3 8 4 5 Simplify

Fraction Calculator

Below are multiple fraction calculators capable of addition, subtraction, multiplication, sectionalisation, simplification, and conversion between fractions and decimals. Fields higher up the solid black line correspond the numerator, while fields below stand for the denominator.

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Mixed Numbers Calculator

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Simplify Fractions Calculator

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Decimal to Fraction Computer

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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. 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 3, and the denominator is 8. A more than illustrative example could involve a pie with eight slices. i of those 8 slices would institute the numerator of a fraction, while the total 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 exist 0, every bit information technology would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned beneath.

Add-on:

Unlike adding and subtracting integers such equally 2 and viii, fractions require 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 product 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 demand to be multiplied past the advisable factors to preserve the value of the fraction equally a whole. This is arguably the simplest way to ensure that the fractions take a common denominator. All the same, in about cases, the solutions to these equations will non announced in simplified form (the provided calculator computes the simplification automatically). Beneath is an example using this method.

This procedure tin be used for whatever 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 ain respective denominator) in the problem.

An culling method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, then add or decrease the numerators equally one would an integer. Using the to the lowest degree mutual multiple can exist more efficient and is more likely to result in a fraction in simplified grade. In the instance higher up, the denominators were iv, vi, and ii. The least mutual multiple is the first shared multiple of these 3 numbers.

Multiples of two: ii, 4, half dozen, 8 10, 12

Multiples of 4: 4, eight, 12

Multiples of vi: 6, 12

The start multiple they all share is 12, so this is the to the lowest degree mutual multiple. To complete an improver (or subtraction) trouble, multiply the numerators and denominators of each fraction in the trouble by whatever value will make the denominators 12, and so add the numerators.

Subtraction:

Fraction subtraction is substantially the same every bit fraction addition. A common denominator is required for the operation to occur. Refer to the improver section besides every bit the equations below for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike calculation and subtracting, it is not necessary to compute a common denominator in order to multiply fractions. Merely, 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 like to that for multiplying fractions. In society 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 be

. Refer to the equations beneath for description.

Simplification:

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

for case, is more cumbersome than

. The calculator provided returns fraction inputs in both improper fraction form likewise equally 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. Information technology does, even so, require the understanding that each decimal place to the right of the decimal betoken represents a power of ten; the first decimal place being 10^one, the second ten², the third tenⁱⁱⁱ, then on. Simply make up one's mind what power of x the decimal extends to, apply that power of 10 equally the denominator, enter each number to the correct of the decimal betoken every bit the numerator, and simplify. For example, looking at the number 0.1234, the number 4 is in the fourth decimal identify, which constitutes 10⁴, or 10,000. This would make the fraction

, which simplifies to

, since the greatest common cistron betwixt the numerator and denominator is 2.

Similarly, fractions with denominators that are powers of 10 (or can be converted to powers of 10) can be translated to decimal form using the same principles. Take the fraction

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

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

tin be converted to 0.5. If the fraction were instead

, the decimal would then exist 0.05, and and then on. Across this, converting fractions into decimals requires the performance of long division.

Common Applied science Fraction to Decimal Conversions

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

64^th	32^nd	xvi^th	8^th	4^th	2^nd	Decimal	Decimal (inch to mm)
1/64						0.015625	0.396875
2/64	1/32					0.03125	0.79375
3/64						0.046875	1.190625
4/64	2/32	1/16				0.0625	1.5875
v/64						0.078125	1.984375
vi/64	3/32					0.09375	2.38125
7/64						0.109375	2.778125
viii/64	four/32	2/16	ane/eight			0.125	3.175
9/64						0.140625	3.571875
10/64	five/32					0.15625	3.96875
xi/64						0.171875	4.365625
12/64	6/32	3/xvi				0.1875	4.7625
13/64						0.203125	5.159375
fourteen/64	7/32					0.21875	5.55625
15/64						0.234375	5.953125
16/64	viii/32	4/xvi	2/eight	i/4		0.25	vi.35
17/64						0.265625	6.746875
xviii/64	9/32					0.28125	7.14375
xix/64						0.296875	vii.540625
twenty/64	x/32	v/sixteen				0.3125	7.9375
21/64						0.328125	8.334375
22/64	11/32					0.34375	eight.73125
23/64						0.359375	9.128125
24/64	12/32	vi/sixteen	3/8			0.375	9.525
25/64						0.390625	9.921875
26/64	13/32					0.40625	x.31875
27/64						0.421875	x.715625
28/64	14/32	7/16				0.4375	eleven.1125
29/64						0.453125	11.509375
30/64	15/32					0.46875	xi.90625
31/64						0.484375	12.303125
32/64	sixteen/32	8/16	iv/viii	2/four	1/2	0.five	12.7
33/64						0.515625	13.096875
34/64	17/32					0.53125	xiii.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	fifteen.08125
39/64						0.609375	15.478125
40/64	20/32	10/sixteen	five/8			0.625	15.875
41/64						0.640625	16.271875
42/64	21/32					0.65625	xvi.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	xviii.653125
48/64	24/32	12/16	6/8	3/4		0.75	19.05
49/64						0.765625	nineteen.446875
l/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	14/sixteen	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	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	sixteen/xvi	8/viii	4/4	2/2	1	25.4