Math operations: result signs (table)
Table shows how sign of arguments (positive, negative) affect the final result for various math operations such as addition, subtraction, multiplication etc.

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 The first argument op The second argument eq Result Example I(positive result) Example II(negative result) positive number + positive number = positive number Show source$3 + 5 = 8$ Show source$-$ positive number + negative number = unknown sign(depends on arguments) Show source$3 + (-2) = 1$ Show source$3 + (-5) = -2$ negative number + positive number = unknown sign(depends on arguments) Show source$-3 + 5 = 2$ Show source$-3 + 2 = -1$ negative number + negative number = negative number Show source$-$ Show source$-3 + (-5) = -8$

# Subtraction: sign of difference#

 The first argument op The second argument eq Result Example I(positive result) Example II(negative result) positive number - positive number = unknown sign(depends on arguments) Show source$3 - 2 = 1$ Show source$3 - 5 = -2$ positive number - negative number = positive number Show source$3 - (-5) = 8$ Show source$-$ negative number - positive number = negative number Show source$-$ Show source$-3 - 5 = -8$ negative number - negative number = unknown sign(depends on arguments) Show source$-3 - (-5) = 2$ Show source$-3 - (-2) = -1$

# Multiplication: sign of product#

 The first argument op The second argument eq Result Example I(positive result) Example II(negative result) positive number × positive number = positive number Show source$3 \cdot 5 = 15$ Show source$-$ positive number × negative number = negative number Show source$-$ Show source$3 \cdot (-5) = -15$ negative number × positive number = negative number Show source$-$ Show source$-3 \cdot 5 = -15$ negative number × negative number = positive number Show source$-3 \cdot (-5) = 15$ Show source$-$

# Division: sign of quotient#

 The first argument op The second argument eq Result Example I(positive result) Example II(negative result) positive number ÷ positive number = positive number Show source$6 \div 3 = 2$ Show source$-$ positive number ÷ negative number = negative number Show source$-$ Show source$6 \div (-3) = -2$ negative number ÷ positive number = negative number Show source$-$ Show source$-6 \div 3 = -2$ negative number ÷ negative number = positive number Show source$-6 \div (-3) = 2$ Show source$-$

# Some facts#

• The sign of the number (positive or negative) obtained as a result of arithmetic operation depends both on type of operation (addition, multiplication, etc.) and the used arguments. However, there are general rules that can be helpful during performing calculations or at least sort out what we already know about various mathematical operations.

• The sum of two numbers with the same signs keep the sign of arguments. If added numbers have different signs, then the result sign is unspecified and depends on the arguments used:
• the sum of two positive numbers is always positive,
$a + b = c$
• the sum of two negative numbers is always negative,
$(-a) + (-b) = -(a + b) = -c$
• sum of numbers with different signs ("positive plus negative" or "negative plus positive") is unspecified and depends on the numbers used.
$a + (-b) = \pm c$
$-a + b = \pm c$

• The difference of two numbers with different signs gives the same sign as the minuend (the first argument, the number from which we subtract). In other cases, the result sign is unspecified and depends on the arguments used:
• subtraction of positive number from the negative one is negative,
$-a - b = -c$
• subtraction of negative number from the positive one is positive,
$a - (-b) = a + b = c$
• subtraction of two numbers with the the same signs gives a result with unspecified sign, which depends on the arguments used.
$a - b = \pm c$
$-a - (-b) = \pm c$

• Product (multiplication) or quotient (division) of two numbers with identical signs is always positive.
$a \cdot b = -a \cdot (-b) = c$
$\dfrac{a}{b} = \dfrac{-a}{-b} = c$

• If the numbers used have a different signs, the obtained product or quotient is always negative.
$a \cdot (-b) = -a \cdot b = -(a \cdot b) = -c$
$\dfrac{a}{-b} = \dfrac{-a}{b} = -\dfrac{a}{b} = -c$