Fraction Calculator (Add, Subtract, Multiply and Divide Fractions)

Enter the two fractions just as they look (top box = numerator, bottom box = denominator) and choose the operation (+ − × ÷) from the menu in the middle. The answer is shown in lowest terms and as a decimal, with the steps.

Enter numbers for the numerators and denominators (negatives and decimals are fine; a denominator cannot be 0).

Result

Enter two fractions on the left, choose the operation (+ − × ÷) in the middle and press "Calculate". The result will appear here.

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What you can do on this page
What is this calculation used for?
How to Use
Formula
Symbols and terms
- Symbols
- Terms
Good to know before you start
How to calculate it in Excel
How to calculate it in Google Sheets
How to calculate it in Python
How to write it in LaTeX and other math languages (copy and paste)
How to have ChatGPT do the calculation
DataChef Features
Related Features
NumberChef Calculators List

What you can do on this page

Add, subtract, multiply and divide two fractions (for example, \(\dfrac{2}{7} + \dfrac{3}{8}\)) on the spot, just by entering the numerators and denominators
The answer is shown in lowest terms. If it is an improper fraction greater than 1, it is also shown as a mixed number, and always as a decimal too
The steps to the answer are shown too: finding a common denominator, multiplying by the reciprocal and simplifying
A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page

A denominator cannot be 0 (you cannot divide by 0). Negative fractions and decimals in the numerator or denominator are fine.

What is this calculation used for?

Scaling a recipe to the number of people

Recipes often use fractions such as "\(\dfrac{1}{3}\) cup" or "\(\dfrac{3}{4}\) cup", and adjusting the amounts is fraction multiplication. For example, "\(\dfrac{2}{3}\) of \(\dfrac{3}{4}\) cup" is \(\dfrac{3}{4} \times \dfrac{2}{3} = \dfrac{1}{2}\) (half a cup).
To double a recipe or cut it in half, just multiply each fraction in the recipe, and you get exact amounts.

Checking ownership shares (money and important decisions)

Suppose one partner owns \(\dfrac{1}{2}\) of a small business and two other partners split the rest equally. Each of the two owns \(\dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4}\).
Check that all the shares add up to \(\dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{4} = 1\), and you know nothing was left out. Shares in jointly owned property are worked out with the same fraction addition and multiplication.

Matching inch sizes in DIY projects

In the US, sizes of screws, wrenches, lumber and pipes are given in fractions such as "\(\dfrac{3}{8}\) inch" or "\(\dfrac{1}{2}\) inch".
Stack two \(\dfrac{3}{8}\)-inch boards, and the total is \(\dfrac{3}{8} + \dfrac{3}{8} = \dfrac{3}{4}\) inch. The step between a \(\dfrac{1}{2}\)-inch part and a \(\dfrac{3}{8}\)-inch part is \(\dfrac{1}{2} - \dfrac{3}{8} = \dfrac{1}{8}\) inch. Choosing tools and matching sizes is fraction addition and subtraction.

Note lengths and rhythm in music

A quarter note is \(\dfrac{1}{4}\) of a whole note and an eighth note is \(\dfrac{1}{8}\): note lengths are fractions to begin with. A dotted quarter note lasts \(\dfrac{1}{4} + \dfrac{1}{8} = \dfrac{3}{8}\).
In 4/4 time, the notes in each measure are arranged so that their lengths add up to \(\dfrac{4}{4} = 1\). Reading or writing rhythms in sheet music is a series of fraction additions.

Estimating time and schedules

"A 45-minute meeting" is \(\dfrac{3}{4}\) hour, and "a 30-minute trip" is \(\dfrac{1}{2}\) hour. An hour has 60 minutes, so time has always worked well with fractions.
Two 45-minute meetings plus a 30-minute trip add up to \(\dfrac{3}{4} + \dfrac{3}{4} + \dfrac{1}{2} = 2\) hours. You can estimate schedule totals and time left with fraction addition and subtraction.

