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Fraction Calculator

Fraction Calculator

Enter the numerators and denominators in the fractions calculator and find the reduced form in seconds.

To Calculate Mixed Fractions

2 Fraction
3 Fraction
4 Fraction
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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 Definition:

“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.

Fraction Image:

Operations On Fractions:

Addition And Subtraction:

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

Multiplication:

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

Division:

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

Fraction Formulas:

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

Add Fractions:

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

Subtract Fractions:

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

Multiply Fractions:

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

Divide Fractions:

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

How To Reduce Fractions?

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:

Adding Fractions:

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

Formula:

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

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

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

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

Subtracting Fractions:

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

Formula:

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

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

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

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

Multiplying Fractions:

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

Formula:

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

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

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

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

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

Dividing Fractions:

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

Formula:

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

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

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

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

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

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

Fraction Table:

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

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

FAQ’s:

What Is A Proper, Improper, And Mixed Fraction?

  • 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.

Is A Fraction A Rational Number?

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.

Related Calculators:

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

References:

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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