Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator.
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Mixed Numbers Calculator
Simplify Fractions Calculator
Decimal to Fraction Calculator
Fraction to Decimal Calculator
Big Number Fraction Calculator
Use this calculator if the numerators or denominators are very big integers.
In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole. For example, in the fraction
, the numerator is 3, and the denominator is 8. A more illustrative example could involve a pie with 8 slices. 1 of those 8 slices would constitute the numerator of a fraction, while the total of 8 slices that comprises the whole pie would be the denominator. If a person were to eat 3 slices, the remaining fraction of the pie would therefore be
as shown in the image to the right. Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below.
Addition:
Unlike adding and subtracting integers such as 2 and 8, fractions require a common denominator to undergo these operations. One method for finding a common denominator involves multiplying the numerators and denominators of all of the fractions involved by the product of the denominators of each fraction. Multiplying all of the denominators ensures that the new denominator is certain to be a multiple of each individual denominator. The numerators also need to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest way to ensure that the fractions have a common denominator. However, in most cases, the solutions to these equations will not appear in simplified form (the provided calculator computes the simplification automatically). Below is an example using this method.
This process can be used for any number of fractions. Just multiply the numerators and denominators of each fraction in the problem by the product of the denominators of all the other fractions (not including its own respective denominator) in the problem.
An alternative method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. Using the least common multiple can be more efficient and is more likely result in a fraction in simplified form. In the example above, the denominators were 4, 6, and 2. The least common multiple is the first shared multiple of these three numbers.
| Multiples of 2: 2, 4, 6, 8 10, 12 |
| Multiples of 4: 4, 8, 12 |
| Multiples of 6: 6, 12 |
The first multiple they all share is 12, so this is the least common multiple. To complete an addition (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by whatever value will make the denominators 12, then add the numerators.
Subtraction:
Fraction subtraction is essentially the same as fraction addition. A common denominator is required for the operation to occur. Refer to the addition section as well as the equations below for clarification.
Multiplication:
Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is not necessary to compute a common denominator in order to multiply fractions. Simply, the numerators and denominators of each fraction are multiplied, and the result forms a new numerator and denominator. If possible, the solution should be simplified. Refer to the equations below for clarification.
Division:
The process for dividing fractions is similar to that for multiplying fractions. In order to divide fractions, the fraction in the numerator is multiplied by the reciprocal of the fraction in the denominator. The reciprocal of a number
a is simply
. When a is a fraction, this essentially involves exchanging the position of the numerator and the denominator. The reciprocal of the fraction
would therefore be
. Refer to the equations below for clarification.
Simplification:
It is often easier to work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms.
for example, is more cumbersome than
. The calculator provided returns fraction inputs in both improper fraction form, as well as mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator by their greatest common factor.
Converting between fractions and decimals:
Converting from decimals to fractions is straightforward. It does however require the understanding that each decimal place to the right of the decimal point represents a power of 10; the first decimal place being 10
1, the second 10
2, the third 10
3, and so on. Simply determine what power of 10 the decimal extends to, use that power of 10 as the denominator, enter each number to the right of the decimal point as the numerator, and simplify. For example, looking at the number 0.1234, the number 4 is in the fourth decimal place which constitutes 10
4, or 10,000. This would make the fraction
, which simplifies to
, since the greatest common factor between the numerator and denominator is 2. Similarly, fractions with denominators that are powers of 10 (or can be converted to powers of 10) can be translated to decimal form using the same principles. Take the fraction
for example. To convert this fraction into a decimal, first convert it into the fraction
. Knowing that the first decimal place represents 10
-1,
can be converted to 0.5. If the fraction were instead
, the decimal would then be 0.05, and so on. Beyond this, converting fractions into decimals requires the operation of long division.
Common Engineering Fraction to Decimal Conversions
In engineering, fractions are widely used to describe the size of components such as pipes and bolts. The most common fractional and decimal equivalents are listed below.
