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# Fraction Calculator

Enter the values and let this calculator will solve your fraction problem.

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## Fraction Calculator

This fraction calculator helps to add, subtract, multiply, and divide fractions and reduces them to the most simplified form. It not only calculates results but also displays step-wise solutions and conversion to decimal notation with respective visual representation.

Our calculator involves few simple steps to make calculations:

• Select the number of fractions
• Enter numerators and denominators in the respective fields
• Select the arithmetic operator
• Click ‘Calculate’ & get the results

If the simplified form is an improper fraction, the calculator will automatically convert it to a mixed number.

## How to Solve Fractions?

Solving fractions involves applying arithmetic operations and reducing to the simplest possible notation, such that:

1. Calculate LCD for all fraction denominators
2. Considering 1st fraction, determine the number that will result in LCD when multiplied by its denominator
3. Multiply that number with the numerator of 1st fraction and write over the LCD
4. Repeat this step one by one for all fractions, starting from left to right
6. Simplify using GCD, if possible

Formula:

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

Example:

$$\dfrac{3}{5}+\dfrac{6}{4}$$ $$=\dfrac{\left(4×3\right)+\left(6×5\right)}{20}$$ $$=\dfrac{12+30}{20}$$ $$=\dfrac{42}{20}$$

Dividing the numerator and the denominator by GCD ‘2

$$=\dfrac{\dfrac{42}{2}}{\dfrac{20}{2}}$$ $$=\dfrac{21}{10}$$

This is an improper fraction so we can convert it to a mixed number:

$$=\dfrac{21}{10} = 2\dfrac{1}{10}$$

To calculate decimal conversion and visualize your fraction addition, input the numerators and denominators in this adding fractions calculator and get instant results.

### Fraction Subtraction:

Subtracting fractions is almost similar to addition. Steps include:

1. Repeat steps 1 to 4 mentioned for fraction addition
2. Subtract all numerators
3. Simplify the new fraction to a simplified form

Formula:

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

Example:

$$\dfrac{2}{8}-\dfrac{4}{9}$$ $$=\dfrac{\left(9×2\right)-\left(8×4\right)}{72}$$ $$=\dfrac{18-32}{72}$$ $$=\dfrac{-14}{72}$$

Dividing the numerator and the denominator by GCD ‘2

$$=\dfrac{\dfrac{-14}{2}}{\dfrac{72}{2}}$$ $$=\dfrac{-7}{36}$$

### Fraction Multiplication:

1. Multiply all numerators
2. In the same way, multiply all denominators
3. Write the new fraction with the product of numerators above the line and the product of denominators below the line
4. Use GCD to simplify to the reduced form, if possible

Formula:

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

Example:

$$\dfrac{2}{4}×\dfrac{5}{8}$$ $$=\dfrac{2×5}{4×8}$$ $$=\dfrac{2×5}{4×8}$$ $$=\dfrac{10}{32}$$

Dividing the numerator and the denominator by GCD, which is ‘2’ here

$$=\dfrac{\dfrac{10}{2}}{\dfrac{32}{2}}$$ $$=\dfrac{5}{16}$$

### Fraction Division:

To divide fractions:

2. Find the reciprocal of the second fraction by flipping its numerator and the denominator
3. Multiply the first fraction with this reciprocal

Formula:

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

Example:

$$\dfrac{6}{4}÷\dfrac{5}{3}$$ $$=\dfrac{6}{4}×\dfrac{3}{5}$$ $$=\dfrac{6×3}{4×5}$$ $$=\dfrac{18}{20}$$

Simplifying to lowest form:

$$=\dfrac{9}{10}$$

When using a fraction calculator or doing it manually, please make sure that the values are noted correctly for the correct solution.

## 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

## Limitations:

• Fractions with very large numerators or denominators might be difficult to add, so the calculator does not support such bigger inputs
• The calculator does not function if any input field is left blank
• Entering ‘0’ in the denominator will make your fractions infinite, thus making the tool unable to calculate results