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Fractions Calculator

Fractions Calculator
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Calculator Use

Use this calculator for adding, subtracting, multiplying and dividing fractions. Answers are provided as simplified fractions in lowest terms, or as mixed numbers in reduced form. Input your fractions, select the math operation and click Calculate.

You can also add, subtract, multiply or divide negative fractions. Insert a negative (minus) sign before the numerator (top number) for each fraction that is negative. For example if one of your fractions is -16/20 just insert a "-" before the "16" and proceed to enter all other numerators and denominators. Choose the math function and click Calculate.

To calculate with mixed numbers (whole numbers and fractions) use the Mixed Numbers Calculator.

Fraction Equations

Adding Fractions

The algebraic formula for adding fractions is:

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

Example steps:

\( \dfrac{2}{6} + \dfrac{1}{4} = \dfrac{(2\times4) + (6\times1)}{6\times4} \)
\( = \dfrac{14}{24} = \dfrac {7}{12} \)

Subtracting Fractions

The formula for subtracting fractions is:

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

Example steps:

\( \dfrac{2}{6} - \dfrac{1}{4} = \dfrac{(2\times4) - (6\times1)}{6\times4} \)
\( = \dfrac{2}{24} = \dfrac {1}{12} \)

Multiplying Fractions

The formula for multiplying fractions is:

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

Example steps:

\( \dfrac{2}{6} \times \dfrac{1}{4} = \dfrac{2\times1}{6\times4} \)
\( = \dfrac{2}{24} = \dfrac {1}{12} \)

Dividing Fractions

The formula for dividing fractions is:

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

Example steps:

\( \dfrac{2}{6} \div \dfrac{1}{4} = \dfrac{2\times4}{6\times1} \)
\( = \dfrac{8}{6} = \dfrac {4}{3} = 1 \dfrac{1}{3} \)

Related Calculators

To perform math operations on mixed number fractions use our Mixed Numbers Calculator. This calculator can also simplify improper fractions into mixed numbers and shows the work involved.

If you want to simplify an individual fraction into lowest terms use our Simplify Fractions Calculator.

For an explanation of how to factor numbers to find the greatest common factor (GCF) see the Greatest Common Factor Calculator.

If you are simplifying large fractions by hand you can use the Long Division with Remainders Calculator to find whole number and remainder values.

Notes

This calculator performs the reducing calculation faster than other calculators you might find. The primary reason is that it utilizes Euclid's Algorithm for reducing fractions which can be found on The Math Forum.



 

Cite this content, page or calculator as:

Furey, Edward "Fractions Calculator"; from http://www.calculatorsoup.com - Online Calculator Resource.

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