7 3 In Simplest Form

Fraction Reckoner

Below are multiple fraction calculators capable of add-on, subtraction, multiplication, sectionalisation, simplification, and conversion between fractions and decimals. Fields above the solid black line correspond the numerator, while fields below correspond the denominator.

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Mixed Numbers Calculator

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Simplify Fractions Calculator

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Decimal to Fraction Estimator

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Fraction to Decimal Calculator

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Large Number Fraction Calculator

Use this reckoner if the numerators or denominators are very large integers.

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In mathematics, a fraction is a number that represents a role 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 three, and the denominator is eight. A more illustrative instance could involve a pie with 8 slices. 1 of those 8 slices would constitute the numerator of a fraction, while the total of 8 slices that comprises the whole pie would exist the denominator. If a person were to eat 3 slices, the remaining fraction of the pie would therefore exist

as shown in the image to the correct. Notation that the denominator of a fraction cannot exist 0, as information technology would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below.

Improver:

Dissimilar adding and subtracting integers such as 2 and viii, fractions require 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 private 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 style to ensure that the fractions have a common denominator. However, in nigh cases, the solutions to these equations will not appear in simplified class (the provided calculator computes the simplification automatically). Below is an example using this method.

This process can exist used for whatever number of fractions. Just multiply the numerators and denominators of each fraction in the trouble by the product of the denominators of all the other fractions (non including its own respective denominator) in the problem.

An alternative method for finding a common denominator is to make up one's mind the to the lowest degree mutual multiple (LCM) for the denominators, then add or decrease the numerators every bit one would an integer. Using the least common multiple can exist more efficient and is more likely to event in a fraction in simplified form. In the case above, the denominators were 4, six, and 2. The least common multiple is the beginning shared multiple of these three numbers.

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

Multiples of 4: 4, eight, 12

Multiples of vi: 6, 12

The outset multiple they all share is 12, so this is the to the lowest degree common multiple. To complete an add-on (or subtraction) trouble, multiply the numerators and denominators of each fraction in the problem by whatever value will brand the denominators 12, then add the numerators.

Subtraction:

Fraction subtraction is substantially the same as fraction improver. A common denominator is required for the operation to occur. Refer to the improver section as well as 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 result forms a new numerator and denominator. If possible, the solution should be simplified. Refer to the equations below for clarification.

Division:

The procedure for dividing fractions is similar to that for multiplying fractions. In order to dissever 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 beneath for clarification.

Simplification:

It is oft easier to work with simplified fractions. Equally such, fraction solutions are usually expressed in their simplified forms.

for instance, is more cumbersome than

. The reckoner provided returns fraction inputs in both improper fraction form too as mixed number course. In both cases, fractions are presented in their everyman forms past dividing both numerator and denominator by their greatest common cistron.

Converting betwixt fractions and decimals:

Converting from decimals to fractions is straightforward. It does, however, require the understanding that each decimal identify to the right of the decimal indicate represents a ability of x; the first decimal place existence x¹, the 2d 10ⁱⁱ, the third 10³, and then on. Only make up one's mind what power of x the decimal extends to, use that power of ten equally the denominator, enter each number to the correct of the decimal point every bit the numerator, and simplify. For example, looking at the number 0.1234, the number 4 is in the quaternary decimal identify, which constitutes x^iv, 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 x (or can exist converted to powers of 10) can be translated to decimal form using the aforementioned principles. Take the fraction

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

. Knowing that the showtime decimal identify represents 10^-1,

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

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

Mutual Engineering Fraction to Decimal Conversions

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

64^th	32^nd	16^th	8^thursday	four^th	ii^nd	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
2/64	ane/32					0.03125	0.79375
3/64						0.046875	1.190625
4/64	2/32	i/sixteen				0.0625	1.5875
five/64						0.078125	ane.984375
6/64	3/32					0.09375	ii.38125
7/64						0.109375	2.778125
8/64	4/32	2/16	1/8			0.125	iii.175
nine/64						0.140625	3.571875
10/64	v/32					0.15625	3.96875
11/64						0.171875	4.365625
12/64	vi/32	three/sixteen				0.1875	4.7625
13/64						0.203125	5.159375
14/64	7/32					0.21875	5.55625
15/64						0.234375	five.953125
16/64	8/32	four/xvi	2/8	1/4		0.25	6.35
17/64						0.265625	6.746875
18/64	9/32					0.28125	seven.14375
nineteen/64						0.296875	vii.540625
xx/64	x/32	5/16				0.3125	vii.9375
21/64						0.328125	viii.334375
22/64	xi/32					0.34375	eight.73125
23/64						0.359375	9.128125
24/64	12/32	6/16	three/viii			0.375	9.525
25/64						0.390625	nine.921875
26/64	13/32					0.40625	10.31875
27/64						0.421875	10.715625
28/64	14/32	7/sixteen				0.4375	11.1125
29/64						0.453125	11.509375
30/64	fifteen/32					0.46875	11.90625
31/64						0.484375	12.303125
32/64	16/32	eight/16	4/8	2/iv	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	9/16				0.5625	14.2875
37/64						0.578125	xiv.684375
38/64	19/32					0.59375	xv.08125
39/64						0.609375	15.478125
40/64	20/32	10/sixteen	5/eight			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	xi/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	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	xiii/sixteen				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	seven/viii			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	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	iv/4	2/2	1	25.iv