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# Positive and Negative Numbers Here are rules you can use to operate on positive and negative numbers.

OperationCaseAlgebraicEnglishExample
a + bBoth positivea + bAdd in the usual way.3+4 = 7
Both negative −(|a| + |b|)Add the absolute values, then make the result negative.-3 + (-4)
= -(|-3| + |-4|)
= -(3 + 4)
= -7
One positive, one negative(Assuming |a| ≥ |b|.) If a is positive, then |a| − |b|, otherwise −(|a| − |b|)Take the difference of the absolute values; if the one with the greater absolute value is positive then the result is positive; otherwise the result is negative.3 + (-4):
First compute the difference of the absolute values:
|-4| - |3|
= 4 - 3
= 1.
Then, since |-4| >|3|, the sign of the result is negative so the result is -1.
aba + (−b)Subtraction is the same as adding the opposite, sometimes called "keep change change" (keep the sign of the first term; change the subtraction operator to an addition operator, and change the sign of the second term.)3 - (-4)
= 3 + (+4).
Then use addition rules above to compute the result.
a × bSame sign|a| × |b|Multiply the absolute values.-3 × (-4)
= |-3| × |-4|
= 3 × 4
= 12
Opposite signs−(|a| × |b|)Multiply the absolute values, then make the result negative.3 × (-4)
= -(|3| × |-4|)
= -(3 × 4)
= -12
a ÷ bJust like multiplication but divide instead of multiply.12 ÷ (-4)
= -(|12| ÷ |-4|)
= -(12 ÷ 4)
= -3

If you are comfortable with the algebraic column in the table above, you may be ready for the proof challenge!