Fraction Calculator

Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator. Enter appropriate values, ideally integers, into each field, select the desired operation, and click the "Calculate" button to calculate. The "Simplify Fractions Calculator" accepts mixed number inputs, and the "Decimal to Fraction Calculator" receives decimal inputs. Further details about each operation and calculator are provided at the bottom of the page.

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Simplify Fractions Calculator

Result

2
13
2
=
17
2
= 8
1
2
= ?

Decimal to Fraction Calculator

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Fraction to Decimal Calculator

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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
3
5
, the numerator is 3, and the denominator is 5. A 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 whole pie would be the denominator. If a person were to eat 3 slices, the remaining fraction of the pie would therefore be
5
8
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 can undergo many different operations, some of which are mentioned below.

Addition:

Unlike adding and subtracting integers such as 2 and 8, fractions require a common denominator to undergo these operations. The equations provided below account for this by multiplying the numerators and denominators of all of the fractions involved in the addition by the denominators of each fraction (excluding multiplying itself by its own denominator). Multiplying all of the denominators ensures that the new denominator is certain to be a multiple of each individual denominator. Multiplying the numerator of each fraction by the same factors is necessary, since fractions are ratios of values and a changed denominator requires that the numerator be changed by the same factor in order for the value of the fraction to remain the same. This is arguably the simplest way to ensure that the fractions have a common denominator. Note that in most cases, the solutions to these equations will not appear in simplified form (though the provided calculator computes the simplification automatically). An alternative to using this equation in cases where the fractions are uncomplicated would be to find a least common multiple and then add or subtract the numerators as one would an integer. Depending on the complexity of the fractions, finding the least common multiple for the denominator can be more efficient than using the equations. Refer to the equations below for clarification.

a
b
+
c
d
= (
a
b
×
d
d
) + (
c
d
×
b
b
) =
ad + bc
bd
EX:
3
4
+
1
6
=
18
24
+
4
24
=
22
24
=
11
12

Subtraction:

Fraction subtraction is essentially the same as fraction addition. A common denominator is required for the operation to occur. Refer to the addition section as well as the equations below for clarification.

a
b
c
d
= (
a
b
×
d
d
) – (
c
d
×
b
b
) =
ad – bc
bd
EX:
3
4
1
6
=
18
24
4
24
=
14
24
=
7
12

Multiplication:

Multiplying fractions is fairly straightforward. Unlike adding 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 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 process for dividing fractions is similar to that for multiplying fractions. In order 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 simply
1
a
. When a is a fraction, this essentially involves exchanging the position of the numerator and the denominator. The reciprocal of the fraction
3
4
would therefore be
4
3
. Refer to the equations 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 often easier to work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms.
220
440
for example, is more cumbersome than
1
2
. The calculator provided returns fraction inputs in both improper fraction form, as well as mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator by their greatest common factor.

Converting between fractions and decimals:

Converting from decimals to fractions is straightforward. It does however require the understanding that each decimal place to the right of the decimal point represents a power of 10; the first decimal place being 101, the second 102, the third 103, and so on. Simply determine what power of 10 the decimal extends to, use that power of 10 as the denominator, enter each number to the right of the decimal point as the numerator, and simplify. For example, looking at the number 0.1234, the number 4 is in the fourth decimal place which constitutes 104, or 10,000. This would make the fraction
1234
10000
, which simplifies to
617
5000
, since the greatest common factor between 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
1
2
for example. To convert this fraction into a decimal, first convert it into the fraction
5
10
. Knowing that the first decimal place represents 101,
5
10
can be converted to 0.5. If the fraction were instead
5
100
, the decimal would then be 0.05, and so on. Beyond this, converting fractions into decimals requires the operation of long division.

Common Engineering Fraction to Decimal Conversions

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

64th32nd16th8th4th2ndDecimalDecimal
(inch to mm)
1/64     0.0156250.396875
2/641/32    0.031250.79375
3/64     0.0468751.190625
4/642/321/16   0.06251.5875
5/64     0.0781251.984375
6/643/32    0.093752.38125
7/64     0.1093752.778125
8/644/322/161/8  0.1253.175
9/64     0.1406253.571875
10/645/32    0.156253.96875
11/64     0.1718754.365625
12/646/323/16   0.18754.7625
13/64     0.2031255.159375
14/647/32    0.218755.55625
15/64     0.2343755.953125
16/648/324/162/81/4 0.256.35
17/64     0.2656256.746875
18/649/32    0.281257.14375
19/64     0.2968757.540625
20/6410/325/16   0.31257.9375
21/64     0.3281258.334375
22/6411/32    0.343758.73125
23/64     0.3593759.128125
24/6412/326/163/8  0.3759.525
25/64     0.3906259.921875
26/6413/32    0.4062510.31875
27/64     0.42187510.715625
28/6414/327/16   0.437511.1125
29/64     0.45312511.509375
30/6415/32    0.4687511.90625
31/64     0.48437512.303125
32/6416/328/164/82/41/20.512.7
33/64     0.51562513.096875
34/6417/32    0.5312513.49375
35/64     0.54687513.890625
36/6418/329/16   0.562514.2875
37/64     0.57812514.684375
38/6419/32    0.5937515.08125
39/64     0.60937515.478125
40/6420/3210/165/8  0.62515.875
41/64     0.64062516.271875
42/6421/32    0.6562516.66875
43/64     0.67187517.065625
44/6422/3211/16   0.687517.4625
45/64     0.70312517.859375
46/6423/32    0.7187518.25625
47/64     0.73437518.653125
48/6424/3212/166/83/4 0.7519.05
49/64     0.76562519.446875
50/6425/32    0.7812519.84375
51/64     0.79687520.240625
52/6426/3213/16   0.812520.6375
53/64     0.82812521.034375
54/6427/32    0.8437521.43125
55/64     0.85937521.828125
56/6428/3214/167/8  0.87522.225
57/64     0.89062522.621875
58/6429/32    0.9062523.01875
59/64     0.92187523.415625
60/6430/3215/16   0.937523.8125
61/64     0.95312524.209375
62/6431/32    0.9687524.60625
63/64     0.98437525.003125
64/6432/3216/168/84/42/2125.4