Formula

Adding fractions (find a common denominator, then add the numerators)

Standard notation (the usual math form)

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

In words (symbols replaced with words)

① \(\dfrac{a}{b}\): first fraction \(+\) ② \(\dfrac{c}{d}\): second fraction \(=\) ③ \(\dfrac{\text{sum of the new numerators}}{\text{common denominator (product of the denominators)}}\)

The formula in words

① Give the \(\dfrac{a}{b}\): first fraction

② and the \(\dfrac{c}{d}\): second fraction the same denominator (find a common denominator), then add the numerators, and you get

③ \(\dfrac{\text{sum of the new numerators}}{\text{common denominator (product of the denominators)}}\)

Quick example

\(\dfrac{2}{7} + \dfrac{3}{8}\) has different denominators, so make both denominators \(7 \times 8 = 56\) first

first fraction \(\dfrac{2}{7}\) \(+\) second fraction \(\dfrac{3}{8}\) \(=\) sum of the two fractions \(\dfrac{37}{56}\)

\(\dfrac{2}{7} + \dfrac{3}{8} = \dfrac{2 \times 8}{7 \times 8} + \dfrac{3 \times 7}{8 \times 7} = \dfrac{16}{56} + \dfrac{21}{56}\)

\(\dfrac{16 + 21}{56} = \dfrac{37}{56}\ \ (\approx 0.661)\)

Key idea

Fractions with different denominators cannot be added as they are. The denominator tells how many equal parts 1 is split into (the size of each piece), and adding up pieces of different sizes does not give a meaningful count. So first give them the same denominator (find a common denominator), then add the numerators. Besides the "product of the denominators" (\(7 \times 8 = 56\)) used in this formula, you can also use the least common multiple of the denominators (the least common denominator). Either way the answer is the same, but the least common denominator keeps the numbers smaller, so simplifying at the end is easier.

Subtracting fractions (find a common denominator, then subtract the numerators)

Standard notation (the usual math form)

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

In words (symbols replaced with words)

① \(\dfrac{a}{b}\): first fraction \(-\) ② \(\dfrac{c}{d}\): second fraction \(=\) ③ \(\dfrac{\text{difference of the new numerators}}{\text{common denominator (product of the denominators)}}\)

The formula in words

① From the \(\dfrac{a}{b}\): first fraction , after giving both the same denominator (finding a common denominator),

② subtract the numerator of the \(\dfrac{c}{d}\): second fraction , and you get

③ \(\dfrac{\text{difference of the new numerators}}{\text{common denominator (product of the denominators)}}\)

Quick example

For \(\dfrac{1}{2} - \dfrac{1}{3}\), make both denominators \(2 \times 3 = 6\) first

first fraction \(\dfrac{1}{2}\) \(-\) second fraction \(\dfrac{1}{3}\) \(=\) first fraction minus second fraction \(\dfrac{1}{6}\)

\(\dfrac{1}{2} - \dfrac{1}{3} = \dfrac{1 \times 3}{2 \times 3} - \dfrac{1 \times 2}{3 \times 2} = \dfrac{3}{6} - \dfrac{2}{6}\)

\(\dfrac{3 - 2}{6} = \dfrac{1}{6}\ \ (\approx 0.167)\)

Key idea

Finding the common denominator works exactly as in addition. After that, just subtract the numerators. If you subtract a larger fraction from a smaller one, the answer is a negative fraction (for example, \(\dfrac{1}{2} - \dfrac{3}{4} = -\dfrac{1}{4}\)). The minus sign is usually written once, in front of the whole fraction.

Multiplying fractions (multiply the numerators and the denominators)

Standard notation (the usual math form)

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

In words (symbols replaced with words)

① \(\dfrac{a}{b}\): first fraction \(\times\) ② \(\dfrac{c}{d}\): second fraction \(=\) ③ \(\dfrac{\text{product of the numerators}}{\text{product of the denominators}}\)

The formula in words

① Multiply the numerators together and the denominators together of the \(\dfrac{a}{b}\): first fraction

② and the \(\dfrac{c}{d}\): second fraction , and you get

③ \(\dfrac{\text{product of the numerators}}{\text{product of the denominators}}\)

