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Calculator Use

Use this fraction calculator for adding, subtracting, multiplying and dividing fractions. Answers are fractions in lowest terms or mixed numbers in reduced form.

Input proper or improper fractions, select the math sign and click Calculate. This is a fraction calculator with steps shown in the solution.

If you have negative fractions insert a minus sign before the numerator. So if one of your fractions is -6/7, insert -6 in the numerator and 7 in the denominator.

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Sometimes math problems include the word 'of,' as in What is 1/3 of 3/8? Of means you should multiply so you need to solve 1/3 × 3/8.

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

Math on Fractions with Unlike Denominators

There are 2 cases where you need to know if your fractions have different denominators:

Feed me Fractions! A's other lessons. Westland High School—Blended Learning Tutorial 103. Learning + Fun 35. Multiplication Madness 203. Kieran's Math Page! 44 Description: N/A. Comments are disabled. Click here to re-enable them. Math Help for Fractions: Easy-to-understand lessons for kids, parents and teachers. Practice what you learn with games and quizzes.

  1. This calculator converts inch and fractions of an inch to decimal format. Example: 3 3/8' # of Inches = 3 Numerator of fraction = 3 Denominator of fraction = 8 3 3/8' in decimal format = 3.375 There is no conversion needed for the Foot value To covert inch to decimal = inch/12 To convert a fraction = numerator/denominator.
  2. Fractions Pictures for Classroom and Therapy Use: Try It Now: No Need to Register! Drag Pictures to Your Tray and click 'Create Materials'.
  3. Equivalent Fractions BINGO is a fun educational game for children to practice equivalent fractions. The game has two modes: Easy & Challenge. Easy mode of play displays a pie graphic to represent the fraction. The denominator is represented by the total number of slices and the numerator is represented by the colored slices.
  • if you are adding fractions
  • if you are subtracting fractions

How to Add or Subtract Fractions

  1. Find the least common denominator
  2. You can use the LCD Calculator to find the least common denominator for a set of fractions
  3. For your first fraction, find what number you need to multiply the denominator by to result in the least common denominator
  4. Multiply the numerator and denominator of your first fraction by that number
  5. Repeat Steps 3 and 4 for each fraction
  6. For addition equations, add the fraction numerators
  7. For subtraction equations, subtract the fraction numerators
  8. Convert improper fractions to mixed numbers
  9. Reduce the fraction to lowest terms

How to Multiply Fractions

  1. Multiply all numerators together
  2. Multiply all denominators together
  3. Reduce the result to lowest terms

How to Divide Fractions

  1. Rewrite the equation as in 'Keep, Change, Flip'
  2. Keep the first fraction
  3. Change the division sign to multiplication
  4. Flip the second fraction by switching the top and bottom numbers
  5. Multiply all numerators together
  6. Multiply all denominators together
  7. Reduce the result to lowest terms

Fraction Formulas

There is a way to add or subtract fractions without finding the least common denominator (LCD). This method involves cross multiplication of the fractions. See the formulas below.

You may find that it is easier to use these formulas than to do the math to find the least common denominator.

The formulas for multiplying and dividing fractions follow the same process as described above.

Adding Fractions

The formula for adding fractions is:

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

Example steps:

( dfrac{2}{6} + dfrac{1}{4} = dfrac{(2times4) + (6times1)}{6times4} )

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{(2times4) - (6times1)}{6times4} )

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{2times1}{6times4} )

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{2times4}{6times1} )
( = 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.

FractionsFeed

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.

How many equal parts of a whole

Slice a pizza, and we get fractions:

1/21/43/8
(One-Quarter)

The top number says how many slices we have.
The bottom number says how many equal slices the whole pizza was cut into.

Have a try yourself:

Equivalent Fractions

Some fractions may look different, but are really the same, for example:

4/8=2/4=1/2
(Four-Eighths)(Two-Quarters)(One-Half)
==
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It is usually best to show an answer using the simplest fraction ( 1/2 in this case ). That is called Simplifying, or Reducing the Fraction

Numerator / Denominator

We call the top number the Numerator, it is the number of parts we have.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.

NumeratorDenominator

You just have to remember those names! (If you forget just think 'Down'-ominator)

Adding Fractions

It is easy to add fractions with the same denominator (same bottom number):

1/4+1/4=2/4=1/2
(One-Quarter)(One-Quarter)(Two-Quarters)(One-Half)
+==
One-quarter plus one-quarter equals two-quarters, equals one-half

Another example:

5/8+1/8=6/8=3/4
+==
Five-eighths plus one-eighth equals six-eighths, equals three-quarters

Adding Fractions with Different Denominators

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But what about when the denominators (the bottom numbers) are not the same?

3/8+1/4=?
+=
Three-eighths plus one-quarter equals ... what?

We must somehow make the denominators the same.

In this case it is easy, because we know that 1/4 is the same as 2/8 :

3/8+2/8=5/8
+=

Abcya Feed Me Fractions

Three-eighths plus two-eighths equals five-eighths

There are two popular methods to make the denominators the same:

  • Least Common Denominator, or

(They both work nicely, use the one you prefer.)

Other Things We Can Do With Fractions

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We can also:

Visit the Fractions Index to find out even more.