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**Table of Content**

This fraction calculator reduces fractions (or mixed numbers) to their lowest possible form. The calculator performs necessary arithmetic operations on the fractions provided and gives you a step-wise solution to understand the calculations better.

To get results by fraction calculator, select the number of fractions, enter numerators and denominators, select the operator, and click ‘Calculate’. The tool will reduce the set of fractions by the division method, accompanied by their greatest common factor (GCF).

For negative fractions, add the sign of subtraction before the numerator or denominator. For instance, if the fraction is \(\dfrac{-7}{9}\) then insert the minus(“-”) sign in the numerator or denominator field of the fractions calculator.

**“Fraction represents the part of a whole thing”**

It contains two parts one is the numerator which is above the line and the other is denominator that is below the line.

The part above the line shows how many equal parts are taken and the denominator indicates the total parts in which a thing is divided.

In case of fraction addition and subtraction, you must keep in mind that if your fractions have like or unlike denominators.

- First of all, get the LCD (least common denominator) for all the fractions with the help of a calculator
- Now divide the denominator of the first fraction by the LCD. After this, multiply the resulting quotient with the numerator of first fraction and write it over LCD
- Do exactly the same for all other fractions in the combination
- For addition, add all the numerators and divide the number by LCD
- For subtraction, subtract all the numerators and divide the number by least common denominator
- Turn the improper fractions into mixed numbers
- Now simplify the fraction till its lowest terms

- Multiply all the numerators
- Likewise, multiply all the denominators
- At last, go for simplifying the result of fraction multiplication to the most reduced form

When it comes to the division of fractions, fraction solver follows the rule as under:

**Keep:**you have to keep the first fraction as it is**Change:**now go for inverting the division sign to the multiplication sign**Flip:**after that, flip the next fractions by replacing numerator and denominator positions

Our fraction calculator considers the following arithmetical formulas to reduce fractions to their simplest part of the whole:

\(\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + bc}{bd}\)

\(\dfrac{a}{b} – \dfrac{c}{d} = \dfrac{ad – bc}{bd}\)

\(\dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{ac}{bd}\)

\(\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{ad}{bc}\)

The best way to do it is using the fraction calculator that finds LCM and then cross multiply all terms to find accurate lowest fraction form. However, there is another easy way to add or subtract the fractions without taking the least common denominator. For this, find the least common multiple of the denominators and perform the cross multiplication as we have done below:

\(\text{Add} \ \dfrac{1}{2}\hspace{0.025in}and\hspace{0.025in}\dfrac{2}{5}\)

**Formula:**

\(\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + bc}{bd}\)

\(= \dfrac{1}{2}+\dfrac{2}{5}\)

\(=\dfrac{5+4}{10}\)

\(=\dfrac{9}{10}\)

\(\text{Subtract} \dfrac{3}{5}\hspace{0.025in}and\hspace{0.025in}\dfrac{2}{9}\)

**Formula:**

\(\dfrac{a}{b} – \dfrac{c}{d} = \dfrac{ad – bc}{bd}\)

\(= \dfrac{3}{5}-\dfrac{2}{9}\)

\(=\dfrac{27-10}{45}\)

\(=\dfrac{17}{45}\)

\(\text{Multiply} \dfrac{4}{6}\hspace{0.025in}and\hspace{0.025in}\dfrac{1}{4}\)

**Formula:**

\(\dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{ac}{bd}\)

\(=\dfrac{4}{6} \times \dfrac{1}{4}\)

\(=\dfrac{4 \times 1}{6 \times4}\)

\(=\dfrac{4}{24}\)

\(=\dfrac{1}{6}\)

\(\text{Divide} \dfrac{5}{4}\hspace{0.025in}and\hspace{0.025in}\dfrac{2}{3}\)

**Formula:**

\(\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{ad}{bc}\)

\(=\dfrac{5}{4} \div \dfrac{2}{3}\)

\(=\dfrac{5}{4} \times \dfrac{2}{3}\)

\(=\dfrac{5 \times 2}{4 \times3}\)

\(=\dfrac{10}{12}\)

\(=\dfrac{5}{6}\)

The following table contains fractions and decimal values that are widely used by engineers, astronomers, constructors, and mathematicians to simplify calculations:

64^{th} |
32^{nd} |
16^{th} |
8^{th} |
4^{th} |
2^{nd} |
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 |

**Proper fractions:**A fraction is called a proper fraction if the numerator is smaller than the denominator.**Improper fractions:**If the denominator is greater than the numerator then it is known as the improper fraction.**Mixed fractions:**When the whole numbers and the proper fraction are put together, then it becomes a mixed fraction. They are also called mixed numbers.

This fraction calculator is intended to solve all of these fractions, helping you to learn fraction simplification easily and in less time.

Yes, all fractions are rational numbers but every rational number can not be a fraction. If the numerator and denominators are whole numbers, then the rational number is a fraction.

If you want to perform mixed number fractions then use mixed numbers calculator.

From the source of Wikipedia, the free encyclopedia: Forms of fractions

From the source of Wikihow: How to Do Fractions – a complete guide to understanding fractions

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