Quick example

For \(\dfrac{2}{3} \times \dfrac{9}{4}\), multiply the numerators and the denominators, then simplify

first fraction \(\dfrac{2}{3}\) \(\times\) second fraction \(\dfrac{9}{4}\) \(=\) product of the two fractions \(\dfrac{3}{2}\)

\(\dfrac{2}{3} \times \dfrac{9}{4} = \dfrac{2 \times 9}{3 \times 4} = \dfrac{18}{12}\)

\(\dfrac{18}{12} = \dfrac{18 \div 6}{12 \div 6} = \dfrac{3}{2}\ \ (= 1.5)\)

Key idea

Multiplication does not need a common denominator. Just multiply the numerators together and the denominators together, then simplify at the end if you can (\(\dfrac{18}{12} \rightarrow \dfrac{3}{2}\)). You may also simplify before you multiply (in \(\dfrac{2}{3} \times \dfrac{9}{4}\), divide the 9 and the 3 by 3 first to get \(\dfrac{2}{1} \times \dfrac{3}{4}\)). This is called cross-canceling. It keeps the numbers small and makes the work much easier. A fraction whose numerator is larger than its denominator, like the answer \(\dfrac{3}{2}\) (an improper fraction), can also be written as the mixed number \(1\dfrac{1}{2}\) (one and one half).

Dividing fractions (multiply by the reciprocal of the divisor)

Standard notation (the usual math form)

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

In words (symbols replaced with words)

③ \(\dfrac{a}{b}\): first fraction \(\div\) ① \(\dfrac{c}{d}\): divisor \(=\) \(\dfrac{a}{b}\): first fraction \(\times\) ② \(\dfrac{d}{c}\): reciprocal of the divisor \(=\) ④ \(\dfrac{\text{product of the numerators (first × reciprocal)}}{\text{product of the denominators (first × reciprocal)}}\)

The formula in words

① Flip the numerator and denominator of the \(\dfrac{c}{d}\): divisor (the second fraction)

② to get the \(\dfrac{d}{c}\): reciprocal of the divisor

③ multiply the \(\dfrac{a}{b}\): first fraction by it, and you get

④ \(\dfrac{\text{product of the numerators (first × reciprocal)}}{\text{product of the denominators (first × reciprocal)}}\)

Quick example

For \(\dfrac{3}{5} \div \dfrac{6}{7}\), flip the divisor \(\dfrac{6}{7}\) to get its reciprocal \(\dfrac{7}{6}\), and multiply by that

first fraction \(\dfrac{3}{5}\) \(\div\) divisor \(\dfrac{6}{7}\) \(=\) first fraction \(\dfrac{3}{5}\) \(\times\) reciprocal \(\dfrac{7}{6}\) \(=\) first fraction divided by the divisor \(\dfrac{7}{10}\)

\(\dfrac{3}{5} \div \dfrac{6}{7} = \dfrac{3}{5} \times \dfrac{7}{6} = \dfrac{3 \times 7}{5 \times 6} = \dfrac{21}{30}\)

\(\dfrac{21}{30} = \dfrac{21 \div 3}{30 \div 3} = \dfrac{7}{10}\ \ (= 0.7)\)

Key idea

"\(\div \dfrac{c}{d}\)" can be rewritten as "\(\times \dfrac{d}{c}\)". This is the most important point in dividing fractions (often remembered as "keep, change, flip"). Dividing by a fraction counts how many of that fraction fit. For example, \(2 \div \dfrac{1}{2}\) asks "how many halves fit in 2?", and the answer is 4. Using the reciprocal, \(2 \times \dfrac{2}{1} = 4\) gives the same answer. The fraction you get by flipping the numerator and denominator is called the reciprocal. For the same reason you cannot divide by 0, you cannot divide by a fraction equal to 0 (one whose numerator is 0).

