# 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.

OperationDescriptionExample
1. Find the least common denominator
2. Convert each fraction to the least common denominator.
3. Add the numerators, copy the common denominator
4. Reduce the fraction, if needed.
Subtraction To subtract 2 fractions:
1. Find the common denominator
2. Convert each fraction to the common denominator.
3. Subtract the numerators, copy the common denominator
4. Reduce the fraction, if needed.
Multiplication To multiply 2 fractions:
1. Multiply the numerators.
2. Multiply the denominators
3. Reduce the fraction, if needed.
Division To divide 2 fraction: Multiply the first fraction by the reciprocal of the second fraction.
Least common denominator To find the least common denominator of two fractions:
1. Find the prime factors of both fractions.
2. Take the product of the prime factors, making sure each factor is multiplied once.
3. The product is the least common denominator.
Reduce a fraction To reduce a fraction:
1. Find the prime factors of both the numerator and the denominator.
2. Cancel common factors.
3. Multiply the remaining factors.

### How to convert a mixed number to a fraction.

Original
Expression

Operation

Calculation

Description
1noneMixed number to convert.
2Multiply the whole number by the denominator. The product is 10.
3Add the product and the numerator. The sum is 13.
4Use 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.

StepOriginal
Expression
OperationDescription
1noneFraction to convert.
2Divide 23 by 7. This gives three wholes and a remainder of 2/7.
3Make the mixed number.

Why this works:

 Figure 2: Representation of converting 23/7 to 3 2/7

### References

1. McAdams, David E.. All Math Words Dictionary, fraction. 2nd Classroom edition 20150108-4799968. pg 82. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Fine, Henry B., Ph. D.. Number-System of Algebra Treated Theoretically and Historically. 2nd edition. pp 12-15. www.archive.org. D. C. Heath & Co., Boston, U.S.A.. 1907. Last Accessed 7/11/2018. http://www.archive.org/stream/thenumbersystemo17920gut/17920-pdf#page/n21/mode/1up/search/fraction. Buy the book
3. Oberg, Erik. Arithmetic Simplified. pp 21-31. www.archive.org. Industrial Press. 1914. Last Accessed 7/11/2018. http://www.archive.org/stream/arithmeticsimpli00oberrich#page/21/mode/1up/search/fraction. Buy the book
4. Oberg, Erik. Elementary Algebra. pg 23. www.archive.org. Industrial Press. 1914. Last Accessed 7/11/2018. http://www.archive.org/stream/elementaryalgebr00oberrich#page/n26/mode/1up/search/fraction. Buy the book
5. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pp 9-11. www.archive.org. International Textbook Company. January 1963. Last Accessed 7/11/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up. Buy the book

McAdams, David E. Fraction. 4/21/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/f/fraction.html.

### Revision History

4/21/2019: Modified equations and expression to match the new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)