Add, subtract, multiply or divide two fractions and see the result reduced to lowest terms with its decimal value.
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1/2 + 1/3 is 5/6, about 0.83333333. Multiplication gives 2/3 × 9/4 = 3/2, which is 1.5, division gives 5/8 ÷ 5/16 = 2/1, and 3/4 − 5/6 is −1/12.
Addition and subtraction put both fractions over a common denominator: 3/4 − 5/6 becomes 9/12 − 10/12 = −1/12. Multiplication multiplies numerators and denominators straight across, and division multiplies by the reciprocal of the second fraction. Every result is divided by the greatest common divisor of its numerator and denominator, and the sign is kept on the numerator.
Numerators and denominators must be whole numbers, and a denominator of 0 is rejected because such a fraction has no value. Dividing by a fraction whose numerator is 0 is undefined and is also rejected. The decimal line is rounded for display, so 5/6 appears as 0.83333333 although the digits repeat forever.
Type each fraction as an integer numerator over an integer denominator and choose the operation. One half plus one third is 5/6, about 0.83333333. For a mixed number such as 2 1/4, convert it to an improper fraction first: 2 × 4 + 1 = 9, so enter 9/4. Negative fractions can be entered with a minus sign on the numerator, and a denominator of zero is rejected because such a fraction has no value.
Addition and subtraction use a common denominator: 3/4 − 5/6 becomes 9/12 − 10/12 = −1/12. Multiplication multiplies straight across, so 2/3 × 9/4 = 18/12, which reduces to 3/2. Division multiplies by the reciprocal of the second fraction: 5/8 ÷ 5/16 = 5/8 × 16/5 = 2. Every result is reduced to lowest terms and the sign is placed on the numerator. Dividing by a fraction whose numerator is zero is undefined and is rejected.
A whole-number answer is shown with a denominator of 1, as in 2/1, and 1/3 + 1/6 simplifies to 1/2. The decimal line is rounded for display, so 5/6 appears as 0.83333333 although the exact value repeats forever; keep the fraction when you need an exact result, such as recipe or measurement adjustments. To turn an improper result like 3/2 back into a mixed number, divide: 3 ÷ 2 is 1 with remainder 1, so 3/2 = 1 1/2.
| Input | Result |
|---|---|
1/2 + 1/3 | 5/6 → 0.83333333 |
3/4 − 5/6 | -1/12 → -0.08333333 |
2/3 × 9/4 | 3/2 → 1.5 |
5/8 ÷ 5/16 | 2/1 → 2 |
1/3 + 1/6 | 1/2 → 0.5 |
Convert it to an improper fraction first: multiply the whole number by the denominator and add the numerator, so 2 × 4 + 1 = 9 and you enter 9/4. To read an improper result back as a mixed number, divide: 3/2 is 3 ÷ 2, which is 1 with remainder 1, so 3/2 = 1 1/2.
Yes. Both parts are divided by their greatest common divisor, so 2/3 × 9/4 gives 18/12, which is shown as 3/2, and 1/3 + 1/6 is shown as 1/2. A whole-number result keeps a denominator of 1, as in 2/1, so you can see that the division came out exactly.
Keep the fraction when the result must be exact, such as adjusting a recipe or a measurement; 5/6 cannot be written exactly as a decimal. Use the decimal when you need to compare values quickly or type them into another tool, remembering that it is rounded for display.