Simplifying (writing a fraction in lowest terms)

Standard notation (the usual math form)

\(\dfrac{a}{b}\) \(=\) \(\dfrac{a \div g}{b \div g}\)

In words (symbols replaced with words)

① \(\dfrac{a}{b}\): fraction before simplifying \(=\) ② \(\dfrac{\text{numerator divided by the GCF}}{\text{denominator divided by the GCF}}\)

The formula in words

① Divide the numerator and the denominator of the \(\dfrac{a}{b}\): fraction before simplifying each by the largest number that divides both (their greatest common factor \(g\)), and you get

② \(\dfrac{\text{numerator divided by the GCF}}{\text{denominator divided by the GCF}}\) (the fraction in lowest terms)

Quick example

To simplify \(\dfrac{18}{12}\) from the multiplication example, divide the numerator and denominator by 6, the greatest common factor of 18 and 12

fraction before simplifying \(\dfrac{18}{12}\) \(=\) simplified fraction \(\dfrac{3}{2}\)

\(\dfrac{18}{12} = \dfrac{18 \div 6}{12 \div 6} = \dfrac{3}{2}\)

Key idea

Multiplying or dividing the numerator and the denominator by the same number does not change the value of a fraction (\(\dfrac{1}{2} = \dfrac{2}{4} = \dfrac{3}{6}\); these are called equivalent fractions, and this is the same property used to find a common denominator). Simplifying uses this property: divide the numerator and denominator by their greatest common factor to reach the form that cannot be simplified any further (lowest terms). Answers on tests and in calculations are usually written in lowest terms. Every answer from this calculator is already simplified.

Fraction arithmetic comes in three patterns. To add or subtract, find a common denominator, then add or subtract the numerators. To multiply, multiply the numerators together and the denominators together. To divide, multiply by the reciprocal instead. Whichever you do, remember to simplify at the end to lowest terms.

Symbols and terms

Symbols

\(\dfrac{a}{b}\)	a over b	The first fraction. The top number \(a\) is the numerator, and the bottom number \(b\) is the denominator. (Example - \(\dfrac{2}{7}\) has numerator 2 and denominator 7)
\(\dfrac{c}{d}\)	c over d	The second fraction. In division it is the divisor (the number you divide by).
\(\dfrac{d}{c}\)	d over c	The fraction you get by flipping the numerator and denominator of \(\dfrac{c}{d}\) (its reciprocal). It is used to change a division into a multiplication.
\(g\)	g	The greatest common factor of the numerator and denominator. To simplify, divide both the numerator and the denominator by it.

Terms

numerator	The top number of a fraction. It tells how many pieces there are.
denominator	The bottom number of a fraction. It tells how many equal parts 1 is split into (the size of each piece). It cannot be 0.
common denominator	A denominator shared by two or more fractions. Rewriting fractions with different denominators to have the same one, without changing their values, is needed before adding or subtracting.
simplifying	Dividing the numerator and denominator by a common number (their greatest common factor) to write a fraction in its simplest form. Also called reducing a fraction.
lowest terms	A fraction is in lowest terms (or simplest form) when it cannot be simplified any further. Every answer from this calculator is shown in lowest terms.
greatest common factor (GCF)	The largest of the numbers that divide both of two numbers evenly (their common factors). It is used to simplify. (Example - for 18 and 12, it is 6)
least common multiple (LCM)	The smallest of the multiples that two numbers share. Using it as the common denominator (the least common denominator) keeps the numbers small. (Example - for 4 and 6, it is 12)
reciprocal	The fraction you get by flipping the numerator and denominator. Multiplied by the original number, it gives 1 (\(\dfrac{6}{7} \times \dfrac{7}{6} = 1\)). It is used to divide fractions.
proper fraction	A fraction whose numerator is smaller than its denominator, so it is less than 1. (Example - \(\dfrac{1}{2}\))
improper fraction	A fraction whose numerator is equal to or larger than its denominator, so it is 1 or more. (Example - \(\dfrac{3}{2}\))
mixed number	An improper fraction written as a whole number plus a proper fraction. (Example - \(\dfrac{3}{2} = 1\dfrac{1}{2}\), read "one and one half") It makes the size easy to picture.

Good to know before you start

Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.

