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Fractions Calculator

Fractions Calculator
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Answer:
\[ \frac{3}{4} + \frac{2}{5} = 1 \frac{3}{20} \]
Solution with Steps
\[ \frac{3}{4} + \frac{2}{5} = \, ? \]The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(3/4, 2/5) = 20

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.\[ \left(\frac{3}{4} \times \frac{5}{5}\right) + \left(\frac{2}{5} \times \frac{4}{4}\right) = \, ? \]Complete the multiplication and the equation becomes\[ \frac{15}{20} + \frac{8}{20} = \, ? \]The two fractions now have like denominators so you can add the numerators.

Then:
\[ \frac{15 + 8}{20} = \frac{23}{20} \]This fraction cannot be reduced.

The fraction \[ \frac{23}{20} \]is the same as \[ 23 \div 20 \]Convert to a mixed number using
long division for 23 ÷ 20 = 1R3, so
\[ \frac{23}{20} = 1 \frac{3}{20} \]Therefore:\[ \frac{3}{4} + \frac{2}{5} = 1 \frac{3}{20} \]
Solution by Formulas
Apply the fractions formula for addition, to\[ \frac{3}{4} + \frac{2}{5} \]and solve\[ \frac{(3 \times 5) + (2 \times 4)}{4 \times 5} \]\[ = \frac{15 + 8}{20} \]\[ = \frac{23}{20} \]Convert to a mixed number using
long division for 23 ÷ 20 = 1R3, so
\[ \frac{23}{20} = 1 \frac{3}{20} \]Therefore:\[ \frac{3}{4} + \frac{2}{5} = 1 \frac{3}{20} \]

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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.

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:

  • 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:

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

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"; CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

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