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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 (21 January 2008)

A fraction is a form of number that 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.

Questions you may have are:

• 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 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.

Note that the denominator cannot be 0.

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

A fraction where the numerator is larger than the denominator is called an improper fraction. It 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.

37/5 is an improper fraction. If you divide 37 by 5, you will get an answer of 7 and a remainder of 2. Thus your mixed number would be 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.

5/4 = 1 1/4

32/3 = 10 2/3

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.

Answers to Readers' Questions

Don't work hard; work smart

Resources

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Mini-quiz to check your understanding

1. Why can't you have the fraction 7/0?

2. If you add 2/3 to 7, what do you get?

3. What mixed number does 27/13 reduce to?

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