Four Fours/1

Puzzle

Using exactly $4$ instances of the number $4$, the task is to write an expression for $1$, using whatever arithmetical operations you consider necessary.

Solutions

Solution $1$

$1 = \dfrac {4 + 4} {4 + 4}$

Solution $2$

$1 = \dfrac {4 \times 4} {4 \times 4}$

Solution $3$

$1 = \dfrac {4 / 4} {4 / 4}$

Solution $4$

$1 = \dfrac 4 4 \times \dfrac 4 4$

Solution $5$

$1 = 4 - 4 + \dfrac 4 4$

Solution $6$

$1 = \dfrac {44} {44}$

General Solutions

Let $\map {e_n} m$ be an expression which uses $n$ instances of $4$ to make $m$.

Then we have:

General Solution $1$

$1 = \dfrac {\map {e_2} m} {\map {e_2} m}$

where $m \in \N$ is arbitrary.

General Solution $2$

$1 = \dfrac {\map {e_1} m} {\map {e_3} m}$

where $m \in \N$ is arbitrary.

Also see

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