Below are multiple fraction slrfc.orgs capable of addition, subtractivity, multiplication, department, simplification, and also convariation between fractions and also decimals. Fields above the solid black line recurrent the numerator, while areas below represent the denominator.

You are watching: 2/3 + 2/3 + 2/3

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## Mixed Numbers slrfc.org

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## Big Number Fractivity slrfc.org

Use this slrfc.org if the numerators or denominators are incredibly huge integers.

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In mathematics, a fraction is a number that represents a component of a totality. It is composed of a numerator and a denominator. The numerator represents the variety of equal parts of a totality, while the denominator is the complete variety of components that comprise shelp entirety. For instance, in the fractivity of
 3 8
, the numerator is 3, and also the denominator is 8. An even more illustrative example 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 totality pie would certainly be the denominator. If a perboy were to eat 3 slices, the staying fraction of the pie would certainly therefore be
 5 8
as presented in the photo to the right. Keep in mind that the denominator of a portion cannot be 0, as it would make the fraction unidentified. Fractions have the right to undergo many various operations, some of which are discussed listed below.

Unchoose adding and also subtracting integers such as 2 and also 8, fractions require a widespread denominator to undergo these operations. One strategy for finding a prevalent denominator requires multiplying the numerators and denominators of all of the fractions connected by the product of the denominators of each fraction. Multiplying every one of the denominators ensures that the brand-new denominator is specific to be a multiple of each individual denominator. The numerators likewise have to be multiplied by the proper components to maintain the value of the fraction all at once. This is arguably the most basic method to encertain that the fractions have actually a widespread denominator. However, in many situations, the remedies to these equations will certainly not appear in streamlined develop (the offered slrfc.org computes the simplification automatically). Below is an instance using this strategy.

 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 process can be provided for any number of fractions. Just multiply the numerators and also denominators of each fraction in the difficulty by the product of the denominators of all the various other fractions (not including its own corresponding denominator) in the difficulty.

 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 strategy for finding a widespread denominator is to identify the least common multiple (LCM) for the denominators, then include or subtract the numerators as one would an integer. Using the leastern widespread multiple can be more reliable and also is more most likely to cause a portion in streamlined create. In the instance over, the denominators were 4, 6, and also 2. The least common multiple is the first mutual multiple 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 first multiple they all share is 12, so this is the leastern prevalent multiple. To complete an addition (or subtraction) difficulty, multiply the numerators and denominators of each fractivity in the difficulty by whatever worth will certainly make the denominators 12, then include 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 subtraction is basically the very same as fractivity addition. A widespread denominator is required for the operation to occur. Refer to the enhancement area and the equations listed below for clarification.

See more: Indicate, By Letter, The Strongest Acid And The Weakest Acid Of Those Below.

 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 fractions is reasonably straightforward. Unchoose adding and subtracting, it is not essential to compute a widespread denominator in order to multiply fractions. Ssuggest, the numerators and also denominators of each fraction are multiplied, and also the result creates a brand-new numerator and also denominator. If possible, the solution should be simplified. Refer to the equations below for clarification.

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

### Division:

The procedure for splitting fractions is equivalent to that for multiplying fractions. In order to divide fractions, the fractivity in the numerator is multiplied by the reciprocal of the fraction in the denominator. The reciprocal of a number a is simply
 1 a
. When a is a fraction, this essentially requires extransforming the position of the numerator and also the denominator. The reciprocal of the fraction
 3 4
would therefore 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 regularly much easier to work via streamlined fractions. Because of this, fraction solutions are commonly expressed in their simplified forms.
 220 440
for example, is more cumbersome than
 1 2
. The slrfc.org gave returns fraction inputs in both imappropriate fractivity form and also blended number form. In both situations, fractions are presented in their lowest develops by splitting both numerator and denominator by their biggest common factor.

### Converting between fractions and also decimals:

Converting from decimals to fractions is straightforward. It does, however, require the expertise that each decimal location to the right of the decimal suggest represents a power of 10; the initially decimal place being 101, the second 102, the third 103, and also so on. Ssuggest identify what power of 10 the decimal exhas a tendency to, usage that power of 10 as the denominator, enter each number to the best of the decimal point as the numerator, and also simplify. For instance, looking at the number 0.1234, the number 4 is in the fourth decimal place, which constitutes 104, or 10,000. This would certainly make the fraction
 1234 10000
, which simplifies to
 617 5000
, because the best common variable between the numerator and also denominator is 2.

Similarly, fractions through denominators that are powers of 10 (or deserve to be converted to powers of 10) can be translated to decimal develop utilizing the exact same principles. Take the fraction
 1 2
for instance. To transform this fraction right into a decimal, first convert it right into the fractivity of
 5 10
. Knowing that the initially decimal location represents 10-1,
 5 10
deserve to be converted to 0.5. If the fraction were instead
 5 100
, the decimal would certainly then be 0.05, and also so on. Beyond this, converting fractions right into decimals calls for the operation of lengthy department.

### Usual Engineering Fraction to Decimal Conversions

In engineering, fractions are extensively offered to describe the size of components such as pipes and bolts. The many common fractional and decimal equivalents are noted below.

 64th 32nd 16th 8th 4th 2nd 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 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