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Fraction Calculator

Below are multiple fraction calculators capable of addition, subtraction, multiplication, segmentation, 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 Figurer

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Decimal to Fraction Calculator

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Fraction to Decimal Calculator

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Large Number Fraction Calculator

Use this estimator 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 instance, in the fraction of

, the numerator is three, and the denominator is viii. A more than illustrative example could involve a pie with 8 slices. ane of those eight slices would constitute the numerator of a fraction, while the total of viii 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 exist

equally shown in the image to the right. Notation 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:

Unlike calculation and subtracting integers such as 2 and eight, fractions crave 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 sure to be a multiple of each individual denominator. The numerators also demand to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest fashion to ensure that the fractions have a common denominator. However, in most cases, the solutions to these equations will not announced in simplified class (the provided calculator computes the simplification automatically). Below is an example using this method.

This process can be used for any number of fractions. Merely multiply the numerators and denominators of each fraction in the trouble by the product of the denominators of all the other fractions (not including its own respective denominator) in the trouble.

An culling method for finding a common denominator is to make up one's mind the least common multiple (LCM) for the denominators, then add together or subtract the numerators as one would an integer. Using the to the lowest degree mutual multiple can be more than efficient and is more than likely to result in a fraction in simplified form. In the instance above, the denominators were four, six, and 2. The to the lowest degree common multiple is the showtime shared multiple of these three numbers.

Multiples of two: two, 4, half dozen, 8 ten, 12

Multiples of 4: 4, viii, 12

Multiples of 6: vi, 12

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

Subtraction:

Fraction subtraction is essentially the same every bit fraction addition. A common denominator is required for the functioning to occur. Refer to the add-on department every bit well every bit the equations below for description.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is non necessary to compute a common denominator in order to multiply fractions. Simply, the numerators and denominators of each fraction are multiplied, and the effect 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 split up fractions, the fraction in the numerator is multiplied by the reciprocal of the fraction in the denominator. The reciprocal of a number a is merely

. When a is a fraction, this substantially involves exchanging the position of the numerator and the denominator. The reciprocal of the fraction

would therefore exist

. Refer to the equations below for clarification.

Simplification:

Information technology is oftentimes easier to work with simplified fractions. As 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 equally well as mixed number form. In both cases, fractions are presented in their lowest forms past dividing both numerator and denominator by their greatest common factor.

Converting between fractions and decimals:

Converting from decimals to fractions is straightforward. It does, still, require the agreement that each decimal identify to the correct of the decimal point represents a power of 10; the first decimal place existence 10¹, the 2nd ten², the third 10^three, and so on. Just decide what power of x the decimal extends to, employ that ability of 10 as the denominator, enter each number to the right of the decimal bespeak every bit 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 x,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 exist converted to powers of 10) can exist translated to decimal form using the same principles. Have the fraction

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

. Knowing that the first decimal place represents 10^-1,

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

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

Common Technology Fraction to Decimal Conversions

In engineering, fractions are widely used to describe the size of components such equally pipes and bolts. The nigh common partial and decimal equivalents are listed below.

64^th	32^nd	xvi^th	8^thursday	four^th	2^nd	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
2/64	1/32					0.03125	0.79375
iii/64						0.046875	1.190625
4/64	2/32	1/16				0.0625	i.5875
5/64						0.078125	1.984375
6/64	3/32					0.09375	2.38125
7/64						0.109375	two.778125
8/64	iv/32	2/16	1/8			0.125	3.175
9/64						0.140625	iii.571875
ten/64	5/32					0.15625	three.96875
11/64						0.171875	4.365625
12/64	vi/32	3/16				0.1875	four.7625
thirteen/64						0.203125	v.159375
fourteen/64	7/32					0.21875	5.55625
15/64						0.234375	5.953125
16/64	8/32	four/16	2/8	one/4		0.25	6.35
17/64						0.265625	6.746875
18/64	nine/32					0.28125	7.14375
19/64						0.296875	seven.540625
20/64	ten/32	5/16				0.3125	7.9375
21/64						0.328125	8.334375
22/64	11/32					0.34375	viii.73125
23/64						0.359375	ix.128125
24/64	12/32	half dozen/16	3/viii			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	xiv/32	seven/16				0.4375	11.1125
29/64						0.453125	11.509375
30/64	15/32					0.46875	xi.90625
31/64						0.484375	12.303125
32/64	xvi/32	viii/16	iv/viii	ii/4	one/2	0.5	12.7
33/64						0.515625	thirteen.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	xv.478125
twoscore/64	20/32	10/16	v/viii			0.625	xv.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	iii/4		0.75	xix.05
49/64						0.765625	xix.446875
50/64	25/32					0.78125	19.84375
51/64						0.796875	20.240625
52/64	26/32	13/xvi				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	xv/sixteen				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	xvi/xvi	8/eight	four/4	2/two	1	25.iv

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

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