What a fraction is (Grades 3–4)	Knowing that a fraction stands for "some number of the equal parts that 1 is split into" (\(\dfrac{1}{4}\) is one of the 4 equal parts of 1) Knowing that the bottom number (the denominator) gives the size of each piece, and the top number (the numerator) gives the number of pieces
Multiplication facts and division (Grades 3–4)	Being able to multiply denominators and numerators quickly Being able to divide, as in 18 ÷ 6 (used when simplifying)
Common factors and common multiples (Grades 4–6)	Being able to find the greatest common factor (used to simplify) and the least common multiple (used to find a common denominator)
Equivalent fractions and adding and subtracting fractions (Grades 4–5)	Knowing that multiplying or dividing the numerator and denominator by the same number does not change the value of a fraction Knowing that fractions with different denominators are added or subtracted after finding a common denominator
Multiplying and dividing fractions (Grades 5–6)	Knowing that to multiply, you multiply the numerators together and the denominators together Knowing that a division can be changed into "multiplying by the reciprocal"

How to calculate it in Excel

Copy the whole table below and paste it into cell A1 in Excel. It works as is.

Table to add fractions

Numerator a of fraction 1	2
Denominator b of fraction 1	7
Numerator c of fraction 2	3
Denominator d of fraction 2	8
Numerator before simplifying (a×d + c×b)	=B1B4+B3B2
Denominator before simplifying (b×d)	=B2*B4
Greatest common factor	=GCD(ABS(B5),ABS(B6))
Answer numerator (simplified)	=B5/B7
Answer denominator (simplified)	=B6/B7
As a decimal	=B5/B6

Table to subtract fractions

Numerator a of fraction 1	1
Denominator b of fraction 1	2
Numerator c of fraction 2	1
Denominator d of fraction 2	3
Numerator before simplifying (a×d − c×b)	=B1B4-B3B2
Denominator before simplifying (b×d)	=B2*B4
Greatest common factor	=GCD(ABS(B5),ABS(B6))
Answer numerator (simplified)	=B5/B7
Answer denominator (simplified)	=B6/B7
As a decimal	=B5/B6

Table to multiply fractions

Numerator a of fraction 1	2
Denominator b of fraction 1	3
Numerator c of fraction 2	9
Denominator d of fraction 2	4
Numerator before simplifying (a×c)	=B1*B3
Denominator before simplifying (b×d)	=B2*B4
Greatest common factor	=GCD(ABS(B5),ABS(B6))
Answer numerator (simplified)	=B5/B7
Answer denominator (simplified)	=B6/B7
As a decimal	=B5/B6

Table to divide fractions

Numerator a of fraction 1	3
Denominator b of fraction 1	5
Numerator c of fraction 2	6
Denominator d of fraction 2	7
Numerator before simplifying (a×d)	=B1*B4
Denominator before simplifying (b×c)	=B2*B3
Greatest common factor	=GCD(ABS(B5),ABS(B6))
Answer numerator (simplified)	=B5/B7
Answer denominator (simplified)	=B6/B7
As a decimal	=B5/B6

Table to simplify a fraction

Numerator before simplifying	18
Denominator before simplifying	12
Greatest common factor	=GCD(ABS(B1),ABS(B2))
Simplified numerator	=B1/B3
Simplified denominator	=B2/B3

In every table, enter numbers in the input cells at the top (numerators and denominators), and the formula cells below are calculated automatically.
"*" is multiplication, "/" is division, and GCD is the Excel function for the greatest common factor (ABS is there just to remove any minus sign).
In the first table (addition), for example, B8 and B9 are the numerator and denominator of the simplified answer: for \(\dfrac{2}{7} + \dfrac{3}{8}\), you get \(\dfrac{37}{56}\) (about 0.6607 as a decimal).
To work with a negative fraction, put the minus sign on the numerator.

How to calculate it in Google Sheets

Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.

