Click Calculate. The result appears in three forms simultaneously: simplified fraction, mixed number (if applicable), and decimal.
    4. The full step-by-step working is shown below the result — including the LCM/LCD for addition and subtraction, or the reciprocal method for division.
    5. Use the Simplify tab to reduce any fraction to its lowest terms, or the Converter tab to switch between fractions, decimals, and percentages.
    6. Click Reset to clear all inputs and start a new calculation.

    The calculator handles positive fractions, negative fractions, and fractions with whole numbers. For operations involving 3 fractions, perform two calculations in sequence: first calculate fractions 1 and 2, then use the result with fraction 3.

    Fraction Formulas Explained

    Adding and Subtracting Fractions

    To add or subtract fractions, both fractions must have the same denominator — called the common denominator. If they already share a denominator, add or subtract the numerators directly. If not, find the least common denominator (LCD) first.

    Same denominator: a/c + b/c = (a + b) / c Different denominators: a/b + c/d = (a×d + b×c) / (b×d) ← then simplify if possible a/b − c/d = (a×d − b×c) / (b×d) ← then simplify if possible Best practice: find the LCD (least common denominator) of b and d, convert both fractions to that denominator, then add or subtract numerators.

    Multiplying Fractions

    Multiplying fractions is the simplest operation — multiply the numerators together and multiply the denominators together. No common denominator is needed. If your result is a percentage you need to interpret, the Percentage Calculator can help convert it directly.

    a/b × c/d = (a×c) / (b×d) ← then simplify the result To multiply a fraction by a whole number: a/b × n = (a×n) / b To multiply mixed numbers: convert to improper fractions first, then multiply numerator × numerator and denominator × denominator.

    Dividing Fractions

    To divide fractions, flip the second fraction (take its reciprocal) and multiply. This is called the "keep, change, flip" method.

    a/b ÷ c/d = a/b × d/c = (a×d) / (b×c) ← then simplify Steps: 1. Keep the first fraction as it is 2. Change the division sign to multiplication 3. Flip the second fraction (swap numerator and denominator) 4. Multiply and simplify

    Simplifying Fractions (Reducing to Lowest Terms)

    A fraction is in its simplest form (lowest terms) when the numerator and denominator share no common factors other than 1. To simplify, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it.

    Simplified form of a/b: Find GCD(a, b) = g Simplified fraction = (a÷g) / (b÷g) Example: Simplify 12/18 GCD(12, 18) = 6 12÷6 = 2 and 18÷6 = 3 Simplified: 2/3

    Worked Example — Step by Step

    Example 1: Add 1/3 + 1/4

    These fractions have different denominators, so we need to find the least common denominator (LCD) first.

    1. Write the fractions to add: 1/3 + 1/4
    2. Find the LCD of 3 and 4: LCM(3, 4) = 12
    3. Convert 1/3 to twelfths: 1/3 = 4/12 (multiply top and bottom by 4)
    4. Convert 1/4 to twelfths: 1/4 = 3/12 (multiply top and bottom by 3)
    5. Add the numerators: 4 + 3 = 7 (keep the denominator: 12)
    6. Result: 7/12
    7. Check if simplifiable: GCD(7, 12) = 1 → already in simplest form
    1/3 + 1/4 = 7/12 = 0.5833...

    Example 2: Subtract 5/6 − 1/4

    1. Write the fractions to subtract: 5/6 − 1/4
    2. Find the LCD of 6 and 4: LCM(6, 4) = 12
    3. Convert 5/6 to twelfths: 5/6 = 10/12 (multiply by 2)
    4. Convert 1/4 to twelfths: 1/4 = 3/12 (multiply by 3)
    5. Subtract the numerators: 10 − 3 = 7 (keep denominator: 12)
    6. Result: 7/12
    7. Check if simplifiable: GCD(7, 12) = 1 → already in simplest form
    5/6 − 1/4 = 7/12 = 0.5833...

    Example 3: Multiply 2/3 × 3/5

    Multiplication requires no common denominator — just multiply across.

    1. Write the fractions to multiply: 2/3 × 3/5
    2. Multiply the numerators: 2 × 3 = 6
    3. Multiply the denominators: 3 × 5 = 15
    4. Result before simplifying: 6/15
    5. Find GCD(6, 15) = 3
    6. Simplify: 6÷3 = 2 and 15÷3 = 5
    7. Final result: 2/5
    2/3 × 3/5 = 2/5 = 0.4

    Example 4: Divide 3/4 ÷ 2/5

    Use the keep, change, flip method — keep the first fraction, change division to multiplication, flip the second fraction.

