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Fraction Calculator

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

Apply this reckoner if the numerators or denominators are very big integers.

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In mathematics, a fraction is a number that represents a office 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

, the numerator is 3, and the denominator is viii. A more than illustrative example could involve a pie with 8 slices. 1 of those eight slices would constitute the numerator of a fraction, while the full of 8 slices that comprises the whole pie would be the denominator. If a person were to eat iii slices, the remaining fraction of the pie would therefore exist

as shown in the image to the right. Note that the denominator of a fraction cannot be 0, every bit information technology 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. I 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 private denominator. The numerators besides need to exist multiplied by the appropriate factors to preserve the value of the fraction equally 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 announced in simplified form (the provided estimator computes the simplification automatically). Below is an example using this method.

This process can be used for whatsoever number of fractions. Just multiply the numerators and denominators of each fraction in the trouble by the production of the denominators of all the other fractions (not including its own corresponding denominator) in the problem.

An alternative method for finding a common denominator is to decide the least common multiple (LCM) for the denominators, then add or subtract the numerators as 1 would an integer. Using the to the lowest degree common multiple can exist more than efficient and is more than likely to event in a fraction in simplified grade. In the case above, the denominators were four, 6, and 2. The least common multiple is the offset shared multiple of these 3 numbers.

Multiples of 2: 2, 4, six, 8 10, 12

Multiples of 4: 4, 8, 12

Multiples of half dozen: vi, 12

The first multiple they all share is 12, and so this is the least common multiple. To complete an addition (or subtraction) trouble, multiply the numerators and denominators of each fraction in the trouble by any value volition brand the denominators 12, and so add the numerators.

Subtraction:

Fraction subtraction is essentially the same as fraction improver. A mutual denominator is required for the operation to occur. Refer to the improver 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 exist simplified. Refer to the equations below for clarification.

Division:

The procedure for dividing fractions is similar to that for multiplying fractions. In gild to split 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 frequently easier to work with simplified fractions. Equally such, fraction solutions are commonly expressed in their simplified forms.

for example, is more than cumbersome than

. The calculator provided returns fraction inputs in both improper fraction form as well equally mixed number class. In both cases, fractions are presented in their lowest forms past dividing both numerator and denominator past their greatest common gene.

Converting between fractions and decimals:

Converting from decimals to fractions is straightforward. It does, however, require the agreement that each decimal place to the right of the decimal indicate represents a ability of 10; the beginning decimal identify being x^ane, the second 10², the third x³, and then on. Simply make up one's mind what ability of 10 the decimal extends to, use that power of ten as the denominator, enter each number to the right of the decimal signal as the numerator, and simplify. For example, looking at the number 0.1234, the number four is in the fourth decimal place, which constitutes x⁴, 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 tin be converted to powers of 10) can be translated to decimal course using the same principles. Take the fraction

for example. To convert this fraction into a decimal, first convert it into the fraction of

. Knowing that the commencement decimal place represents ten^-i,

tin can be converted to 0.5. If the fraction were instead

, the decimal would then exist 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 science, fractions are widely used to describe the size of components such as pipes and bolts. The almost common fractional and decimal equivalents are listed below.

64^thursday	32^nd	16^th	8^thursday	4^thursday	2^nd	Decimal	Decimal (inch to mm)
one/64						0.015625	0.396875
two/64	1/32					0.03125	0.79375
3/64						0.046875	1.190625
4/64	2/32	one/16				0.0625	1.5875
five/64						0.078125	one.984375
vi/64	three/32					0.09375	2.38125
7/64						0.109375	2.778125
8/64	4/32	2/xvi	1/eight			0.125	3.175
9/64						0.140625	3.571875
10/64	5/32					0.15625	three.96875
xi/64						0.171875	four.365625
12/64	6/32	3/16				0.1875	4.7625
13/64						0.203125	5.159375
14/64	7/32					0.21875	v.55625
15/64						0.234375	5.953125
16/64	eight/32	four/16	2/8	1/4		0.25	6.35
17/64						0.265625	vi.746875
18/64	ix/32					0.28125	7.14375
19/64						0.296875	7.540625
twenty/64	10/32	v/sixteen				0.3125	7.9375
21/64						0.328125	eight.334375
22/64	xi/32					0.34375	eight.73125
23/64						0.359375	9.128125
24/64	12/32	six/16	iii/8			0.375	9.525
25/64						0.390625	9.921875
26/64	thirteen/32					0.40625	10.31875
27/64						0.421875	10.715625
28/64	14/32	seven/xvi				0.4375	11.1125
29/64						0.453125	11.509375
xxx/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	xviii/32	9/xvi				0.5625	xiv.2875
37/64						0.578125	14.684375
38/64	19/32					0.59375	15.08125
39/64						0.609375	15.478125
40/64	twenty/32	10/16	5/8			0.625	15.875
41/64						0.640625	xvi.271875
42/64	21/32					0.65625	16.66875
43/64						0.671875	17.065625
44/64	22/32	xi/xvi				0.6875	17.4625
45/64						0.703125	17.859375
46/64	23/32					0.71875	eighteen.25625
47/64						0.734375	18.653125
48/64	24/32	12/16	vi/eight	3/4		0.75	19.05
49/64						0.765625	nineteen.446875
50/64	25/32					0.78125	xix.84375
51/64						0.796875	20.240625
52/64	26/32	thirteen/16				0.8125	twenty.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	xiv/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
threescore/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/four	ii/2	1	25.4

4 Divided By 5 9,

Source: https://www.calculator.net/fraction-calculator.html

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