How to use the fraction calculator
- Choose what you want to do: work with two fractions, simplify one fraction, or convert a decimal to a fraction.
- For each fraction, enter the whole number (leave it empty for a plain fraction), the numerator (top) and the denominator (bottom). For a negative mixed number, put the minus sign on the whole number only, as in -2 1/3.
- Pick the operation: add, subtract, multiply or divide.
- For a decimal, type it as you would write it. Put repeating digits in brackets, so 0.1(6) means 0.1666… forever.
- Read the answer as a simplified fraction, a mixed number and a decimal, with the working underneath.
How fraction arithmetic works
The numerator a and denominator b describe the first fraction, and c/d the second. Adding and subtracting need a common denominator. The calculator uses the least common multiple of the two denominators, which keeps the numbers small. Multiplying works straight across. Dividing flips the second fraction (its reciprocal) and multiplies. Every answer is then divided top and bottom by the greatest common divisor (GCD), which leaves the fraction in lowest terms.
A mixed number such as 1 1/2 is first turned into an improper fraction: multiply the whole number by the denominator and add the numerator, so 1 1/2 = (1 × 2 + 1)/2 = 3/2.
Worked example
The calculator opens with 1 1/2 + 2/3:
- Convert the mixed number: 1 1/2 = (1 × 2 + 1)/2 = 3/2.
- The least common multiple of 2 and 3 is 6.
- Rewrite both fractions over 6: 3/2 = 9/6 and 2/3 = 4/6.
- Add the numerators: 9/6 + 4/6 = 13/6.
- GCD(13, 6) = 1, so 13/6 is already in lowest terms.
- As a mixed number: 13 ÷ 6 = 2 remainder 1, so 13/6 = 2 1/6.
- As a decimal: 13 ÷ 6 = 2.1666…, written 2.1(6) because the 6 repeats.
Switch the operation to divide and the same two numbers give 3/2 × 3/2 = 9/4, or 2 1/4.
Turning a decimal into a fraction
A decimal that ends is a fraction over a power of 10. 0.375 has three decimal places, so it is 375/1000. The GCD of 375 and 1000 is 125, which simplifies it to 3/8.
A repeating decimal needs one extra trick. For x = 0.1(6), multiply by 100 and by 10 so the repeating tails line up: 100x = 16.66… and 10x = 1.66…. Subtracting removes the tail: 90x = 15, so x = 15/90 = 1/6. The calculator does this for any repeating block of up to 15 digits in total.
Common mistakes
| Mistake | Why it's wrong | Correct |
|---|---|---|
| 1/2 + 1/3 = 2/5 | Adding the denominators | 3/6 + 2/6 = 5/6 |
| 1 1/2 × 2 = 2 1/2 | Multiplying only the whole part | 3/2 × 2 = 3 |
| 3/4 ÷ 1/2 = 3/8 | Forgetting to flip the divisor | 3/4 × 2/1 = 3/2 |
| -1 1/2 = -1 + 1/2 | Applying the sign to the whole only | -(1 + 1/2) = -3/2 |
Frequently asked questions
How do I simplify a fraction?
Divide the numerator and the denominator by their greatest common divisor. For 18/24 the GCD is 6, so 18/24 = 3/4. If the GCD is 1, as with 13/6, the fraction is already in lowest terms.
What is the difference between an improper fraction and a mixed number?
An improper fraction has a numerator at least as large as its denominator, like 13/6. A mixed number writes the same value as a whole number plus a proper fraction, like 2 1/6. Improper fractions are easier to calculate with, and mixed numbers are easier to picture.
Why does the decimal show digits in brackets?
Some fractions never end as decimals. One sixth is 0.1666… with the 6 repeating forever, so the calculator writes it as 0.1(6). Only fractions whose simplified denominator has no prime factors other than 2 and 5 give a decimal that ends.
Can I enter negative fractions?
Yes. Type a minus sign in front of the numerator for a plain fraction, such as -3/4, or in front of the whole number for a mixed number, such as -2 1/3. The whole mixed number is then negative, so -2 1/3 equals -7/3.
Related calculators
- Percentage Calculator — Percent of a number, what percent one number is of another, percentage change and difference.
- Ratio Calculator — Simplify ratios, solve A : B = C : D for a missing value, scale a ratio or split a total, with fractions and percentages.
- Long Division Calculator — Long division with every step shown: quotient, remainder and the decimal answer with repeating digits marked.
- GCF Calculator — Greatest common factor of two or more whole numbers, with Euclid's algorithm and a prime factorization check.
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