    1. Write the division: 3/4 ÷ 2/5
    2. Keep the first fraction: 3/4
    3. Change ÷ to ×
    4. Flip the second fraction: 2/5 becomes 5/2
    5. Multiply: 3/4 × 5/2 = (3×5) / (4×2) = 15/8
    6. Check if simplifiable: GCD(15, 8) = 1 → already in simplest form
    7. Convert to mixed number: 15/8 = 1 and 7/8 (1 whole + 7/8 remaining)
    3/4 ÷ 2/5 = 15/8 = 1 7/8 = 1.875

    Example 5: Add Mixed Numbers — 2 1/3 + 1 3/4

    Convert mixed numbers to improper fractions first, then add. Once you have your result, the Standard Deviation Calculator can help if you need to average multiple fraction results across a dataset.

    1. Convert 2 1/3 to an improper fraction: (2×3 + 1)/3 = 7/3
    2. Convert 1 3/4 to an improper fraction: (1×4 + 3)/4 = 7/4
    3. Now add: 7/3 + 7/4
    4. Find LCD of 3 and 4: LCM(3, 4) = 12
    5. Convert 7/3 → 28/12 and 7/4 → 21/12
    6. Add numerators: 28 + 21 = 49
    7. Result: 49/12
    8. Convert to mixed number: 49 ÷ 12 = 4 remainder 1 → 4 1/12
    2 1/3 + 1 3/4 = 4 1/12 = 4.0833...

    Example 6: Convert a Fraction to a Decimal and Percentage

    1. Fraction to convert: 3/8
    2. To decimal: divide numerator by denominator: 3 ÷ 8 = 0.375
    3. To percentage: multiply the decimal by 100: 0.375 × 100 = 37.5%
    4. Verify: 37.5% of 8 = 0.375 × 8 = 3 ✓
    3/8 = 0.375 = 37.5%
    Quick reference — common fraction conversions: 1/2 = 0.5 = 50% | 1/4 = 0.25 = 25% | 3/4 = 0.75 = 75% 1/3 = 0.333... = 33.33% | 2/3 = 0.666... = 66.67% 1/5 = 0.2 = 20% | 1/8 = 0.125 = 12.5% | 1/10 = 0.1 = 10%

    Working with Mixed Numbers and Whole Numbers

    A mixed number contains a whole number and a fraction together — for example, 2¾ means 2 whole units plus three-quarters of another unit. To perform arithmetic with mixed numbers, convert them to improper fractions first.

    To multiply a fraction by a whole number, treat the whole number as a fraction with 1 as its denominator. For example: 4 × 2/3 = (4/1) × (2/3) = 8/3 = 2 2/3.

    Converting a mixed number to an improper fraction: Multiply the whole number by the denominator, then add the numerator 2 3/4 → (2 × 4) + 3 = 11 → improper fraction: 11/4 Converting an improper fraction back to a mixed number: Divide the numerator by the denominator 15/4 → 15 ÷ 4 = 3 remainder 3 → mixed number: 3 3/4

    When to Use Mixed Numbers vs Improper Fractions

    FormBest used when
    Mixed number (2 3/4)Communicating a measurement or quantity — more intuitive to read. Preferred in everyday contexts: cooking, construction, measuring.
    Improper fraction (11/4)Performing arithmetic — easier to multiply and divide. Always convert to improper fractions before calculating.

    Equivalent Fractions and Comparing Fractions

    Equivalent fractions are different fractions that represent the same value. For example, 1/2 = 2/4 = 4/8 = 50/100. To find equivalent fractions, multiply or divide both the numerator and denominator by the same non-zero number. To determine whether two fractions are equivalent, use cross multiplication: a/b = c/d if and only if a×d = b×c.

    To compare two fractions and find which is larger: 1. Convert both fractions to a common denominator 2. The fraction with the larger numerator is greater Example: Which is bigger — 3/5 or 5/8? LCD of 5 and 8 = 40 3/5 = 24/40 | 5/8 = 25/40 25/40 > 24/40 → 5/8 is larger

    Partial Fraction Decomposition

    Partial fraction decomposition breaks a complex rational expression — a single fraction with a polynomial denominator — into a sum of simpler fractions. This technique is widely used in calculus (for integration) and in engineering (for signal processing and Laplace transforms).

    Example of partial fraction decomposition: (2x + 3) / (x² + 3x + 2) Step 1: Factor the denominator: x² + 3x + 2 = (x + 1)(x + 2) Step 2: Set up partial fractions: (2x + 3) / [(x+1)(x+2)] = A/(x+1) + B/(x+2) Step 3: Solve for A and B by substituting x = -1 and x = -2 x = -1: 2(-1)+3 = A(-1+2) → 1 = A → A = 1 x = -2: 2(-2)+3 = B(-2+1) → -1 = -B → B = 1 Step 4: Result: 1/(x+1) + 1/(x+2) Use the Partial Fraction tab in the calculator above for automatic decomposition.

    Common Mistakes When Working with Fractions

    Mistake 1: Adding the denominators instead of finding a common denominator

    The most frequent error. Students write 1/3 + 1/4 = 2/7 — adding both numerators and both denominators. This is always wrong. The denominator represents the total equal parts in the whole — it only changes when you convert to an equivalent fraction, not when you add.

