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

lookagain

Elite Member
Joined
Aug 22, 2010
Messages
3,259
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:

4+44/44\displaystyle 4 + 44/44
 
Re: Order of Operations -- Use five 4s to make the value of

4+4-4+4/4
4(4/4)+4/4
 
Re: Order of Operations -- Use five 4s to make the value of

Loren said:
4+4-4+4/4 . . . . Sorry, this cannot contain a minus/negative/subtraction sign.\displaystyle Sorry, \ this \ cannot \ contain \ a \ minus/negative/subtraction \ sign.

4(4/4)+4/4 . . . . . Good one!\displaystyle Good \ one!
 
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
 
Re: Order of Operations -- Use five 4s to make the value of

Denis said:
4 / 4 * (4 + 4 / 4) . . . . Checks.\displaystyle Checks.

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

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


More examples?
 
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:


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

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

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

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

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

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

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

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

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

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

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