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We can display parts of a whole with fractions. We can clearly see this with surfaces (resume further down the page). Fraction numbers are another variety to writing quotients (a quotient is the result after dividing). The quantity of this number is defined as F (Fraction), later it is defined by a  (Quotient).

Written:  (said: one fourth)

The top number is called nominator, the line between the numbers is the fraction bar and the bottom number is the denominator.

How can we imagine what  is?

The whole rectangle is 1. This rectangle is divides by four. Now we have four fourths. But only one fourth is needed (in green). The remaining three fourth are ignored.

What do we do when we want  of a surface? We need to divide the surface into five equal pats and then take three of the five. Now we have  of the surface.

There are following types of fractions:

Unit fractions:

The nominator is always 1 in this case.

Real fractions:

The nominator is always smaller than the denominator in this case.

Fake fractions:

The nominator is bigger than the denominator. The fake fractions can also be represented by mixed numbers:

Extension of fractions

We extend fractions, by multiplying the nominator and denominator with the same number.

Example:

Shortening of fractions

We shorten fractions, by dividing the nominator and denominator by the same number.

Example

Arrangements of fractions

It is not complicated to arrange fractions by their size when they

a)  posses the same denominator

b) have the same nominator

We have to either extend or shorten fractions to accommodate them to each other so they have the same denominator (or nominator). Then we can arrange them by size.

Examples:

1)           2)           3)

Addition and subtraction of fractions

To add (or subtract) two fractions with the same denominator, we add (or subtract) the nominator and keep the denominator the same.

Examples:

When adding (or subtracting) fractions with unequal denominators, we either have to shorten or extend to give them the same denominator. Afterwards, you can add the nominators (or subtract them) while keeping the denominators the same.

Examples:

Multiplication and division of fractions

Multiplication

When a fractions is multiplied with any number, we just multiply the nominator with the number. When fractions are multiplied with each other, the nominator is multiplied with the nominator and the denominator is multiplied with the denominator. Advice: It is often possible to shorten before calculating.

Examples 

1.  

2.  

Division

When dividing a fraction through any number, we have to multiply the denominator with the number. To divide a fraction through another fraction (even with compound fractions) you have to multiply the fraction with the reciprocal value (exchange of nominator and denominator) of the other fraction.

Examples:

1.  

2.  

Copyright © 2005 Christian Franzki - Emkacom Group
Mathematik-Wissen.de - Math-Knowledge.com - Mathe-online.eu - Mathematik-online.eu - Physik-Wissen.de - Pysik-online.eu  - Deviation-Studios.de - 11G1-online
02/09/07