| 64th | 32nd | 16th | 8th | 4th | 2nd | Decimal | Decimal
(inch to mm) |
| 1/64 | 0.015625 | 0.396875 |
| 2/64 | 1/32 | 0.03125 | 0.79375 |
| 3/64 | 0.046875 | 1.190625 |
| 4/64 | 2/32 | 1/16 | 0.0625 | 1.5875 |
| 5/64 | 0.078125 | 1.984375 |
| 6/64 | 3/32 | 0.09375 | 2.38125 |
| 7/64 | 0.109375 | 2.778125 |
| 8/64 | 4/32 | 2/16 | 1/8 | 0.125 | 3.175 |
| 9/64 | 0.140625 | 3.571875 |
| 10/64 | 5/32 | 0.15625 | 3.96875 |
| 11/64 | 0.171875 | 4.365625 |
| 12/64 | 6/32 | 3/16 | 0.1875 | 4.7625 |
| 13/64 | 0.203125 | 5.159375 |
| 14/64 | 7/32 | 0.21875 | 5.55625 |
| 15/64 | 0.234375 | 5.953125 |
| 16/64 | 8/32 | 4/16 | 2/8 | 1/4 | 0.25 | 6.35 |
| 17/64 | 0.265625 | 6.746875 |
| 18/64 | 9/32 | 0.28125 | 7.14375 |
| 19/64 | 0.296875 | 7.540625 |
| 20/64 | 10/32 | 5/16 | 0.3125 | 7.9375 |
| 21/64 | 0.328125 | 8.334375 |
| 22/64 | 11/32 | 0.34375 | 8.73125 |
| 23/64 | 0.359375 | 9.128125 |
| 24/64 | 12/32 | 6/16 | 3/8 | 0.375 | 9.525 |
| 25/64 | 0.390625 | 9.921875 |
| 26/64 | 13/32 | 0.40625 | 10.31875 |
| 27/64 | 0.421875 | 10.715625 |
| 28/64 | 14/32 | 7/16 | 0.4375 | 11.1125 |
| 29/64 | 0.453125 | 11.509375 |
| 30/64 | 15/32 | 0.46875 | 11.90625 |
| 31/64 | 0.484375 | 12.303125 |
| 32/64 | 16/32 | 8/16 | 4/8 | 2/4 | 1/2 | 0.5 | 12.7 |
| 33/64 | 0.515625 | 13.096875 |
| 34/64 | 17/32 | 0.53125 | 13.49375 |
| 35/64 | 0.546875 | 13.890625 |
| 36/64 | 18/32 | 9/16 | 0.5625 | 14.2875 |
| 37/64 | 0.578125 | 14.684375 |
| 38/64 | 19/32 | 0.59375 | 15.08125 |
| 39/64 | 0.609375 | 15.478125 |
| 40/64 | 20/32 | 10/16 | 5/8 | 0.625 | 15.875 |
| 41/64 | 0.640625 | 16.271875 |
| 42/64 | 21/32 | 0.65625 | 16.66875 |
| 43/64 | 0.671875 | 17.065625 |
| 44/64 | 22/32 | 11/16 | 0.6875 | 17.4625 |
| 45/64 | 0.703125 | 17.859375 |
| 46/64 | 23/32 | 0.71875 | 18.25625 |
| 47/64 | 0.734375 | 18.653125 |
| 48/64 | 24/32 | 12/16 | 6/8 | 3/4 | 0.75 | 19.05 |
| 49/64 | 0.765625 | 19.446875 |
| 50/64 | 25/32 | 0.78125 | 19.84375 |
| 51/64 | 0.796875 | 20.240625 |
| 52/64 | 26/32 | 13/16 | 0.8125 | 20.6375 |
| 53/64 | 0.828125 | 21.034375 |
| 54/64 | 27/32 | 0.84375 | 21.43125 |
| 55/64 | 0.859375 | 21.828125 |
| 56/64 | 28/32 | 14/16 | 7/8 | 0.875 | 22.225 |
| 57/64 | 0.890625 | 22.621875 |
| 58/64 | 29/32 | 0.90625 | 23.01875 |
| 59/64 | 0.921875 | 23.415625 |
| 60/64 | 30/32 | 15/16 | 0.9375 | 23.8125 |
| 61/64 | 0.953125 | 24.209375 |
| 62/64 | 31/32 | 0.96875 | 24.60625 |
| 63/64 | 0.984375 | 25.003125 |
| 64/64 | 32/32 | 16/16 | 8/8 | 4/4 | 2/2 | 1 | 25.4 |
How many equal parts of a whole
Slice a pizza, and we get fractions:
The top number says how many slices we have.
The bottom number says how many equal slices the whole pizza was cut into.
Have a try yourself:
Equivalent Fractions
Some fractions may look different, but are really the same, for example:
| 4/8 | = | 2/4 | = | 1/2 |
| (Four-Eighths) | (Two-Quarters) | (One-Half) |
| = | = |
It is usually best to show an answer using the simplest fraction ( 1/2 in this case ). That is called Simplifying, or Reducing the Fraction
Numerator / Denominator
We call the top number the Numerator, it is the number of parts we have.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.
NumeratorDenominator
Scenario 2 Part 1.2.1&your Digital Footprint Software
You just have to remember those names! (If you forget just think 'Down'-ominator)
Adding Fractions
Scenario 2 Part 1.2.1&your Digital Footprint Worksheet
It is easy to add fractions with the same denominator (same bottom number):
| 1/4 | + | 1/4 | = | 2/4 | = | 1/2 |
| (One-Quarter) | (One-Quarter) | (Two-Quarters) | (One-Half) |
| + | = | = |
One-quarter plus one-quarter equals two-quarters, equals one-half
Riddle school 5clout games. Another example:
Five-eighths plus one-eighth equals six-eighths, equals three-quarters
Scenario 2 Part 1.2.1&your Digital Footprints
Adding Fractions with Different Denominators
But what about when the denominators (the bottom numbers) are not the same?
Three-eighths plus one-quarter equals .. what? We must somehow make the denominators the same.
In this case it is easy, because we know that 1/4 is the same as 2/8 :
Three-eighths plus two-eighths equals five-eighths
Scenario 2 Part 1.2.1&your Digital Footprint System
There are two popular methods to make the denominators the same:
- Least Common Denominator, or
(They both work nicely, use the one you prefer.)
Other Things We Can Do With Fractions
We can also:
Visit the Fractions Index to find out even more.