What Multiplies To 2 And Adds To 1

Fraction Calculator

Beneath are multiple fraction calculators capable of addition, subtraction, multiplication, segmentation, simplification, and conversion between fractions and decimals. Fields above the solid black line stand for the numerator, while fields beneath 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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Big Number Fraction Calculator

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 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 full number of parts that make up said whole. For example, in the fraction of

, the numerator is 3, 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 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 exist

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 tin can undergo many dissimilar operations, some of which are mentioned beneath.

Addition:

Unlike adding and subtracting integers such as 2 and viii, fractions require a mutual denominator to undergo these operations. One method for finding a mutual denominator involves multiplying the numerators and denominators of all of the fractions involved past 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 besides need to be multiplied past the appropriate factors to preserve the value of the fraction equally a whole. This is arguably the simplest fashion to ensure that the fractions take a common denominator. Nevertheless, in most cases, the solutions to these equations volition non appear in simplified class (the provided calculator computes the simplification automatically). Below is an example using this method.

This procedure tin can be used for any number of fractions. Only multiply the numerators and denominators of each fraction in the trouble past 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 least common multiple (LCM) for the denominators, so add or subtract the numerators as one would an integer. Using the least common multiple tin can be more efficient and is more likely to upshot in a fraction in simplified form. In the example above, the denominators were 4, half-dozen, and two. The to the lowest degree common multiple is the starting time shared multiple of these three numbers.

Multiples of 2: 2, iv, half dozen, 8 10, 12

Multiples of 4: iv, 8, 12

Multiples of 6: 6, 12

The starting time multiple they all share is 12, then this is the least mutual multiple. To consummate an addition (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by whatever value volition make the denominators 12, then add the numerators.

Subtraction:

Fraction subtraction is essentially the aforementioned as fraction addition. A common denominator is required for the operation to occur. Refer to the add-on section also as the equations below for description.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike calculation and subtracting, it is not 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 exist simplified. Refer to the equations below for clarification.

Partition:

The process for dividing fractions is like 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 but

. 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 beneath for clarification.

Simplification:

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

for example, is more cumbersome than

. The estimator provided returns fraction inputs in both improper fraction form likewise as 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, yet, require the agreement that each decimal place to the correct of the decimal point represents a power of 10; the first decimal place beingness 10¹, the 2nd 10², the third xⁱⁱⁱ, and so on. Only make up one's mind what power of 10 the decimal extends to, use that power of ten as the denominator, enter each number to the right of the decimal signal as the numerator, and simplify. For instance, looking at the number 0.1234, the number 4 is in the fourth decimal place, which constitutes 10^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 10 (or tin can be converted to powers of 10) can be translated to decimal class using the same principles. Take the fraction

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

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

can exist converted to 0.5. If the fraction were instead

, the decimal would and then be 0.05, and so on. Beyond this, converting fractions into decimals requires the performance of long partitioning.

Common Engineering Fraction to Decimal Conversions

In engineering, fractions are widely used to describe the size of components such every bit pipes and bolts. The most common fractional and decimal equivalents are listed below.

64^th	32^nd	16^th	8^thursday	4^th	two^nd	Decimal	Decimal (inch to mm)
one/64						0.015625	0.396875
2/64	1/32					0.03125	0.79375
3/64						0.046875	ane.190625
4/64	2/32	ane/16				0.0625	1.5875
5/64						0.078125	i.984375
6/64	3/32					0.09375	2.38125
seven/64						0.109375	2.778125
8/64	4/32	2/16	1/8			0.125	3.175
9/64						0.140625	3.571875
10/64	v/32					0.15625	iii.96875
11/64						0.171875	iv.365625
12/64	half dozen/32	3/16				0.1875	four.7625
13/64						0.203125	5.159375
14/64	vii/32					0.21875	5.55625
xv/64						0.234375	five.953125
xvi/64	8/32	four/16	2/viii	i/4		0.25	6.35
17/64						0.265625	6.746875
18/64	9/32					0.28125	7.14375
xix/64						0.296875	7.540625
20/64	10/32	5/16				0.3125	7.9375
21/64						0.328125	viii.334375
22/64	11/32					0.34375	eight.73125
23/64						0.359375	nine.128125
24/64	12/32	6/xvi	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	7/xvi				0.4375	eleven.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	viii/16	4/eight	2/4	1/2	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	eighteen/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	15.478125
40/64	xx/32	10/sixteen	5/8			0.625	15.875
41/64						0.640625	16.271875
42/64	21/32					0.65625	sixteen.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/sixteen	6/8	iii/four		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/16				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/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	four/4	ii/2	ane	25.4