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Fraction Calculator

Below are multiple fraction calculators capable of improver, subtraction, multiplication, sectionalization, 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 Reckoner

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Decimal to Fraction Calculator

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Fraction to Decimal Calculator

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Big Number Fraction Figurer

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 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 iii, and the denominator is viii. A more illustrative example could involve a pie with 8 slices. one of those 8 slices would constitute the numerator of a fraction, while the full of eight slices that comprises the whole pie would be the denominator. If a person were to consume three 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, as it would make the fraction undefined. Fractions can undergo many dissimilar operations, some of which are mentioned below.

Addition:

Unlike adding and subtracting integers such as 2 and 8, fractions crave a mutual 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 production 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. All the same, in nearly 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.

This process tin 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 (non including its own respective denominator) in the trouble.

An alternative method for finding a common denominator is to determine the to the lowest degree common multiple (LCM) for the denominators, so add or decrease the numerators as one would an integer. Using the least common multiple can exist more efficient and is more likely to consequence in a fraction in simplified grade. In the example in a higher place, the denominators were 4, half-dozen, and 2. The least mutual multiple is the first shared multiple of these three numbers.

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

Multiples of iv: 4, 8, 12

Multiples of 6: six, 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 past whatever value volition brand the denominators 12, then add the numerators.

Subtraction:

Fraction subtraction is essentially the same as fraction addition. A common denominator is required for the performance to occur. Refer to the addition section as well every bit the equations below for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is non necessary to compute a common denominator in guild 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.

Partition:

The process for dividing fractions is similar to that for multiplying fractions. In guild 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 only

. When a is a fraction, this essentially 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 ofttimes easier to work with simplified fractions. As such, fraction solutions are usually expressed in their simplified forms.

for example, is more cumbersome than

. The calculator provided returns fraction inputs in both improper fraction form also every bit mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator past their greatest common factor.

Converting betwixt 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 10^two, the tertiary 10³, then on. Merely decide what power of x the decimal extends to, use that power of x equally the denominator, enter each number to the right of the decimal point as the numerator, and simplify. For instance, 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 can exist converted to powers of 10) tin be translated to decimal class using the same principles. Have the fraction

for example. To catechumen this fraction into a decimal, first convert information technology into the fraction of

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

tin be converted to 0.five. If the fraction were instead

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

Common Engineering Fraction to Decimal Conversions

In applied science, fractions are widely used to describe the size of components such as pipes and bolts. The most mutual fractional and decimal equivalents are listed below.

64^thursday	32^nd	16^th	eight^thursday	iv^thursday	2^nd	Decimal	Decimal (inch to mm)
ane/64						0.015625	0.396875
2/64	1/32					0.03125	0.79375
three/64						0.046875	i.190625
four/64	ii/32	i/16				0.0625	1.5875
5/64						0.078125	one.984375
six/64	3/32					0.09375	2.38125
7/64						0.109375	ii.778125
viii/64	four/32	two/16	1/8			0.125	3.175
9/64						0.140625	3.571875
10/64	5/32					0.15625	3.96875
11/64						0.171875	4.365625
12/64	six/32	3/xvi				0.1875	four.7625
13/64						0.203125	five.159375
14/64	vii/32					0.21875	5.55625
15/64						0.234375	5.953125
xvi/64	viii/32	4/16	2/8	1/4		0.25	vi.35
17/64						0.265625	6.746875
18/64	9/32					0.28125	7.14375
19/64						0.296875	7.540625
20/64	ten/32	5/xvi				0.3125	7.9375
21/64						0.328125	8.334375
22/64	11/32					0.34375	eight.73125
23/64						0.359375	nine.128125
24/64	12/32	6/16	3/8			0.375	9.525
25/64						0.390625	9.921875
26/64	thirteen/32					0.40625	x.31875
27/64						0.421875	x.715625
28/64	14/32	7/sixteen				0.4375	11.1125
29/64						0.453125	eleven.509375
xxx/64	xv/32					0.46875	11.90625
31/64						0.484375	12.303125
32/64	sixteen/32	8/16	4/viii	2/iv	one/ii	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	eighteen/32	9/16				0.5625	14.2875
37/64						0.578125	14.684375
38/64	19/32					0.59375	fifteen.08125
39/64						0.609375	15.478125
40/64	twenty/32	10/xvi	5/8			0.625	15.875
41/64						0.640625	16.271875
42/64	21/32					0.65625	16.66875
43/64						0.671875	17.065625
44/64	22/32	eleven/16				0.6875	17.4625
45/64						0.703125	17.859375
46/64	23/32					0.71875	18.25625
47/64						0.734375	eighteen.653125
48/64	24/32	12/16	half-dozen/viii	3/4		0.75	19.05
49/64						0.765625	19.446875
50/64	25/32					0.78125	19.84375
51/64						0.796875	20.240625
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	14/16	7/eight			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	xvi/16	eight/8	four/4	2/2	one	25.four

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

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