Fraction Calculator
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1 1/2 + 2/3 = 13/6 (2 1/6)
1. Mixed number to improper fraction: 1 1/2 = (1 × 2 + 1)/2 = 3/2 2. Least common denominator of 2 and 3: LCD = 6 3. Rewrite: 3/2 = 9/6 (× 3/3) and 2/3 = 4/6 (× 2/2) 4. Add the numerators: 9/6 + 4/6 = 13/6 5. 13/6 is already in lowest terms. 6. As a mixed number: 13 ÷ 6 = 2 remainder 1, so 2 1/6 7. As a decimal: 2.1(6)
How to use the fraction calculator
- Enter the first fraction. For a mixed number such as 2 3/4, put 2 in Whole number, 3 in Numerator and 4 in Denominator; for a plain fraction leave the whole number blank.
- Choose +, −, × or ÷, then enter the second fraction the same way.
- Read the simplified answer, the mixed number and the decimal. The working below them shows each step, ready to copy.
- For a negative mixed number, put the minus sign on the whole number: −2 3/4 means −(2 + 3/4).
Fraction formulas
a/b − c/d = (a × d − c × b) / (b × d)
a/b × c/d = (a × c) / (b × d)
a/b ÷ c/d = a/b × d/c = (a × d) / (b × c)
Mixed number: w n/d = (w × d + n) / d
The top number (numerator) counts parts and the bottom number (denominator) says how many parts make a whole. To add or subtract, both fractions must count the same size of part, so the calculator rewrites them over the least common denominator (the LCD, the smallest number both denominators divide into). Multiplying needs no common denominator: multiply the tops and the bottoms. Dividing flips the second fraction (its reciprocal) and multiplies. Every answer is then simplified by dividing the top and bottom by their greatest common divisor (GCD).
Worked example: 3/4 + 5/6
- Least common denominator of 4 and 6: LCD = 12
- Rewrite: 3/4 = 9/12 (× 3/3) and 5/6 = 10/12 (× 2/2)
- Add the numerators: 9/12 + 10/12 = 19/12
- 19/12 is already in lowest terms.
- As a mixed number: 19 ÷ 12 = 1 remainder 7, so 1 7/12
- As a decimal: 1.58(3)
So 3/4 + 5/6 = 19/12, or 1 7/12. Notice that the LCD is 12, not 4 × 6 = 24: using the smallest common denominator keeps the numbers small, although any common denominator gives the same simplified answer.
Multiplying mixed numbers: 2 1/3 × 1 1/2
- Mixed number to improper fraction: 2 1/3 = (2 × 3 + 1)/3 = 7/3
- Mixed number to improper fraction: 1 1/2 = (1 × 2 + 1)/2 = 3/2
- Multiply across: 7/3 × 3/2 = (7 × 3)/(3 × 2) = 21/6
- Simplify: GCD(21, 6) = 3, so 21/6 = 7/2
- As a mixed number: 7 ÷ 2 = 3 remainder 1, so 3 1/2
- As a decimal: 3.5
A common mistake is to multiply the whole numbers and the fractions separately (2 × 1 and 1/3 × 1/2), which gives 2 1/6 instead of the correct 3 1/2. Always convert mixed numbers to improper fractions first.
Dividing: 3/4 ÷ 3/8
Dividing is multiplying by the reciprocal: 3/4 ÷ 3/8 = 3/4 × 8/3. Multiply across: (3 × 8)/(4 × 3) = 24/12. The answer is 2: three eighths fit into three quarters exactly twice.
Common fractions as decimals and percentages
Digits in brackets repeat forever, so 0.(3) means 0.333…
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.(3) | 33.(3)% |
| 2/3 | 0.(6) | 66.(6)% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1(6) | 16.(6)% |
| 5/6 | 0.8(3) | 83.(3)% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 1/9 | 0.(1) | 11.(1)% |
| 1/12 | 0.08(3) | 8.(3)% |
Tips for working with fractions
- Simplify as you go. Cancelling a common factor before multiplying (cross-cancelling) keeps the numbers small; the final answer is the same.
- A fraction ends as a decimal only if its denominator has no prime factors other than 2 and 5. That is why 3/8 = 0.375 stops, while 1/6 and 1/12 repeat.
- Check with decimals. 3/4 + 5/6 should be a little more than 1.5 (0.75 + 0.83), and 1.58(3) is.
- Zero rules. A denominator can never be 0, and you can't divide by a fraction that equals 0.
- For long division of the numerator by the denominator, digit by digit, use the long division calculator. To express one number as a percent of another, try the percentage calculator.
Frequently asked questions
How do you add fractions with different denominators?
Rewrite both fractions over a common denominator, add the numerators and simplify. For 3/4 + 5/6, the least common denominator is 12: 9/12 + 10/12 = 19/12, which is 1 7/12 as a mixed number.
How do you multiply mixed numbers?
Convert each mixed number to an improper fraction, multiply the numerators and the denominators, then simplify. 2 1/3 × 1 1/2 = 7/3 × 3/2 = 21/6 = 7/2 = 3 1/2.
How do you divide fractions?
Multiply the first fraction by the reciprocal of the second (flip it upside down). 3/4 ÷ 3/8 = 3/4 × 8/3 = 24/12 = 2.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. For 18/12 the GCD is 6, so 18/12 = 3/2. A fraction is in lowest terms when the GCD of its top and bottom is 1.
Why do some fractions give repeating decimals?
A fraction in lowest terms has a terminating decimal only when its denominator has no prime factors except 2 and 5. 3/8 = 0.375 ends, but 1/6 = 0.1666… repeats, shown here as 0.1(6).