Table to add fractions

Numerator a of fraction 1	2
Denominator b of fraction 1	7
Numerator c of fraction 2	3
Denominator d of fraction 2	8
Numerator before simplifying (a×d + c×b)	=B1B4+B3B2
Denominator before simplifying (b×d)	=B2*B4
Greatest common factor	=GCD(ABS(B5),ABS(B6))
Answer numerator (simplified)	=B5/B7
Answer denominator (simplified)	=B6/B7
As a decimal	=B5/B6

Table to subtract fractions

Numerator a of fraction 1	1
Denominator b of fraction 1	2
Numerator c of fraction 2	1
Denominator d of fraction 2	3
Numerator before simplifying (a×d − c×b)	=B1B4-B3B2
Denominator before simplifying (b×d)	=B2*B4
Greatest common factor	=GCD(ABS(B5),ABS(B6))
Answer numerator (simplified)	=B5/B7
Answer denominator (simplified)	=B6/B7
As a decimal	=B5/B6

Table to multiply fractions

Numerator a of fraction 1	2
Denominator b of fraction 1	3
Numerator c of fraction 2	9
Denominator d of fraction 2	4
Numerator before simplifying (a×c)	=B1*B3
Denominator before simplifying (b×d)	=B2*B4
Greatest common factor	=GCD(ABS(B5),ABS(B6))
Answer numerator (simplified)	=B5/B7
Answer denominator (simplified)	=B6/B7
As a decimal	=B5/B6

Table to divide fractions

Numerator a of fraction 1	3
Denominator b of fraction 1	5
Numerator c of fraction 2	6
Denominator d of fraction 2	7
Numerator before simplifying (a×d)	=B1*B4
Denominator before simplifying (b×c)	=B2*B3
Greatest common factor	=GCD(ABS(B5),ABS(B6))
Answer numerator (simplified)	=B5/B7
Answer denominator (simplified)	=B6/B7
As a decimal	=B5/B6

Table to simplify a fraction

Numerator before simplifying	18
Denominator before simplifying	12
Greatest common factor	=GCD(ABS(B1),ABS(B2))
Simplified numerator	=B1/B3
Simplified denominator	=B2/B3

The same formulas and functions as in Excel (GCD, ABS) work as is in Google Sheets.
Copy the whole table, paste it into cell A1, and replace the numbers in the input cells at the top (numerators and denominators) with your own.

How to calculate it in Python

from fractions import Fraction

fraction_1 = Fraction(2, 7)   # first fraction (numerator, denominator)
fraction_2 = Fraction(3, 8)   # second fraction (numerator, denominator)

print(fraction_1 + fraction_2)         # addition -> 37/56
print(fraction_1 - fraction_2)         # subtraction -> -5/56
print(fraction_1 * fraction_2)         # multiplication -> 3/28
print(fraction_1 / fraction_2)         # division -> 16/21
print(float(fraction_1 + fraction_2))  # the sum as a decimal -> 0.6607142857142857

With the fractions module (Fraction) from the standard library, finding common denominators and simplifying are done for you. Change the numbers in Fraction(numerator, denominator) and run it.

How to write it in LaTeX and other math languages (copy and paste)

Adding fractions (find a common denominator, then add the numerators)

a/b + c/d = (a×d + c×b)/(b×d)

\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + cb}{bd}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mfrac><mi>a</mi><mi>b</mi></mfrac>
    <mo>+</mo>
    <mfrac><mi>c</mi><mi>d</mi></mfrac>
    <mo>=</mo>
    <mfrac>
      <mrow><mi>a</mi><mo>&#xD7;</mo><mi>d</mi><mo>+</mo><mi>c</mi><mo>&#xD7;</mo><mi>b</mi></mrow>
      <mrow><mi>b</mi><mo>&#xD7;</mo><mi>d</mi></mrow>
    </mfrac>
  </mrow>
</math>

a/b + c/d = (a*d + c*b)/(b*d)

Together[a/b + c/d]

r := normal(a/b + c/d);

r = simplifyFraction(a/b + c/d);

a/b + c/d = (a×d + c×b)/(b×d)

Subtracting fractions (find a common denominator, then subtract the numerators)

a/b − c/d = (a×d − c×b)/(b×d)

