Main denominator

When calculating with fractions in arithmetic , a branch of mathematics , the main denominator or general denominator of several fractions is understood as the least common multiple ( ) of the denominators of these fractions. ${\displaystyle {\rm {kgV}}}$

If fractions are to be compared or added together, they are first brought to a common denominator by expanding them . The main denominator can always be used as the common denominator, which in many practical cases allows even the simplest calculation.

Examples

comparison

One way to compare two fractions that have neither numerator nor denominator in common is to expand them so that they match in numerator or denominator. Mostly you bring them to the same denominator, conveniently the main denominator.

For example, to determine whether is greater or less than , you can bring both fractions to the main denominator and then see: ${\displaystyle {\frac {5}{8}}}$ ${\displaystyle {\frac {11}{18}}}$ ${\displaystyle \operatorname {kgV} (8,18)=72}$

${\displaystyle {\frac {5}{8}}={\frac {45}{72}}>{\frac {44}{72}}={\frac {11}{18}}}$

The same result is obtained by leveling the counter, which is rather unusual. In the example, 11 would be added to the left and 5 to the right:

${\displaystyle {\frac {5}{8}}={\frac {55}{88}}>{\frac {55}{90}}={\frac {11}{18}}}$

Addition and subtraction

In order to add or subtract fractions with different denominators , you must first expand all fractions to a common denominator . The main denominator is usually preferred, e.g. B.

${\displaystyle {5 \over 6}+{3 \over 4}+{4 \over 5}={50 \over 60}+{45 \over 60}+{48 \over 60}={143 \over 60}}$

${\displaystyle 60}$is the least common multiple of , and and thus the main denominator of the three fractions to be added. ${\displaystyle 6}$ ${\displaystyle 4}$ ${\displaystyle 5}$

See also

• Common denominator

Individual evidence

1. ↑ main denominator . In: Guido Walz (Ed.): Lexicon of Mathematics . 1st edition. Spectrum Academic Publishing House, Mannheim / Heidelberg 2000, ISBN 3-8274-0439-8 .