What number could replace

below?`SYMBOL`

`FIRST` `OP` `SECOND` = `FAKE_SECOND` `OP` `FAKE_FIRST`

`ANSWER`

With `OP_WORD`, the order of the two `ADDENDS` does not matter.

Evaluating the left side:

`FIRST` `OP` `SECOND` = `RESULT`

Re-ordering the `ADDENDS` and evaluating:

`SECOND` `OP` `FIRST` = `RESULT`

We see that re-ordering the `ADDENDS` did not affect the final result:

`FIRST` `OP` `SECOND` = `SECOND` `OP` `FIRST`

Comparing with the original equation, the symbol

could be replaced with the number `SYMBOL`

.`ANSWER`

This fact about `OP_WORD` is known as the commutative property.

What number could replace

below?`SYMBOL`

`FIRST_OPEN``TERMS[ 0 ]`
`OP``SECOND_OPEN``TERMS[ 1 ]``FIRST_CLOSE`
`OP``TERMS[ 2 ]``SECOND_CLOSE` =
`SECOND_OPEN``FAKE_TERMS[ 0 ]`
`OP``FIRST_OPEN``FAKE_TERMS[ 1 ]``SECOND_CLOSE`
`OP``FAKE_TERMS[ 2 ]``FIRST_CLOSE`

`ANSWER`

With `OP_WORD`, the parentheses around the `ADDENDS` do not affect the final result.

Evaluating the left side:

`FIRST_OPEN``TERMS[ 0 ]`
`OP``SECOND_OPEN``TERMS[ 1 ]``FIRST_CLOSE`
`OP``TERMS[ 2 ]``SECOND_CLOSE` = `FIRST_OPEN === "(" ? FIRST_PAIR : TERMS[ 0 ]` `OP` `FIRST_OPEN === "(" ? TERMS[ 2 ] : SECOND_PAIR` = `FINAL_RESULT`

Changing the grouping and evaluating:

`SECOND_OPEN``TERMS[ 0 ]`
`OP``FIRST_OPEN``TERMS[ 1 ]``SECOND_CLOSE`
`OP``TERMS[ 2 ]``FIRST_CLOSE` = `SECOND_OPEN === "(" ? FIRST_PAIR : TERMS[ 0 ]` `OP` `SECOND_OPEN ==="(" ? TERMS[ 2 ] : SECOND_PAIR` = `FINAL_RESULT`

We see that moving the parentheses did not affect the final result:

`FIRST_OPEN``TERMS[ 0 ]`
`OP``SECOND_OPEN``TERMS[ 1 ]``FIRST_CLOSE`
`OP``TERMS[ 2 ]``SECOND_CLOSE` = `SECOND_OPEN``TERMS[ 0 ]`
`OP``FIRST_OPEN``TERMS[ 1 ]``SECOND_CLOSE`
`OP``TERMS[ 2 ]``FIRST_CLOSE`

Comparing with the original equation, the symbol

could be replaced with the number `SYMBOL`

.`ANSWER`

This fact about `OP_WORD` is known as the associative property.