    Wrong: 1/3 + 1/4 = 2/7 ✗ Correct: 1/3 + 1/4 = 4/12 + 3/12 = 7/12 ✓

    Mistake 2: Forgetting to simplify the result

    After any operation, check whether the result can be simplified. A fraction is not in its final form until it is in lowest terms. The calculator always simplifies automatically, but when working by hand, always find the GCD of the result and divide both parts by it.

    Wrong: 2/3 × 3/5 = 6/15 ✗ (left unsimplified) Correct: 6/15 → GCD(6,15)=3 → 2/5 ✓

    Mistake 3: Flipping the wrong fraction when dividing

    In the keep, change, flip method, only the second fraction (the divisor) gets flipped — never the first. Flipping the first fraction instead gives a completely different result.

    Wrong: 3/4 ÷ 2/5 → flip 3/4 = 4/3 × 2/5 = 8/15 ✗ Correct: 3/4 ÷ 2/5 → keep 3/4, flip 2/5 = 3/4 × 5/2 = 15/8 ✓

    Mistake 4: Not converting mixed numbers before calculating

    Mixed numbers cannot be multiplied or divided directly. Always convert to improper fractions first. For addition and subtraction you can work with the whole number and fraction parts separately, but converting first is the safer habit.

    Wrong: 2 1/3 × 1 1/2 → 2×1=2 and 1/3×1/2=1/6 → 2 1/6 ✗ Correct: 2 1/3 = 7/3 and 1 1/2 = 3/2 → 7/3 × 3/2 = 21/6 = 7/2 = 3 1/2 ✓

    Mistake 5: Averaging percentages without accounting for group size

    When converting a fraction result to a percentage, a simple average of two percentages is only valid if the denominators (group sizes) are equal. If they differ, the weighted average gives the correct result. Use the percentage calculator to check.

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    Frequently Asked Questions

    How do you add fractions with different denominators?
    Find the least common denominator (LCD) of the two fractions — this is the smallest number that both denominators divide into evenly. Convert each fraction to an equivalent fraction with that LCD as the denominator. Then add the numerators and keep the common denominator. For example, to add 1/3 + 1/4: the LCD is 12, so 1/3 = 4/12 and 1/4 = 3/12, giving 7/12.
    How do you multiply fractions?
    Multiply the numerators together to get the new numerator, then multiply the denominators together to get the new denominator. No common denominator is needed. For example: 2/3 × 3/5 = (2×3)/(3×5) = 6/15, which simplifies to 2/5. You can also simplify before multiplying (cross-cancellation) to keep numbers smaller.
    How do you divide fractions?
    Use the keep, change, flip method: keep the first fraction unchanged, change the division sign to multiplication, and flip the second fraction (swap numerator and denominator to get the reciprocal). Then multiply the two fractions and simplify. For example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8.
    How do you simplify a fraction?
    Find the greatest common divisor (GCD) of the numerator and denominator — the largest number that divides both without a remainder. Then divide both the numerator and denominator by the GCD. For example, to simplify 12/18: GCD(12, 18) = 6, so 12÷6 = 2 and 18÷6 = 3, giving the simplified form 2/3.
    How do you convert a fraction to a decimal?
    Divide the numerator by the denominator. For example, 3/8 = 3 ÷ 8 = 0.375. Some fractions produce terminating decimals (like 1/4 = 0.25) while others produce repeating decimals (like 1/3 = 0.333...). The calculator shows both the exact fraction and the decimal approximation simultaneously.
    How do you convert a decimal to a fraction?
    Count the decimal places in the number. Write the decimal as a fraction with 1 followed by that many zeros as the denominator, then simplify. For example, 0.375 has 3 decimal places, so it becomes 375/1000. GCD(375, 1000) = 125, giving 3/8. For repeating decimals, use algebra: let x = 0.333..., then 10x = 3.333..., subtract: 9x = 3, so x = 3/9 = 1/3.
    How do you add fractions with whole numbers?
    Convert the mixed number to an improper fraction first. Multiply the whole number by the denominator and add the numerator to get the new numerator — keep the same denominator. For example, 2 1/3 = (2×3+1)/3 = 7/3. Then add the fractions normally. The calculator's Mixed Number tab handles this conversion automatically.
    What is an improper fraction and how do you convert it to a mixed number?
    An improper fraction has a numerator greater than or equal to its denominator — for example 11/4. To convert to a mixed number, divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the new numerator over the original denominator. For 11/4: 11 ÷ 4 = 2 remainder 3, giving 2 3/4.
    What is the least common denominator (LCD)?
    The least common denominator is the smallest number that is a multiple of both denominators in a pair of fractions. It is the same as the least common multiple (LCM) of the denominators. You need the LCD when adding or subtracting fractions with different denominators. For example, the LCD of 1/3 and 1/4 is 12, because 12 is the smallest number divisible by both 3 and 4.