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Fraction Estimator

Below are multiple fraction calculators capable of improver, subtraction, multiplication, partitioning, 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 Computer

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Simplify Fractions Computer

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Decimal to Fraction Computer

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Fraction to Decimal Figurer

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Big Number Fraction Computer

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 function 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 8. A more 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 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, as information technology would make the fraction undefined. Fractions can undergo many unlike operations, some of which are mentioned below.

Addition:

Unlike adding and subtracting integers such every bit 2 and 8, 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 production of the denominators of each fraction. Multiplying all of the denominators ensures that the new denominator is certain to exist a multiple of each individual denominator. The numerators also need to exist multiplied by the appropriate factors to preserve the value of the fraction every bit a whole. This is arguably the simplest style to ensure that the fractions have a common denominator. Yet, in nigh cases, the solutions to these equations will non appear in simplified grade (the provided computer computes the simplification automatically). Below is an example using this method.

This process tin 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 ain respective denominator) in the problem.

An alternative method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, then add or decrease the numerators as one would an integer. Using the least common multiple can exist more than efficient and is more likely to upshot in a fraction in simplified course. In the example above, the denominators were 4, six, and 2. The least common multiple is the first shared multiple of these 3 numbers.

Multiples of ii: 2, 4, six, eight 10, 12

Multiples of four: 4, 8, 12

Multiples of six: 6, 12

The starting time multiple they all share is 12, and then this is the to the lowest degree common multiple. To consummate an addition (or subtraction) problem, multiply the numerators and denominators of each fraction in the trouble past whatsoever value volition make the denominators 12, then add together the numerators.

Subtraction:

Fraction subtraction is substantially the same equally fraction addition. A mutual denominator is required for the operation to occur. Refer to the addition section also every bit the equations below for description.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is not necessary to compute a mutual 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 club to divide fractions, the fraction in the numerator is multiplied past 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 often easier to work with simplified fractions. Equally such, fraction solutions are commonly expressed in their simplified forms.

for instance, is more cumbersome than

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

Converting between 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 existence x¹, the second 10², the third 10³, and then on. Simply decide what power of 10 the decimal extends to, use that power of 10 every bit the denominator, enter each number to the right of the decimal point every bit the numerator, and simplify. For example, looking at the number 0.1234, the number four is in the fourth decimal place, which constitutes 10⁴, or 10,000. This would make the fraction

, which simplifies to

, since the greatest common gene between the numerator and denominator is 2.

Similarly, fractions with denominators that are powers of 10 (or tin can be converted to powers of 10) tin be translated to decimal form 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 first decimal place represents ten^-1,

can exist converted to 0.5. If the fraction were instead

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

64^th	32^nd	16^th	8^th	iv^th	ii^nd	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
2/64	1/32					0.03125	0.79375
3/64						0.046875	ane.190625
four/64	2/32	one/xvi				0.0625	1.5875
5/64						0.078125	i.984375
6/64	3/32					0.09375	two.38125
7/64						0.109375	2.778125
8/64	4/32	2/sixteen	1/8			0.125	3.175
nine/64						0.140625	3.571875
10/64	five/32					0.15625	3.96875
11/64						0.171875	4.365625
12/64	half-dozen/32	iii/xvi				0.1875	iv.7625
13/64						0.203125	5.159375
14/64	vii/32					0.21875	five.55625
fifteen/64						0.234375	5.953125
xvi/64	eight/32	4/16	2/eight	ane/four		0.25	6.35
17/64						0.265625	six.746875
18/64	9/32					0.28125	vii.14375
xix/64						0.296875	vii.540625
20/64	x/32	5/16				0.3125	7.9375
21/64						0.328125	eight.334375
22/64	xi/32					0.34375	8.73125
23/64						0.359375	9.128125
24/64	12/32	6/16	3/8			0.375	nine.525
25/64						0.390625	9.921875
26/64	13/32					0.40625	x.31875
27/64						0.421875	x.715625
28/64	xiv/32	7/16				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/four	1/ii	0.5	12.7
33/64						0.515625	13.096875
34/64	17/32					0.53125	xiii.49375
35/64						0.546875	13.890625
36/64	xviii/32	9/16				0.5625	xiv.2875
37/64						0.578125	14.684375
38/64	19/32					0.59375	15.08125
39/64						0.609375	15.478125
forty/64	xx/32	10/16	v/8			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/sixteen				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/eight	3/iv		0.75	19.05
49/64						0.765625	xix.446875
50/64	25/32					0.78125	nineteen.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	fourteen/xvi	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
sixty/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	16/16	eight/8	4/4	2/2	ane	25.4