# Fraction Calculator

A simple, but powerful, calculator to solve multiple types of fraction math problems.

 + - × ÷ of ^ + - × ÷

This Fraction calculator simplify fractions of addition, subtraction, multiplication, and division. Perform simplifying fractions effortlessly by entering the numerator and denominator.

Whether you have fractions or mixed numbers, The fraction calculator will reduce them to the most simplified form within seconds.

## Formula Used By Fraction Calculator:

The mixed number calculator displays a fraction addition, subtraction, multiplication, and division. This utilizes the below formulas by taking the hassle out of fractions and gives you accurate results.

• Identify the common denominators
• Find the least common multiple (LCM) or least common denominator (LCD)
• If the denominators are not the same, multiply each fraction by a factor that makes its common denominator equal to the LCM
• Add the numerators and convert the given improper fractions to the mixed.

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

Example:

How to add fractions 4/3 & 2/3?

Solution:

4/3 + 2/3
= (4+2)/3 (LCD is 3)
= 6/3
= 2

## How to Subtract Fractions?

• Identify the common denominators
• Find the least common multiple or the least common denominator
• If the denominators are not the same, multiply each fraction by a factor that makes its denominator equal to the LCM
• Subtract the numerators and simplify fractions to the lowest terms

### Formula for Fractions Subtraction:

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

Example:

How to subtract fractions 2/7 & 8/3?

Solution:

2/7 - 8/3
= 2(3) - 7(8) / 21 (LCD is 21)
= (6-56) / 21
= -50 / 21

## How to Multiply Fractions?

• Multiply numerators of all fractions
• Likewise, go by multiplying denominators as well
• Write the results as a single fraction
• Simplify to reduce the fraction to lowest terms

### Formula for Fractions Multiplication:

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

Example:

How to multiply the numbers 1/7 & 8/9?

Solution:

1/7 & 8/9
= (1*8)/(7*9)
= 8/63

## How to Divide Fractions?

• Find the reciprocal and rewrite the Division as Multiplication
• Flip the second fractions by switching the top and bottom numbers
• Multiply Numerators and Denominators
• Simplify the results to the lowest form

### Formula for Fractions Division:

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

Example:

How to divide fractions 7/3 ÷ 7/2?

Solution:

Here we have:

7/3 ÷ 7/2

The reciprocal of the divisor (7/2) is 2/7. So we have;

7/3 x 2/7
= (7*2)/(3*7)
= 14/21
= 2/3

## Common Fractions to Decimals:

Our fraction calculator helps you to simplify and reduce fractions to the lowest form. It performs fraction operations, and expressions with integers, decimals, and mixed numbers.

The following table is packed with fractions values that you may encounter on a daily basis and may help you simplify fractions value in seconds:

64th 32nd 16th 8th 4th 2nd Decimal
1/64           0.015625
2/64 1/32         0.03125
3/64           0.046875
4/64 2/32 1/16       0.0625
5/64           0.078125
6/64 3/32         0.09375
7/64           0.109375
8/64 4/32 2/16 1/8     0.125
9/64           0.140625
10/64 5/32         0.15625
11/64           0.171875
12/64 6/32 3/16       0.1875
13/64           0.203125
14/64 7/32         0.21875
15/64           0.234375
16/64 8/32 4/16 2/8 1/4   0.25
17/64           0.265625
18/64 9/32         0.28125
19/64           0.296875
20/64 10/32 5/16       0.3125
21/64           0.328125
22/64 11/32         0.34375
23/64           0.359375
24/64 12/32 6/16 3/8     0.375
25/64           0.390625
26/64 13/32         0.40625
27/64           0.421875
28/64 14/32 7/16       0.4375
29/64           0.453125
30/64 15/32         0.46875
31/64           0.484375
32/64 16/32 8/16 4/8 2/4 1/2 0.5
33/64           0.515625
34/64 17/32         0.53125
35/64           0.546875
36/64 18/32 9/16       0.5625
37/64           0.578125
38/64 19/32         0.59375
39/64           0.609375
40/64 20/32 10/16 5/8     0.625
41/64           0.640625
42/64 21/32         0.65625
43/64           0.671875
44/64 22/32 11/16       0.6875
45/64           0.703125
46/64 23/32         0.71875
47/64           0.734375
48/64 24/32 12/16 6/8 3/4   0.75
49/64           0.765625
50/64 25/32         0.78125
51/64           0.796875
52/64 26/32 13/16       0.8125
53/64           0.828125
54/64 27/32         0.84375
55/64           0.859375
56/64 28/32 14/16 7/8     0.875
57/64           0.890625
58/64 29/32         0.90625
59/64           0.921875
60/64 30/32 15/16       0.9375
61/64           0.953125
62/64 31/32         0.96875
63/64           0.984375
64/64 32/32 16/16 8/8 4/4 2/2 1

## References:

Wikipedia: Fractions, Reciprocals and the "invisible denominator", Ratios, Decimal fractions and percentages, Historical notions, Arithmetic with fractions.