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
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Simplify Fractions Calculator
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Decimal to Fraction Calculator
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Fraction to Decimal Calculator
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Big Number Fraction Calculator
Use this calculator if the numerators or denominators are very big integers.
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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 of
38, 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 58 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:
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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.
ab + cd = a×db×d + c×bd×b = ad + bcbd EX: 34 + 16 = 3×64×6 + 1×46×4 = 2224 = 1112
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.
EX: 14 + 16 + 12 = 1×6×24×6×2 + 1×4×26×4×2 + 1×4×62×4×6 = 1248 + 848 + 2448 = 4448 = 1112
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 to 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.
EX: 14 + 16 + 12 = 1×34×3 + 1×26×2 + 1×62×6 = 312 + 212 + 612 = 1112
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.
ab – cd = a×db×d – c×bd×b = ad – bcbd EX: 34 – 16 = 3×64×6 – 1×46×4 = 1424 = 712
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.
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ab × cd = acbd EX: 34 × 16 = 324 = 18
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
1a . When a is a fraction, this essentially involves exchanging the position of the numerator and the denominator. The reciprocal of the fraction 34 would therefore be 43. Refer to the equations below for clarification. ab / cd = ab × dc = adbc EX: 34 / 16 = 34 × 61 = 184 = 92
Simplification:
It is often easier to work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms.
220440 for example, is more cumbersome than 12. 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 101, the second 102, the third 103, 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 104, or 10,000. This would make the fraction
123410000, which simplifies to 6175000, 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
12 for example. To convert this fraction into a decimal, first convert it into the fraction of 510. Knowing that the first decimal place represents 10-1, 510 can be converted to 0.5. If the fraction were instead 5100, 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.
64th32nd16th8th4th2ndDecimalDecimal(inch to mm) 1/64 0.0156250.396875 2/641/32 0.031250.79375 3/64 0.0468751.190625 4/642/321/16 0.06251.5875 5/64 0.0781251.984375 6/643/32 0.093752.38125 7/64 0.1093752.778125 8/644/322/161/8 0.1253.175 9/64 0.1406253.571875 10/645/32 0.156253.96875 11/64 0.1718754.365625 12/646/323/16 0.18754.7625 13/64 0.2031255.159375 14/647/32 0.218755.55625 15/64 0.2343755.953125 16/648/324/162/81/4 0.256.35 17/64 0.2656256.746875 18/649/32 0.281257.14375 19/64 0.2968757.540625 20/6410/325/16 0.31257.9375 21/64 0.3281258.334375 22/6411/32 0.343758.73125 23/64 0.3593759.128125 24/6412/326/163/8 0.3759.525 25/64 0.3906259.921875 26/6413/32 0.4062510.31875 27/64 0.42187510.715625 28/6414/327/16 0.437511.1125 29/64 0.45312511.509375 30/6415/32 0.4687511.90625 31/64 0.48437512.303125 32/6416/328/164/82/41/20.512.7 33/64 0.51562513.096875 34/6417/32 0.5312513.49375 35/64 0.54687513.890625 36/6418/329/16 0.562514.2875 37/64 0.57812514.684375 38/6419/32 0.5937515.08125 39/64 0.60937515.478125 40/6420/3210/165/8 0.62515.875 41/64 0.64062516.271875 42/6421/32 0.6562516.66875 43/64 0.67187517.065625 44/6422/3211/16 0.687517.4625 45/64 0.70312517.859375 46/6423/32 0.7187518.25625 47/64 0.73437518.653125 48/6424/3212/166/83/4 0.7519.05 49/64 0.76562519.446875 50/6425/32 0.7812519.84375 51/64 0.79687520.240625 52/6426/3213/16 0.812520.6375 53/64 0.82812521.034375 54/6427/32 0.8437521.43125 55/64 0.85937521.828125 56/6428/3214/167/8 0.87522.225 57/64 0.89062522.621875 58/6429/32 0.9062523.01875 59/64 0.92187523.415625 60/6430/3215/16 0.937523.8125 61/64 0.95312524.209375 62/6431/32 0.9687524.60625 63/64 0.98437525.003125 64/6432/3216/168/84/42/2125.4
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