difference between 'sign of number', 'sign of operation'...?
- Thread starter taragbeh
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The sign of a number is either a "plus sign" (+) or a "negative sign" (-). It tells which direction on the number line that the number in question lies. A +3 lies 3 units to the right of zero. A -3 lies 3 units to the left of zero.
The sign of an operation tells you whether to add, subtract, multiply, or divide. The plus sign (+) is also used to indicate addition and the minus sign (-) is used to indicate subtraction. 5 + 3 = 8 which really means "a positive 5 added to a positive 3 equals a positive 8, or (+5) + (+3) = (+8). The absence of a sign immediately preceding a number is assumed to be a positive.
5 - 3 = 2 means (+5) - (+2) = (+3).
5 - (-3) means a negative 3 subtracted from a positive 5 or (+5) - (-3) which becomes (+5) + (+3) = +8.
One of the difficulties is that the plus sign has more than one meaning. It may mean "positive" as in "+3 is 3 units to the right of zero on the number line." It also may mean to add the two numbers on each side of it as in "3 + 5 = 8" Also, a plus sign might mean "the opposite of" as in "a negative 3 is the opposite of a positive 3" which symbolically is written "-3 = -(+3)".
I could go on, but I won't.
The sign of an operation tells you whether to add, subtract, multiply, or divide. The plus sign (+) is also used to indicate addition and the minus sign (-) is used to indicate subtraction. 5 + 3 = 8 which really means "a positive 5 added to a positive 3 equals a positive 8, or (+5) + (+3) = (+8). The absence of a sign immediately preceding a number is assumed to be a positive.
5 - 3 = 2 means (+5) - (+2) = (+3).
5 - (-3) means a negative 3 subtracted from a positive 5 or (+5) - (-3) which becomes (+5) + (+3) = +8.
One of the difficulties is that the plus sign has more than one meaning. It may mean "positive" as in "+3 is 3 units to the right of zero on the number line." It also may mean to add the two numbers on each side of it as in "3 + 5 = 8" Also, a plus sign might mean "the opposite of" as in "a negative 3 is the opposite of a positive 3" which symbolically is written "-3 = -(+3)".
I could go on, but I won't.
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- Apr 12, 2005
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It is, admittedly, a little duplicitous. The best answer, I think, is that it doesn't much matter.
What is the nature of the "-" in this expression.
x - 5 = 2 -- Here, it appears to mean SUBTRACTION
If we now subtract 'x' from both sides:
-5 = 2 - x -- That same "-" has magically changed to a NEGATIVE SIGN.
If I write it like this:
-(5) = 2 - x -- Now it appears to mean MULTIPLICATION BY -1.
So what...
From either of the first two expressions, what happens when we add five to both sides.
x - 5 = 2 ==> x = 2 + 5
- 5 = 2 - x ==> 0 = 2 - x + 5
Okay, whichever one it was on the left, it has gone away and both resulted it ADDITION on the right.
Have I convinced you?
Some symbols have multiple interpretations. Sometimes it matters.
What is the nature of the "-" in this expression.
x - 5 = 2 -- Here, it appears to mean SUBTRACTION
If we now subtract 'x' from both sides:
-5 = 2 - x -- That same "-" has magically changed to a NEGATIVE SIGN.
If I write it like this:
-(5) = 2 - x -- Now it appears to mean MULTIPLICATION BY -1.
So what...
From either of the first two expressions, what happens when we add five to both sides.
x - 5 = 2 ==> x = 2 + 5
- 5 = 2 - x ==> 0 = 2 - x + 5
Okay, whichever one it was on the left, it has gone away and both resulted it ADDITION on the right.
Have I convinced you?
Some symbols have multiple interpretations. Sometimes it matters.