Fraction Calculator (Add, Subtract, Multiply, Divide, and More) – See Steps
Fraction Calculator
Add, subtract, multiply, divide, simplify, compare, convert fractions, and solve many other fraction problems.
Step By Step Solution
Follow each part of the calculation below.
How to Use the Fraction Calculator
This calculator is designed for much more than simple fraction addition. You can work with proper fractions, improper fractions, mixed numbers, negative fractions, decimals and percentages. Choose the type of calculation from the menu, enter the values in the boxes and press Solve Fraction.
A proper fraction has a numerator that is smaller than its denominator, such as \( \frac{3}{5} \). An improper fraction has a numerator that is equal to or larger than its denominator, such as \( \frac{11}{4} \). You can also type a mixed number with a space between the whole number and the fraction, such as \( 2\frac{1}{3} \), by entering 2 1/3.
Add Fractions
Use the Add Fractions option when you want to combine two fractional amounts. If the fractions already have the same denominator, only the numerators need to be added.
For example,
\[ \frac{3}{7}+\frac{2}{7} = \frac{5}{7} \]When the denominators are different, the fractions first need a common denominator. For \( \frac{3}{4}+\frac{2}{5} \), the least common denominator is \(20\).
\[ \frac{3}{4} = \frac{15}{20} \] \[ \frac{2}{5} = \frac{8}{20} \] \[ \frac{15}{20}+\frac{8}{20} = \frac{23}{20} = 1\frac{3}{20} \]Mixed numbers can be entered directly as well. For example, type 2 1/3 and 1 5/6 to solve \(2\frac{1}{3}+1\frac{5}{6}\).
Subtract Fractions
Fraction subtraction works in a similar way to addition. The denominators must match before the numerators can be subtracted.
Suppose we want to calculate \( \frac{7}{8}-\frac{2}{3} \). The least common denominator of \(8\) and \(3\) is \(24\).
\[ \frac{7}{8} = \frac{21}{24} \] \[ \frac{2}{3} = \frac{16}{24} \] \[ \frac{21}{24}-\frac{16}{24} = \frac{5}{24} \]You can also subtract mixed numbers and negative fractions. A value such as -3/5 can be typed exactly as it appears.
Multiply Fractions
Fraction multiplication does not require a common denominator. Multiply the numerators together, multiply the denominators together and then simplify the result if possible.
\[ \frac{4}{5}\times\frac{7}{9} = \frac{4\times7}{5\times9} = \frac{28}{45} \]Mixed numbers should first be changed into improper fractions. For example,
\[ 2\frac{1}{2} = \frac{5}{2} \]so
\[ 2\frac{1}{2}\times\frac{3}{4} = \frac{5}{2}\times\frac{3}{4} = \frac{15}{8} = 1\frac{7}{8} \]Divide Fractions
To divide by a fraction, change the division into multiplication and turn the second fraction upside down. This upside-down fraction is called its reciprocal.
For example,
\[ \frac{3}{4}\div\frac{2}{5} \]becomes
\[ \frac{3}{4}\times\frac{5}{2} \]and therefore
\[ \frac{3\times5}{4\times2} = \frac{15}{8} = 1\frac{7}{8} \]The calculator will show this reciprocal step automatically so it is easier to understand why the answer is correct.
Simplify a Fraction
Simplifying a fraction means writing it with the smallest possible numerator and denominator while keeping exactly the same value.
Consider \( \frac{18}{24} \). Both numbers can be divided by \(6\).
\[ \frac{18}{24} = \frac{18\div6}{24\div6} = \frac{3}{4} \]The value has not changed. Only the way the fraction is written has become simpler.
Mixed Number to Improper Fraction
A mixed number contains a whole-number part and a fraction, such as \(3\frac{2}{5}\). To change it into an improper fraction, multiply the whole number by the denominator and add the numerator.
\[ 3\times5+2=17 \]The denominator stays the same.
\[ 3\frac{2}{5} = \frac{17}{5} \]In the calculator, type the mixed number with a space: 3 2/5.
