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Fraction Calculator

Beneath are multiple fraction calculators capable of addition, subtraction, multiplication, sectionalization, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields beneath correspond the denominator.

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Mixed Numbers Computer

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Simplify Fractions Calculator

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Decimal to Fraction Figurer

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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 large integers.

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In mathematics, a fraction is a number that represents a part of a whole. Information technology 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 8. A more illustrative example could involve a pie with 8 slices. ane of those 8 slices would constitute the numerator of a fraction, while the total of eight 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, equally it would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below.

Addition:

Different adding and subtracting integers such as 2 and eight, fractions crave a common denominator to undergo these operations. One method for finding a mutual 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 likewise demand to be multiplied by the advisable factors to preserve the value of the fraction as a whole. This is arguably the simplest mode to ensure that the fractions accept a mutual denominator. Withal, in most cases, the solutions to these equations will not announced in simplified course (the provided calculator computes the simplification automatically). Below is an instance using this method.

This procedure can exist 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 corresponding denominator) in the problem.

An culling method for finding a common denominator is to determine the least mutual multiple (LCM) for the denominators, then add or subtract the numerators as i would an integer. Using the least common multiple can be more than efficient and is more probable to result in a fraction in simplified course. In the instance in a higher place, the denominators were 4, 6, and ii. The to the lowest degree mutual multiple is the first shared multiple of these iii numbers.

Multiples of 2: 2, 4, 6, 8 ten, 12

Multiples of four: 4, viii, 12

Multiples of 6: 6, 12

The commencement multiple they all share is 12, then this is the least common multiple. To complete an improver (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by whatever value will make the denominators 12, and then add the numerators.

Subtraction:

Fraction subtraction is essentially the same as fraction addition. A mutual 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 adequately straightforward. Dissimilar calculation and subtracting, it is non necessary to compute a mutual 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 description.

Sectionalization:

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:

Information technology is often easier to piece of work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms.

for example, is more cumbersome than

. The figurer provided returns fraction inputs in both improper fraction course as well as mixed number class. In both cases, fractions are presented in their lowest forms past dividing both numerator and denominator by their greatest common factor.

Converting betwixt 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 betoken represents a power of 10; the kickoff decimal place beingness 10¹, the second 10², the third x³, and then on. Simply determine what power of 10 the decimal extends to, use that ability 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 iv is in the fourth decimal place, which constitutes x⁴, or ten,000. This would make the fraction

, which simplifies to

, since the greatest mutual factor between the numerator and denominator is 2.

Similarly, fractions with denominators that are powers of ten (or can be converted to powers of 10) tin can exist translated to decimal form using the same principles. Take the fraction

for case. To convert this fraction into a decimal, outset catechumen it into the fraction of

. Knowing that the first decimal place represents ten^-ane,

can be converted to 0.v. If the fraction were instead

, the decimal would then be 0.05, and then on. Beyond this, converting fractions into decimals requires the operation of long division.

Common Technology Fraction to Decimal Conversions

In engineering, fractions are widely used to depict the size of components such as pipes and bolts. The most common partial and decimal equivalents are listed beneath.

64^th	32^nd	16^th	8^th	4^thursday	2^nd	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
two/64	1/32					0.03125	0.79375
three/64						0.046875	1.190625
4/64	2/32	1/16				0.0625	1.5875
five/64						0.078125	1.984375
6/64	3/32					0.09375	2.38125
7/64						0.109375	2.778125
8/64	4/32	2/xvi	1/8			0.125	three.175
9/64						0.140625	iii.571875
10/64	five/32					0.15625	3.96875
xi/64						0.171875	4.365625
12/64	six/32	3/16				0.1875	four.7625
thirteen/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	ii/8	1/4		0.25	6.35
17/64						0.265625	6.746875
xviii/64	nine/32					0.28125	7.14375
19/64						0.296875	7.540625
20/64	10/32	5/16				0.3125	seven.9375
21/64						0.328125	eight.334375
22/64	11/32					0.34375	8.73125
23/64						0.359375	9.128125
24/64	12/32	six/16	3/8			0.375	nine.525
25/64						0.390625	ix.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	eleven.90625
31/64						0.484375	12.303125
32/64	xvi/32	viii/16	4/8	2/4	one/2	0.5	12.vii
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	fourteen.2875
37/64						0.578125	14.684375
38/64	19/32					0.59375	15.08125
39/64						0.609375	xv.478125
40/64	20/32	10/16	five/viii			0.625	fifteen.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/xvi	6/viii	3/iv		0.75	xix.05
49/64						0.765625	19.446875
l/64	25/32					0.78125	19.84375
51/64						0.796875	twenty.240625
52/64	26/32	13/16				0.8125	xx.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/sixteen	seven/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	iv/4	2/ii	i	25.4

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

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