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Recipricols
The Property of Multiplicative Identity applies to fractions as well as to whole numbers:
\frac{a}{b} \cdot 1 = \frac{a}{b}
With fractions there is a related property: the Multiplicative Inverse.
If
\frac{a}{b}is any fraction, the fraction\frac{b}{a}is called the multiplicative inverse or reciprocol of\frac{a}{b}. The product of a fraction multiplied by its reciprocol will always be 1.\frac{a}{b} \cdot \frac{b}{a} = 1$$
For example:
\frac{3}{4} \cdot \frac{4}{3} = \frac{12}{12} = 1
In this case \frac{4}{3} is the reciprocol or multiplicative inverse of
\frac{3}{4}.
This accords with what we know a fraction to be: a representation of an amount that is less than one whole. When we multiply a fraction by its reciprocol, we demonstrate that it makes up one whole.
This also means that whenever we have a whole number n, we can represent it
fractionally by expressing it as \frac{n}{1}