Order of Operations -- Use five 4s to make the value of 5

[lookagain]

My problem
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Type out as many expressions as you can that are equal to a value of five.


What you may use:
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You must use exactly five 4s

Optional concatenation (digits forming a longer number)

Unlimited plus signs - - -> "+"

Unlimited division signs - - -> "/"

Unlimited sets of parentheses for grouping and/or multiplication - - -> "( )"

No other digits, no other operations, no exponentiation, no other symbols

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Example:

\(\displaystyle 4 + 44/44\)

 

[Loren]

Re: Order of Operations -- Use five 4s to make the value of

4+4-4+4/4
4(4/4)+4/4

 

[lookagain]

Re: Order of Operations -- Use five 4s to make the value of

4+4-4+4/4 . . . . \(\displaystyle Sorry, \ this \ cannot \ contain \ a \ minus/negative/subtraction \ sign.\)

4(4/4)+4/4 . . . . . \(\displaystyle Good \ one!\)

 

[Denis]

Re: Order of Operations -- Use five 4s to make the value of

4 / 4 * (4 + 4 / 4)

4 * 4 / 4 + 4 / 4

4 / 4 / 4 * 4 + 4

 

[lookagain]

Re: Order of Operations -- Use five 4s to make the value of

4 / 4 * (4 + 4 / 4) . . . . \(\displaystyle Checks.\)

4 * 4 / 4 + 4 / 4 . . . . \(\displaystyle Checks.\)

4 / 4 / 4 * 4 + 4 . . . . \(\displaystyle Checks.\)

More examples?

 

[lookagain]

Re: Order of Operations -- Use five 4s to make the value of

You can look for redundancies in the following, but here are additional ways:

Edits follow:


\(\displaystyle 4(4 + 4/4)/4\)

\(\displaystyle 4 + (4 + 4)/(4 + 4)\)

\(\displaystyle (4 + 4/4)/4(4)\)

\(\displaystyle 4 + 4(4)/(4(4))\)

\(\displaystyle 4 + 4(4)/4/4\)

\(\displaystyle 4/(4/(4 + 4/4))\)

\(\displaystyle 4 + 4(4/((4)(4))\)

\(\displaystyle 4 + 4/4(4/4)\)

\(\displaystyle 4 + 4/(4(4)/4)\)

\(\displaystyle 4 + 4/((4)(4))4\)

\(\displaystyle 4 + (4/4)4/4\)