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Fractions Calculator

Calculator Utilize

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

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

If yous have negative fractions insert a minus sign before the numerator. Then if 1 of your fractions is -half dozen/7, insert -six in the numerator and 7 in the denominator.

Sometimes math problems include the discussion "of," as in What is 1/3 of 3/viii? Of ways you should multiply then you lot demand to solve i/iii × 3/viii.

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

Math on Fractions with Dissimilar Denominators

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

if yous are adding fractions
if y'all are subtracting fractions

How to Add together or Subtract Fractions

Find the least common denominator
You can apply the LCD Computer to observe the least common denominator for a set of fractions
For your commencement fraction, discover what number you demand to multiply the denominator past to result in the least common denominator
Multiply the numerator and denominator of your first fraction past that number
Repeat Steps 3 and 4 for each fraction
For addition equations, add the fraction numerators
For subtraction equations, subtract the fraction numerators
Convert improper fractions to mixed numbers
Reduce the fraction to lowest terms

How to Multiply Fractions

Multiply all numerators together
Multiply all denominators together
Reduce the effect to lowest terms

How to Divide Fractions

Rewrite the equation as in "Keep, Change, Flip"
Keep the first fraction
Change the partition sign to multiplication
Flip the second fraction by switching the top and bottom numbers
Multiply all numerators together
Multiply all denominators together
Reduce the effect to lowest terms

Fraction Formulas

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

You may discover 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 every bit described to a higher place.

Adding Fractions

The formula for adding fractions is:

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

Example steps:

\( \dfrac{2}{6} + \dfrac{ane}{iv} = \dfrac{(2\times4) + (6\times1)}{6\times4} \)

\( = \dfrac{14}{24} = \dfrac {7}{12} \)

Subtracting Fractions

The formula for subtracting fractions is:

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

Instance steps:

\( \dfrac{ii}{6} - \dfrac{one}{4} = \dfrac{(ii\times4) - (half-dozen\times1)}{half dozen\times4} \)

\( = \dfrac{two}{24} = \dfrac {ane}{12} \)

Multiplying Fractions

The formula for multiplying fractions is:

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

Example steps:

\( \dfrac{ii}{6} \times \dfrac{1}{iv} = \dfrac{2\times1}{6\times4} \)

\( = \dfrac{2}{24} = \dfrac {1}{12} \)

Dividing Fractions

The formula for dividing fractions is:

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

Example steps:

\( \dfrac{2}{half-dozen} \div \dfrac{1}{iv} = \dfrac{2\times4}{vi\times1} \)

\( = \dfrac{8}{6} = \dfrac {four}{three} = 1 \dfrac{i}{3} \)

Related Calculators

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

If you want to simplify an individual fraction into everyman terms use our Simplify Fractions Estimator.

For an explanation of how to factor numbers to find the greatest common gene (GCF) come across the Greatest Mutual Factor Reckoner.

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