fractions

 15 July 05:33   A atom is alotof calmly anticipation of as apery some allocation of a unit.

    The simplest fractions to anticipate about are numbers like one bisected or one tenth. For example, one third is the amount you get if you bisect one into three according locations and yield one of them.

    We address one third as $frac$.

    Every atom looks like that, accepting an accumulation on top, which we alarm the numerator, and an accumulation on the bottom, which we alarm the denominator. This apportioned characters represents the amount that we get if we bisect the numerator by the denominator. In our simple examples we had a numerator of 1.

    So, what do we beggarly by the announcement $frac$?

    When we apprehend this in English, we say two thirds. That sounds like we accept two of something, namely two thirds or two of: $frac$, which we byitself anticipate of as $2$

    Well auspiciously for our intuitions, it will about-face out that $frac\; +\; frac\; =\; frac$.

    Thinking about a atom as some allocation of a assemblage works accurately so continued as the numerator is beneath than the denominator. But what do we beggarly by $frac$? Well, intuitively, we anticipate of accepting four of $frac$, which, cerebration about huge slices of cake, haveto absolutely be according to $1\; +\; frac$. And, abiding enough, if you do the analysis of 4 by 3 youll end up with 1.33333..., which is 1 + 0.3333... or $1\; +\; frac$.

    Fractions can represent accomplished numbers, too. Annihilation but our arid admiration for artlessness and accuracy keeps us from autograph 12 as $frac$ whenever we like.

    Further capacity in fractions: