Below space multiple portion betterworld2016.orgs capable of addition, subtraction, multiplication, division, simplification, and also conversion in between fractions and decimals. Fields over the solid black line represent the numerator, when fields listed below represent the denominator.

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## Mixed numbers betterworld2016.org

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## Big Number portion betterworld2016.org

Use this betterworld2016.org if the molecule or denominators room very large integers.

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In mathematics, a fraction is a number the represents a component of a whole. It is composed of a numerator and also a denominator. The molecule represents the variety of equal components of a whole, when the denominator is the total number of parts that consist of said whole. Because that example, in the portion of
 3 8
, the molecule is 3, and the denominator is 8. A more illustrative example might involve a pie with 8 slices. 1 of those 8 slices would certainly constitute the molecule of a fraction, when the total of 8 slices the comprises the entirety pie would certainly be the denominator. If a person were come eat 3 slices, the remaining fraction of the pie would because of this be
 5 8
as shown in the picture to the right. Note that the denominator that a fraction cannot be 0, together it would make the portion undefined. Fractions deserve to undergo countless different operations, several of which are discussed below.

Unlike including and individually integers such as 2 and 8, fractions need a typical denominator come undergo these operations. One method for recognize a typical denominator entails multiplying the numerators and also denominators of all of the fractions connected by the product of the platform of every fraction. Multiplying every one of the platform ensures that the brand-new denominator is certain to be a many of every individual denominator. The numerators also need come be multiply by the ideal factors to maintain the value of the fraction as a whole. This is maybe the simplest method to ensure that the fractions have actually a usual denominator. However, in many cases, the solutions to this equations will certainly not show up in simplified type (the noted betterworld2016.org computes the leveling automatically). Below is an example using this method.

 a b
+ c
d
= a×d
b×d
+ c×b
d×b
bd
 EX: 3 4
+ 1
6
= 3×6
4×6
+ 1×4
6×4
= 22
24
= 11
12

This procedure can be used for any number of fractions. Just multiply the numerators and also denominators the each fraction in the difficulty by the product the the denominators of all the other fractions (not consisting of its own respective denominator) in the problem.

 EX: 1 4
+ 1
6
+ 1
2
= 1×6×2
4×6×2
+ 1×4×2
6×4×2
+ 1×4×6
2×4×6
=12
 48
+ 8
48
+ 24
48
= 44
48
= 11
12

An alternative technique for detect a typical denominator is to identify the least typical multiple (LCM) for the denominators, then add or subtract the numerators together one would an integer. Using the least typical multiple deserve to be more efficient and is more likely to result in a portion in simplified form. In the instance above, the denominators were 4, 6, and 2. The least common multiple is the first shared many of these three numbers.

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

The very first multiple they all share is 12, therefore this is the least typical multiple. To finish an enhancement (or subtraction) problem, multiply the numerators and denominators the each fraction in the difficulty by every little thing value will certainly make the platform 12, then add the numerators.

 EX: 1 4
+ 1
6
+ 1
2
= 1×3
4×3
+ 1×2
6×2
+ 1×6
2×6
=3
 12
+ 2
12
+ 6
12
= 11
12

### Subtraction:

Fraction individually is essentially the same as portion addition. A common denominator is required for the operation to occur. Describe the enhancement section and also the equations listed below for clarification.

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 a b
– c
d
= a×d
b×d
– c×b
d×b
bd
 EX: 3 4
– 1
6
= 3×6
4×6
– 1×4
6×4
= 14
24
= 7
12

### Multiplication:

Multiplying fountain is fairly straightforward. Unlike including and subtracting, it is not important to compute a common denominator in bespeak to main point fractions. Simply, the numerators and also denominators the each portion are multiplied, and the an outcome forms a brand-new numerator and denominator. If possible, the solution should be simplified. Describe the equations below for clarification.

 a b
× c
d
= ac
bd
 EX: 3 4
× 1
6
= 3
24
= 1
8

### Division:

The procedure for dividing fractions is comparable to the for multiply fractions. In bespeak to division fractions, the portion in the molecule is multiplied by the reciprocal of the portion in the denominator. The mutual of a number a is just
 1 a
. As soon as a is a fraction, this essentially requires exchanging the position of the numerator and the denominator. The mutual of the fraction
 3 4
would thus be
 4 3
. Refer to the equations listed below for clarification.

 a b
/ c
d
= a
b
× d
c
bc
 EX: 3 4
/ 1
6
= 3
4
× 6
1
= 18
4
= 9
2

### Simplification:

It is often much easier to work-related with simplified fractions. As such, portion solutions are commonly expressed in their simplified forms.
 220 440
for example, is more cumbersome 보다
 1 2
. The betterworld2016.org detailed returns portion inputs in both not correct fraction type as well as combined number form. In both cases, fractions space presented in their lowest develops by separating both numerator and denominator by their greatest usual factor.

### Converting between fractions and also decimals:

Converting from decimals to fountain is straightforward. It does, however, need the expertise that each decimal ar to the appropriate of the decimal point represents a power of 10; the first decimal ar being 101, the second 102, the third 103, and also so on. Simply recognize what power of 10 the decimal extends to, use that power of 10 together the denominator, get in each number to the best of the decimal point as the numerator, and also simplify. For example, looking in ~ the number 0.1234, the number 4 is in the 4th decimal place, which constitutes 104, or 10,000. This would make the portion
 1234 10000
, i beg your pardon simplifies come
 617 5000
, because the greatest typical factor between the numerator and also denominator is 2.

Similarly, fractions v denominators that space powers the 10 (or have the right to be convert to strength of 10) can be interpreted to decimal form using the same principles. Take the portion
 1 2
for example. To convert this fraction into a decimal, first convert it into the portion of
 5 10
. Learning that the very first decimal location represents 10-1,
 5 10
have the right to be converted to 0.5. If the fraction were instead
 5 100
, the decimal would certainly then it is in 0.05, and also so on. Past this, convert fractions into decimals requires the operation of lengthy division.

### Common Engineering portion to Decimal Conversions

In engineering, fractions room widely supplied to define the size of components such together pipes and also bolts. The most usual fractional and decimal equivalents are detailed below.

 64th 32nd 16th 8th 4th 2nd Decimal Decimal(inch come 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 5/64 0.078125 1.984375 6/64 3/32 0.09375 2.38125 7/64 0.109375 2.778125 8/64 4/32 2/16 1/8 0.125 3.175 9/64 0.140625 3.571875 10/64 5/32 0.15625 3.96875 11/64 0.171875 4.365625 12/64 6/32 3/16 0.1875 4.7625 13/64 0.203125 5.159375 14/64 7/32 0.21875 5.55625 15/64 0.234375 5.953125 16/64 8/32 4/16 2/8 1/4 0.25 6.35 17/64 0.265625 6.746875 18/64 9/32 0.28125 7.14375 19/64 0.296875 7.540625 20/64 10/32 5/16 0.3125 7.9375 21/64 0.328125 8.334375 22/64 11/32 0.34375 8.73125 23/64 0.359375 9.128125 24/64 12/32 6/16 3/8 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 14/32 7/16 0.4375 11.1125 29/64 0.453125 11.509375 30/64 15/32 0.46875 11.90625 31/64 0.484375 12.303125 32/64 16/32 8/16 4/8 2/4 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 18/32 9/16 0.5625 14.2875 37/64 0.578125 14.684375 38/64 19/32 0.59375 15.08125 39/64 0.609375 15.478125 40/64 20/32 10/16 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 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 12/16 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 13/16 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 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 16/16 8/8 4/4 2/2 1 25.4