# Fraction Calculator

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## Table of Content

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With our online fraction calculator, simplify addition, subtraction, multiplication, and division of fractional terms and also carry out other operations with ease. This reduce fractions calculator can also handle any type of fraction including mixed, improper, and complex fractions.

## Arithmetic Operations of Fraction:

The Fraction Calculator will reduce fractional terms to its simplest form. You can also add, subtract, multiply, and divide fractions, as well as, convert to a decimal and work with mixed numbers and reciprocals. We also offer step by step solutions.

### How to Add or Subtract The Fractions?

Here is a more general rule to understand how to add and subtract fractions:

• Find the least common multiple of the denominators.
• Rewrite each fraction with the least common multiple as the denominator.
• For subtraction equations, subtract the fraction numerators

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

#### Fraction Subtraction Formula:

$$\dfrac{a}{b} - \dfrac{c}{d} = \dfrac{ad - bc}{bd}$$

$$= \dfrac{3}{2}+\dfrac{1}{3} = \dfrac{11}{6}$$

$$= \dfrac{3}{4}+\dfrac{2}{5} = \dfrac{23}{20}$$

$$= \dfrac{5}{6}+\dfrac{7}{8} = \dfrac{82}{48}$$

#### Fraction Subtraction Example:

$$= \dfrac{3}{2}-\dfrac{1}{3} = \dfrac{4}{6}$$

$$= \dfrac{3}{4}-\dfrac{2}{5} = \dfrac{7}{20}$$

$$= \dfrac{5}{6}-\dfrac{7}{8} = \dfrac{-2}{48}$$

To add fractions it is necessary to have the same denominators and if there is a difference in denominators then find out common denominators. This is the LCM of two denominators.

Once you have a common denominator, simply add the numerators and keep the denominator the same.

### How to Multiply Fractions?

To understand the basic rules of fractional multiplication, easily solve a variety of math problems. The basic factors are as follows:

• For multiplying fractions, multiply the numerators together and the denominators together.
• After that simplify the results by canceling out the common factors

Use a fraction calculator to get the multiplication and division of fractional values because it has the ability to turn a number of fractions into their lowest decimal and mixed number fractions.

#### Fraction Multiplication Formula:

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

#### Multiplication Example:

$$= \dfrac{2}{3} \times \dfrac{2}{5} = \dfrac {4}{15}$$

$$= \dfrac{1}{6} \times \dfrac{5}{4} = \dfrac {5}{24}$$

$$= \dfrac{4}{6} \times \dfrac{5}{7} = \dfrac {10}{21}$$

### How to Divide Fractions:

Our fraction calculator can perform arithmetic operations on fractions. Their division rules are as follows:

• Invert the divisor same to divide by a/b, and it becomes b/a
• Instead of dividing fractions, change the division operation to multiplication.
• Multiply the numerators of the fractions to get the new numerator
• Multiply the denominators to get the new denominator

Dividing fractions is the same as multiplying the first fractions by the reciprocal of the second fraction. The fractional division is made easy by taking into service the below formula:

#### Fraction Division Formula:

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

#### Division Example:

$$= \dfrac{2}{3} \div \dfrac{3}{4} = \dfrac {8}{9}$$

$$= \dfrac{4}{7} \div \dfrac{5}{4} = \dfrac {16}{35}$$

$$= \dfrac{6}{7} \div \dfrac{5}{3} = \dfrac {18}{35}$$

## Important Fraction Symbols:

Symbol Symbol name Symbol Meaning
- minus sign subtraction
* asterisk multiplication
× times sign multiplication
: division sign division
/ division slash division
: colon complex fraction
^ caret exponentiation / power
() parentheses calculate expression inside first

## Fraction Table:

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

## Honors:

Wikipedia: Fraction, Forms of fractions, Arithmetic with fractions, Fractions in abstract mathematics.

Wikihow: How to Do Fractions. ### Alan Walker

Studies mathematics sciences, and Technology. Tech geek and a content writer. Wikipedia addict who wants to know everything. Loves traveling, nature, reading. Math and Technology have done their part, and now it's the time for us to get benefits.