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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Simplify Fractions slrfc.org

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Decimal to Fraction slrfc.org

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Fraction to Decimal 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.

Addition:

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
= ad + bc
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
= ad – bc
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
= ad
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.

64th32nd16th8th4th2ndDecimalDecimal(inch to mm)
1/640.0156250.396875
2/641/320.031250.79375
3/640.0468751.190625
4/642/321/160.06251.5875
5/640.0781251.984375
6/643/320.093752.38125
7/640.1093752.778125
8/644/322/161/80.1253.175
9/640.1406253.571875
10/645/320.156253.96875
11/640.1718754.365625
12/646/323/160.18754.7625
13/640.2031255.159375
14/647/320.218755.55625
15/640.2343755.953125
16/648/324/162/81/40.256.35
17/640.2656256.746875
18/649/320.281257.14375
19/640.2968757.540625
20/6410/325/160.31257.9375
21/640.3281258.334375
22/6411/320.343758.73125
23/640.3593759.128125
24/6412/326/163/80.3759.525
25/640.3906259.921875
26/6413/320.4062510.31875
27/640.42187510.715625
28/6414/327/160.437511.1125
29/640.45312511.509375
30/6415/320.4687511.90625
31/640.48437512.303125
32/6416/328/164/82/41/20.512.7
33/640.51562513.096875
34/6417/320.5312513.49375
35/640.54687513.890625
36/6418/329/160.562514.2875
37/640.57812514.684375
38/6419/320.5937515.08125
39/640.60937515.478125
40/6420/3210/165/80.62515.875
41/640.64062516.271875
42/6421/320.6562516.66875
43/640.67187517.065625
44/6422/3211/160.687517.4625
45/640.70312517.859375
46/6423/320.7187518.25625
47/640.73437518.653125
48/6424/3212/166/83/40.7519.05
49/640.76562519.446875
50/6425/320.7812519.84375
51/640.79687520.240625
52/6426/3213/160.812520.6375
53/640.82812521.034375
54/6427/320.8437521.43125
55/640.85937521.828125
56/6428/3214/167/80.87522.225
57/640.89062522.621875
58/6429/320.9062523.01875
59/640.92187523.415625
60/6430/3215/160.937523.8125
61/640.95312524.209375
62/6431/320.9687524.60625
63/640.98437525.003125
64/6432/3216/168/84/42/2125.4