\dfrac{a}{b} - \dfrac{c}{d} = \dfrac{ad - cb}{bd}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mfrac><mi>a</mi><mi>b</mi></mfrac>
    <mo>&#x2212;</mo>
    <mfrac><mi>c</mi><mi>d</mi></mfrac>
    <mo>=</mo>
    <mfrac>
      <mrow><mi>a</mi><mo>&#xD7;</mo><mi>d</mi><mo>&#x2212;</mo><mi>c</mi><mo>&#xD7;</mo><mi>b</mi></mrow>
      <mrow><mi>b</mi><mo>&#xD7;</mo><mi>d</mi></mrow>
    </mfrac>
  </mrow>
</math>

a/b - c/d = (a*d - c*b)/(b*d)

Together[a/b - c/d]

r := normal(a/b - c/d);

r = simplifyFraction(a/b - c/d);

a/b - c/d = (a×d - c×b)/(b×d)

Multiplying fractions (multiply the numerators and the denominators)

a/b × c/d = (a×c)/(b×d)

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

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mfrac><mi>a</mi><mi>b</mi></mfrac>
    <mo>&#xD7;</mo>
    <mfrac><mi>c</mi><mi>d</mi></mfrac>
    <mo>=</mo>
    <mfrac>
      <mrow><mi>a</mi><mo>&#xD7;</mo><mi>c</mi></mrow>
      <mrow><mi>b</mi><mo>&#xD7;</mo><mi>d</mi></mrow>
    </mfrac>
  </mrow>
</math>

a/b xx c/d = (a*c)/(b*d)

Together[(a/b)*(c/d)]

r := normal((a/b)*(c/d));

r = simplifyFraction((a/b)*(c/d));

a/b × c/d = (a×c)/(b×d)

Dividing fractions (multiply by the reciprocal of the divisor)

a/b ÷ c/d = a/b × d/c = (a×d)/(b×c)

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

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mfrac><mi>a</mi><mi>b</mi></mfrac>
    <mo>&#xF7;</mo>
    <mfrac><mi>c</mi><mi>d</mi></mfrac>
    <mo>=</mo>
    <mfrac><mi>a</mi><mi>b</mi></mfrac>
    <mo>&#xD7;</mo>
    <mfrac><mi>d</mi><mi>c</mi></mfrac>
    <mo>=</mo>
    <mfrac>
      <mrow><mi>a</mi><mo>&#xD7;</mo><mi>d</mi></mrow>
      <mrow><mi>b</mi><mo>&#xD7;</mo><mi>c</mi></mrow>
    </mfrac>
  </mrow>
</math>

a/b -: c/d = a/b xx d/c = (a*d)/(b*c)

Together[(a/b)/(c/d)]

r := normal((a/b)/(c/d));

r = simplifyFraction((a/b)/(c/d));

a/b ÷ c/d = (a×d)/(b×c)

Simplifying (writing a fraction in lowest terms)

a/b = (a÷g)/(b÷g)  (g = GCD(a, b))

\dfrac{a}{b} = \dfrac{a \div g}{b \div g} \quad (g = \gcd(a, b))

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mfrac><mi>a</mi><mi>b</mi></mfrac>
    <mo>=</mo>
    <mfrac>
      <mrow><mi>a</mi><mo>&#xF7;</mo><mi>g</mi></mrow>
      <mrow><mi>b</mi><mo>&#xF7;</mo><mi>g</mi></mrow>
    </mfrac>
  </mrow>
</math>

a/b = (a-:g)/(b-:g)

Simplify[a/b]

r := normal(a/b);

r = simplifyFraction(a/b);

a/b = (a÷g)/(b÷g)

How to have ChatGPT do the calculation

You are a fraction calculation assistant. Do the following calculations by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). In Python, use the fractions module (Fraction) from the standard library.

Calculate each of the following, and give each answer both as a fraction in lowest terms and as a decimal.
1. 2/7 + 3/8
2. 1/2 - 3/4
3. 2/3 × 9/4
4. 3/5 ÷ 6/7

Show the formulas you used and the numbers from the execution result.

How to Use

1

Enter your numbers

Type the numbers you want to calculate with into the input fields
2

Calculate

Press the "Calculate" button
3

Check the result

The result appears on the spot. The same page also explains the idea behind the calculation and the formula