Basic Algebra/Working with Numbers/Rational Numbers


Rational numbers


Rational numbersEdit

A rational number is a fraction, written   where   and   are integers.   is called the numerator and   the denominator. Applied to a cake, it means   parts of a cake divided equally into   parts. For example   means a half. But note that   and   can be negative.   means gaining a half and   means losing a half.

Fractions of negative numbersEdit

If   and   are positive, then the fraction or rational number is positive. This is the way we commonly think of fractions (   of a cake...).

There is no difference whether   is negative or   is negative. The reason for this is simple : if you talk about losing parts of a cake (   ), or about parts of a lost cake (   ), in both cases, you talk about lost parts. In these cases, the fraction is said to be negative.

Finally, if   and   are negative, then their effect is canceled by each other and the fraction is positive. As rational numbers are on one axis, the second time you take the opposite you obtain the original fraction. Thus, the fraction   is the fraction  .

Example ProblemsEdit

I have been given 1 piece of cake, my father who is very hungry has taken 2. My mother has taken 1 and my sister has taken 1 too. There were 10 pieces. What fraction of the cake has been eaten?

  of the cake, which is half of the cake.

Note that in this case, the addition is very simple because the denominator is always 10. We just have to add the numerators.

Practice GamesEdit

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Practice ProblemsEdit

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