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Explanation of Fractions - Succeed in Algebra. Also refer to quotient, numerator, denominator, improper fraction, mixed number, reduced, mathematics, math, maths, Ron Kurtus, School for Champions. Copyright © Restrictions
Overview of Fractions
by Ron Kurtus (revised 18 February 2009)
A fraction is a part of the whole. It is a form of number that indicates the quotient or division of two whole numbers, except 0.
The top number of a fraction is called the numerator and the bottom number is the denominator. An improper fraction is one where the numerator is larger than the denominator. A mixed number is a whole number plus a proper fraction. An improper fraction should be reduced to a mixed number.
Questions you may have include:
- What is a description of a fraction?
- What are examples of mixed numbers?
- How do you reduce an improper fraction?
This lesson will answer those questions. There is a mini-quiz near the end of the lesson.
Fraction definition
A fraction indicates a part of the whole or the quotient of two whole numbers, except 0.
Note: If the numerator is 0, the number is not a fraction. For example, 0/5 = 0. The denominator cannot be 0, since dividing by 0 is forbidden.
Fraction is part of the whole
If you would take a pie and divide it into five equal pieces, then one piece would be one-fifth (1/5) of the whole pie. In this way, a fraction indicates it is part of the whole. Two pieces of this pie would be 2/5 of the whole pie.
Since a fraction is part of the whole, a proper positive fraction is always less than 1.
Incomplete division
Typically, you divide a number by a smaller number, such as 6 ÷ 2 = 3. If you try to divide a number by a larger number, the result is called a fraction. It is incomplete division. For example, 2 ÷ 3 = 2/3, which is a fraction.
Note that the the ÷ sign almost looks like a fraction, with the dots representing numbers. Also, the / sign is often used as division instead of the ÷ sign.
Numerator and denominator
The top number in a fraction is called the numerator. The bottom number is called the denominator. I don't know of any easy way to remember that, but since the words are used so much when dealing with fractions, it is worthwhile to learn them.
Can't use 0 in a fraction
If the numerator in a quotient is 0, then the number cannot be a fraction, since 0 divided by any number is 0. For example 0/5 = 0.
On the other hand, you cannot have a denominator equal to 0. You cannot have 3/0, because that is 3 ÷ 0, and you cannot divide by 0. That is a basic rule in arithmetic.
Mixed numbers
A mixed number is a whole number plus a fraction. 5 2/3 is a mixed number. It is called "five and two-thirds" and is the same as the sum of 5 + 2/3.
Other examples of mixed numbers include 1 1/2, 3200 7/10 and 15 23/24.
Reducing an improper fraction
An improper fraction is a fraction where the numerator is larger than the denominator. For example, 7/5 is an improve fraction, since 7 is greater than 5.
An improper fraction can be reduced to a mixed number, consisting of a whole number and a fraction. This is done by dividing numerator by the denominator. The remainder of the division is the numerator of the new fraction.
Consider the improper fraction 37/5. If you divide 37 by 5, you will get an answer of 7 and a remainder of 2. Thus your mixed number is 7 2/5.
Examples
Since most improper fractions do not entail large numbers, you can usually perform the division in your head, as opposed to using long division.
Consider 5/4. 5 divided by 4 equals 1 with a remainder of 1.
5/4 = 1 1/4
32/3 is 32 divided by 3 equals 10 with a remainder of 2.
32/3 = 10 2/3
126 divided by 25 equals 5 with a remainder of 1.
126/25 = 5 1/25
No remainder
If there is no remainder, the improper fraction simply becomes a whole number:
27/9 = 3
64/4 = 16
Summary
A fraction indicates a part of the whole or the quotient of two whole numbers except 0. The top number of a fraction is called the numerator and the bottom number is the denominator. An improper fraction is one where the numerator is larger than the denominator. A mixed number is a whole number plus a proper fraction. An improper fraction should be reduced to a mixed number.
Don't work hard; work smart
Resources
The following resources provide information on this subject:
Websites
Books
Mini-quiz to check your understanding
If you got all three correct, you are on your way to becoming a Champion in Arithmetic. If you had problems, you had better look over the material again.
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Overview of Fractions