32 lines
1 KiB
Markdown
32 lines
1 KiB
Markdown
---
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categories:
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- Mathematics
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tags:
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- prealgebra
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- fractions
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- theorems
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---
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# Recipricols
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The [Property of Multiplicative Identity](Multiplicative%20identity.md) applies to fractions as well as to whole numbers:
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$$
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\frac{a}{b} \cdot 1 = \frac{a}{b}
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$$
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With fractions there is a related property: the **Multiplicative Inverse**.
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> 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. $$ \frac{a}{b} \cdot \frac{b}{a} = 1$$
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For example:
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$$
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\frac{3}{4} \cdot \frac{4}{3} = \frac{12}{12} = 1
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$$
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In this case $\frac{4}{3}$ is the reciprocol or multiplicative inverse of $\frac{3}{4}$.
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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.
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This also means that whenever we have a whole number $n$, we can represent it fractionally by expressing it as $\frac{n}{1}$
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