# Fraction calculator

Below are multiple fraction bulongvietlong.coms capable of addition, subtraction, multiplication, division, simplification, & conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator.

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## Mixed Numbers bulongvietlong.com

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## Simplify Fractions bulongvietlong.com

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## Decimal to Fraction bulongvietlong.com

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## Fraction to lớn Decimal bulongvietlong.com

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## Big Number Fraction bulongvietlong.com

Use this bulongvietlong.com 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 ảo diệu said whole. For example, in the fraction of

3 |

8 |

5 |

8 |

### Addition:

Unlike adding and subtracting integers such as 2 and 8, fractions require a common denominator khổng lồ undergo these operations. One method for finding a common denominator involves multiplying the numerators & 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 need to lớn be multiplied by the appropriate factors to lớn preserve the value of the fraction as a whole. This is arguably the simplest way lớn ensure that the fractions have a common denominator. However, in most cases, the solutions lớn these equations will not appear in simplified form (the provided bulongvietlong.com computes the simplification automatically). Below is an example using this method.

a |

b |

d |

b×d |

d×b |

bd |

EX: | 3 |

4 |

6 |

4×6 |

6×4 |

24 |

12 |

This process can be used for any number of fractions. Just multiply the numerators & denominators of each fraction in the problem by the product of the denominators of all the other fractions (not including its own respective denominator) in the problem.

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EX: | 1 |

4 |

6 |

2 |

4×6×2 |

6×4×2 |

2×4×6 |

48 |

48 |

48 |

48 |

12 |

An alternative method for finding a common denominator is to lớn determine the least common multiple (LCM) for the denominators, then địa chỉ cửa hàng or subtract the numerators as one would an integer. Using the least common multiple can be more efficient & is more likely to lớn result in a fraction in simplified form. In the example above, the denominators were 4, 6, và 2. The least common multiple is the first shared 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 giới thiệu is 12, so this is the least common multiple. Lớn complete an addition (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by whatever value will make the denominators 12, then showroom the numerators.

EX: | 1 |

4 |

6 |

2 |

4×3 |

6×2 |

2×6 |

12 |

12 |

12 |

12 |

### Subtraction:

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

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a |

b |

d |

b×d |

d×b |

bd |

EX: | 3 |

4 |

6 |

4×6 |

6×4 |

24 |

12 |

### Multiplication:

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is not necessary to lớn compute a common denominator in order khổng lồ multiply fractions. Simply, the numerators và denominators of each fraction are multiplied, và the result forms a new numerator and denominator. If possible, the solution should be simplified. Refer to lớn the equations below for clarification.

a |

b |

d |

bd |

EX: | 3 |

4 |

6 |

24 |

8 |

### Division:

The process for dividing fractions is similar lớn that for multiplying fractions. In order lớn 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 |

3 |

4 |

4 |

3 |

a |

b |

d |

b |

c |

bc |

EX: | 3 |

4 |

6 |

4 |

1 |

4 |

2 |

### Simplification:

It is often easier khổng lồ work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms.

220 |

440 |

1 |

2 |

### Converting between fractions & decimals:

Converting from decimals to lớn fractions is straightforward. It does, however, require the understanding that each decimal place khổng lồ the right of the decimal point represents a nguồn 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 nguồn of 10 as the denominator, enter each number to lớn the right of the decimal point as the numerator, & 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 |

617 |

5000 |

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

1 |

2 |

5 |

10 |

5 |

10 |

5 |

100 |

### Common Engineering Fraction to lớn Decimal Conversions

In engineering, fractions are widely used khổng lồ describe the kích cỡ of components such as pipes and bolts. The most common fractional và decimal equivalents are listed below.

64th | 32nd | 16th | 8th | 4th | 2nd | Decimal | Decimal(inch khổng lồ 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 |