Improper Fraction to Mixed Number
An improper fraction can be rewritten as a whole number plus a proper fraction. Divide the numerator by the denominator to find the whole-number part.
For example,
\[ \frac{23}{6} \]Since \(23\div6\) gives \(3\) with a remainder of \(5\),
\[ \frac{23}{6} = 3\frac{5}{6} \]The remainder becomes the new numerator while the original denominator stays underneath it.
Fraction to Decimal
Every fraction represents division. Converting a fraction to a decimal therefore means dividing the numerator by the denominator.
\[ \frac{3}{8} = 3\div8 = 0.375 \]Some fractions produce terminating decimals, while others produce repeating decimals. For example,
\[ \frac{1}{3} = 0.333\ldots \]Decimal to Fraction
A decimal can be turned into a fraction by using its place value. The decimal \(0.375\) has three digits after the decimal point, so it can first be written over \(1000\).
\[ 0.375 = \frac{375}{1000} \]Both numbers are divisible by \(125\).
\[ \frac{375}{1000} = \frac{3}{8} \]You can enter positive or negative decimal values such as 0.625, 1.25 or -0.4.
Fraction to Percent
To turn a fraction into a percentage, first find its decimal value and then multiply by \(100\).
\[ \frac{3}{5} = 0.6 \] \[ 0.6\times100 = 60\% \]This means that \( \frac{3}{5} \), \(0.6\), and \(60\%\) all describe the same quantity.
Percent to Fraction
A percentage means an amount out of one hundred. Because of this, \(35\%\) can first be written as \( \frac{35}{100} \).
\[ 35\% = \frac{35}{100} = \frac{7}{20} \]Decimal percentages work too. For example,
\[ 62.5\% = \frac{62.5}{100} = \frac{625}{1000} = \frac{5}{8} \]You can type the percent symbol directly, such as 62.5%.
Compare Fractions
The comparison tool tells you which of two fractions is larger, or whether they are equal. One useful method is to rewrite them with the same denominator.
Compare \( \frac{5}{8} \) and \( \frac{2}{3} \). Their common denominator is \(24\).
\[ \frac{5}{8} = \frac{15}{24} \] \[ \frac{2}{3} = \frac{16}{24} \]Since \(15<16\),
\[ \frac{5}{8} < \frac{2}{3} \]Find the Reciprocal
The reciprocal of a fraction is found by exchanging its numerator and denominator.
\[ \frac{7}{9} \longrightarrow \frac{9}{7} \]For a mixed number, the calculator first converts it into an improper fraction.
\[ 2\frac{1}{3} = \frac{7}{3} \]Its reciprocal is therefore
\[ \frac{3}{7} \]A fraction multiplied by its reciprocal equals \(1\), provided the original value is not zero.
\[ \frac{7}{9}\times\frac{9}{7}=1 \]Find a Common Denominator
Fractions often need the same denominator before they can be added, subtracted or easily compared. The calculator finds the least common denominator and rewrites both fractions.
For \( \frac{3}{4} \) and \( \frac{5}{6} \), the least common denominator is \(12\).
\[ \frac{3}{4} = \frac{9}{12} \] \[ \frac{5}{6} = \frac{10}{12} \]The two fractions now have matching denominators without changing their values.
Fraction of a Number
This option is useful for questions such as “What is \( \frac{3}{5} \) of \(40\)?” The word “of” represents multiplication.
\[ \frac{3}{5}\text{ of }40 = \frac{3}{5}\times40 \]Write \(40\) as \( \frac{40}{1} \).
\[ \frac{3}{5}\times\frac{40}{1} = \frac{120}{5} = 24 \]So \( \frac{3}{5} \) of \(40\) is \(24\). This tool can also handle mixed fractions and decimal values.
Types of Fractions You Can Enter
The calculator understands several common ways of writing fractions. You do not need to convert everything before using the tool.
Don’t get the habit of using this calculator
It’s good to have something to verify the answer. However, don’t rely on this calculator to solve all of your problems. If you do so, it will weaken your mathematics strength. Read our article about how to calculate fractions. It will teach you pretty much everything you may need to solve fractions.
