Fraction Calculator

Under are a number of fraction calculators able to addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the strong black line symbolize the numerator, whereas fields under symbolize the denominator.

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Blended 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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Massive Quantity Fraction Calculator

Use this calculator if the numerators or denominators are very massive integers.

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In arithmetic, a fraction is a quantity that represents part of a complete. It consists of a numerator and a denominator. The numerator represents the variety of equal elements of a complete, whereas the denominator is the whole variety of elements that make up mentioned entire. For instance, within the fraction of

38, the numerator is 3, and the denominator is 8. A extra illustrative instance might contain a pie with Eight slices. 1 of these Eight slices would represent the numerator of a fraction, whereas the whole of Eight slices that includes the entire pie could be the denominator. If an individual have been to eat Three slices, the remaining fraction of the pie would due to this fact be 58 as proven within the picture to the proper. Notice that the denominator of a fraction can’t be 0, as it will make the fraction undefined. Fractions can endure many various operations, a few of that are talked about under.

Addition:

In contrast to including and subtracting integers akin to 2 and eight, fractions require a typical denominator to endure these operations. One methodology for locating a typical denominator includes multiplying the numerators and denominators of all the fractions concerned by the product of the denominators of every fraction. Multiplying all the denominators ensures that the brand new denominator is for certain to be a a number of of every particular person denominator. The numerators additionally should be multiplied by the suitable elements to protect the worth of the fraction as a complete. That is arguably the best means to make sure that the fractions have a typical denominator. Nonetheless, normally, the options to those equations won’t seem in simplified type (the offered calculator computes the simplification robotically). Under is an instance utilizing this methodology.

ab + cd = a×db×d + c×bd×b = advert + bcbd EX: 34 + 16 = 3×64×6 + 1×46×4 = 2224 = 1112

This course of can be utilized for any variety of fractions. Simply multiply the numerators and denominators of every fraction in the issue by the product of the denominators of all the opposite fractions (not together with its personal respective denominator) in the issue.

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 alternate methodology for locating a typical denominator is to find out the least widespread a number of (LCM) for the denominators, then add or subtract the numerators as one would an integer. Utilizing the least widespread a number of may be extra environment friendly and is extra prone to lead to a fraction in simplified type. Within the instance above, the denominators have been 4, 6, and a pair of. The least widespread a number of is the primary shared a number of of those three numbers.

Multiples of two: 2, 4, 6, 8 10, 12 Multiples of 4: 4, 8, 12 Multiples of 6: 6, 12

The primary a number of all of them share is 12, so that is the least widespread a number of. To finish an addition (or subtraction) downside, multiply the numerators and denominators of every fraction in the issue by no matter worth 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 basically the identical as fraction addition. A typical denominator is required for the operation to happen. Consult with the addition part in addition to the equations under for clarification.

ab – cd = a×db×d – c×bd×b = advert – bcbd EX: 34 – 16 = 3×64×6 – 1×46×4 = 1424 = 712

Multiplication:

Multiplying fractions is pretty simple. In contrast to including and subtracting, it isn’t essential to compute a typical denominator with a purpose to multiply fractions. Merely, the numerators and denominators of every fraction are multiplied, and the consequence types a brand new numerator and denominator. If potential, the answer ought to be simplified. Consult with the equations under for clarification.

ab × cd = acbd EX: 34 × 16 = 324 = 18

Division:

The method for dividing fractions is just like that for multiplying fractions. With a view to divide fractions, the fraction within the numerator is multiplied by the reciprocal of the fraction within the denominator. The reciprocal of a quantity a is just

1a . When a is a fraction, this primarily includes exchanging the place of the numerator and the denominator. The reciprocal of the fraction 34 would due to this fact be 43. Consult with the equations under for clarification. ab / cd = ab × dc = adbc EX: 34 / 16 = 34 × 61 = 184 = 92

Simplification:

It’s typically simpler to work with simplified fractions. As such, fraction options are generally expressed of their simplified types.

220440 for instance, is extra cumbersome than 12. The calculator offered returns fraction inputs in each improper fraction type in addition to combined quantity type. In each instances, fractions are introduced of their lowest types by dividing each numerator and denominator by their best widespread issue.

Changing between fractions and decimals:

Changing from decimals to fractions is simple. It does, nonetheless, require the understanding that every decimal place to the proper of the decimal level represents an influence of 10; the primary decimal place being 101, the second 102, the third 103, and so forth. Merely decide what energy of 10 the decimal extends to, use that energy of 10 because the denominator, enter every quantity to the proper of the decimal level because the numerator, and simplify. For instance, trying on the quantity 0.1234, the quantity Four is within the fourth decimal place, which constitutes 104, or 10,000. This could make the fraction

123410000, which simplifies to 6175000, for the reason that best widespread issue between the numerator and denominator is 2.

Equally, fractions with denominators which might be powers of 10 (or may be transformed to powers of 10) may be translated to decimal type utilizing the identical rules. Take the fraction

12 for instance. To transform this fraction right into a decimal, first convert it into the fraction of 510. Understanding that the primary decimal place represents 10-1, 510 may be transformed to 0.5. If the fraction have been as an alternative 5100, the decimal would then be 0.05, and so forth. Past this, changing fractions into decimals requires the operation of lengthy division.

Frequent Engineering Fraction to Decimal Conversions

In engineering, fractions are extensively used to explain the dimensions of parts akin to pipes and bolts. The commonest fractional and decimal equivalents are listed under.

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/Eight 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/Four 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/Eight 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/Eight 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/Four 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/Eight 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