eolas/neuron/10a99c7d-3445-4f21-a0e2-3c028de3bb75/Reciprocals.md
2024-10-23 15:05:28 +01:00

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tags
prealgebra
fractions
theorems

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}