Fraction
Pronunciation: /ˈfræk ʃən/ Explain
A fraction is an expression divided by an expression.^{[1]}
Examples of fractions are:
The expression on the top is called the
numerator
and the expression on the bottom is called the
denominator.
Fractions whose values are greater than one are sometimes called
improper fractions. Improper fractions are
often easier to use than mixed numbers, especially when using computers.
A whole number followed by a fraction is called a mixed number.
Two examples of mixed numbers are:
A complex fraction
is a fraction with another fraction in the numerator and/or denominator:
.
Operations on Fractions
For a complete list of rules for operations on fractions, see Fraction Rules.
Operation  Description  Example 
Addition  To add 2 fractions:  Find the least common denominator
 Convert each fraction to the least common denominator.
 Add the numerators, copy the common denominator
 Reduce the fraction, if needed.
 5/6+2/10 = 25/30+6/30=(25+6)/30=31/30 
Subtraction  To subtract 2 fractions:  Find the common denominator
 Convert each fraction to the common denominator.
 Subtract the numerators, copy the common denominator
 Reduce the fraction, if needed.
 5/62/10 = 25/306/30=(256)/30=19/30 
Multiplication  To multiply 2 fractions:  Multiply the numerators.
 Multiply the denominators
 Reduce the fraction, if needed.
 3/4*2/3=(3*2)/(4*3)=6/12=1/2. 
Division  To divide 2 fraction: Multiply the first fraction by the reciprocal of the second fraction.  (3/7)/(3/4)=(3/7)*(4/3)=12/21=7/4. 
Least common denominator  To find the least common denominator of two fractions:  Find the prime factors of both fractions.
 Take the product of the prime factors, making sure each factor is multiplied once.
 The product is the least common denominator.
 5/6 and 3/8. 6=2*3, 8=2*2*2,lcd(6,8)=2*2*2*3=24 
Reduce a fraction  To reduce a fraction: Find the prime factors of both the numerator and the denominator.
 Cancel common factors.
 Multiply the remaining factors.
 4/12=(2*2)/(2*2*3)=1/3 
How to convert a mixed number to a fraction.
Original Expression  Operation  Calculation  Description 
1   none  Mixed number to convert. 
2    Multiply the whole number by the denominator. The product is 10. 
3    Add the product and the numerator. The sum is 13. 
4    Use the sum as the numerator and copy the denominator from the fraction. 
Why this works:

Figure 1: Representation of converting 2 3/5 to 13/5. 
How to convert a fraction to a mixed number.
Step  Original Expression  Operation  Description 
1   none  Fraction to convert. 
2    Divide 23 by 7. This gives three wholes and a remainder of 2/7. 
3    Make the mixed number. 
Why this works:

Figure 2: Representation of converting 23/7 to 3 2/7 
References
 Fine, Henry B., Ph. D.. NumberSystem of Algebra Treated Theoretically and Historically. 2nd edition. pp 1215. www.archive.org. D. C. Heath & Co., Boston, U.S.A.. 1907. Last Accessed 8/6/2018. http://www.archive.org/stream/thenumbersystemo17920gut/17920pdf#page/n21/mode/1up/search/fraction. Buy the book
 Oberg, Erik. Arithmetic Simplified. pp 2131. www.archive.org. Industrial Press. 1914. Last Accessed 8/6/2018. http://www.archive.org/stream/arithmeticsimpli00oberrich#page/21/mode/1up/search/fraction. Buy the book
 Oberg, Erik. Elementary Algebra. pg 23. www.archive.org. Industrial Press. 1914. Last Accessed 8/6/2018. http://www.archive.org/stream/elementaryalgebr00oberrich#page/n26/mode/1up/search/fraction. Buy the book
 Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pp 911. www.archive.org. International Textbook Company. January 1963. Last Accessed 8/6/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up. Buy the book
Cite this article as:
McAdams, David E. Fraction. 7/11/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/f/fraction.html.
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Revision History
7/9/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (
McAdams, David E.)
12/19/2009: Added "References". (
McAdams, David E.)
12/29/2008: Changed 'complex fraction' from keyword to vocabulary link. (
McAdams, David E.)
11/28/2008: Added section 'Complex Fractions'. (
McAdams, David E.)
11/26/2008: Changed equations to images. (
McAdams, David E.)
9/16/2008: Added text describing numerator and denominator, changed some expressions to hot_eqn. (
McAdams, David E.)
10/19/2007: Clarified examples in How To section. (
McAdams, David E.)
9/23/2007: Removed alert. (
McAdams, David E.)
8/20/2007: Add this revision history. (
McAdams, David E.)
8/8/2007: Initial version. (
McAdams, David E.)