Fraction Calculator: Add, Subtract, Multiply, Divide, Simplify, and Convert

What is a fraction calculator?

A fraction calculator is a tiny tool that performs exact arithmetic with rational numbers. It accepts simple fractions like 3/4 and mixed numbers like 1 2/5. It handles unlike denominators, shows a simplified result, and converts to a decimal when you need one.

If you want to review the core ideas behind fractions, skim the concise overview on Wikipedia. If you prefer structured practice with hints, try the free lessons on Khan Academy.

How to use the fraction calculator

1. Choose an operation. Pick add, subtract, multiply, divide, simplify, fraction → decimal, or decimal → fraction.
2. Select the input style. Use simple fraction form for numerators and denominators or mixed number form when you have a whole number and a fractional part.
3. Enter values. The calculator accepts 12.5 or 12,5 and ignores thousands separators. That keeps inputs forgiving and fast.
4. Set rounding when a decimal appears. Choose Auto or specify the number of places. You can also select the rounding rule for tie cases.
5. Read the result and steps. You’ll see a simplified fraction, a mixed number view, and a decimal if relevant.
6. Copy the answer. Use the Copy button to paste the value into a worksheet, a spreadsheet, or a message.

   a     c      a·LCD/b + c·LCD/d
  ─── + ───  = ───────────────────
   b     d            LCD
    

Fraction operations with clear formulas

Here are the algorithms teachers rely on. Each rule includes a compact formula and a short explanation that sticks.

Mixed numbers vs simple fractions

Simple fraction: a numerator over a denominator, like 7/4. Mixed number: a whole part plus a proper fraction, like 1 3/4.

• To improper: 1 3/4 = (1×4 + 3)/4 = 7/4
• To mixed: 7/4 = 1 and remainder 3, so 1 3/4

Mixed numbers read smoothly in recipes and building plans. Improper fractions keep algebra neat since you carry a single ratio through each step.

Rounding methods you can trust

Different rounding rules handle ties differently. Choose once then keep it consistent across your work.

• Nearest (half up): 2.5 becomes 3 and −2.5 becomes −2
• Banker’s rounding (half to even): 2.5 becomes 2 and 3.5 becomes 4
• Half down: tie goes toward zero
• Truncate: chop off extra digits toward zero
• Floor: round down toward negative infinity
• Ceiling: round up toward positive infinity

Worked examples

Example 1 — Add two unlike fractions

Problem: 4/7 + 3/6

1. LCD of 7 and 6 is 42
2. Rewrite: 4/7 = 24/42 and 3/6 = 21/42
3. Add: (24 + 21)/42 = 45/42
4. Simplify by 3 → 15/14 which is 1 1/14

Example 2 — Subtract a quarter from five eighths

Problem: 5/8 − 1/4 = 5/8 − 2/8 = 3/8

Example 3 — Multiply mixed numbers

Problem: (2 1/3) × (1 1/2)

1. Convert to improper: 7/3 × 3/2
2. Cross-cancel the 3s
3. Multiply: 7/2 which equals 3 1/2

Example 4 — Divide fractions

Problem: 3/5 ÷ 9/10

1. Flip the second: 3/5 × 10/9
2. Reduce 10/5 to 2/1
3. Multiply: 6/9 then simplify to 2/3

Example 5 — Convert a fraction to a decimal with four places

Problem: 4/7 → 4 decimals. Compute 4 ÷ 7 = 0.571428… then round half up → 0.5714.

Example 6 — Convert a decimal to a fraction

Problem: 0.875 → place value gives 875/1000 which reduces to 7/8.

Common mistakes and quick fixes

• Adding denominators directly. 1/2 + 1/3 is not 2/5. Use LCD to get 5/6.
• Skipping simplification. 12/16 should become 3/4. Reduced answers help you spot patterns.
• Dividing by zero. A denominator must never be zero. Stop and check inputs if you see 0 below the line.
• Misplacing the minus sign. Keep a single sign on the numerator, like −3/7, to avoid confusion.
• Forgetting units. Add or subtract only when units match. You may multiply or divide with units if you track the new unit.

Helpful reference tables

Prime numbers under 50

Use these primes to factor numerators and denominators fast.

Fraction ↔ decimal benchmarks

FAQ: quick answers

What is a fraction calculator used for?

It performs exact arithmetic with fractions and mixed numbers, shows steps, and converts between forms. You save time and you avoid mistakes during study and everyday work.

How do you add fractions with different denominators?

Find the least common denominator, rewrite each fraction over that denominator, add numerators, and simplify.

How do you simplify a fraction quickly?

Divide numerator and denominator by their greatest common divisor. If both are even, divide by two first which shrinks the numbers at once.

How do you turn a decimal into a fraction?

Use place value for terminating decimals or use continued fractions to approximate repeating or rounded decimals.

What is the difference between a mixed number and an improper fraction?

A mixed number shows a whole part and a fraction while an improper fraction packs the value into a single ratio. Both represent the same quantity.

Fractions keep numbers exact, and that matters in schoolwork, kitchens, workshops, and labs. This fraction calculator handles the arithmetic while you focus on the task at hand. Pick your operation, choose simple or mixed input, then read the clear result with steps and a mixed or decimal view when you need it. Bookmark the page and reach for it whenever precision counts.