# Beta version

BETA TEST VERSION OF THIS ITEM

This online calculator is currently under heavy development. It may or it may NOT work correctly.

You CAN try to use it. You CAN even get the proper results.

However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.

Feel free to send any ideas and comments !

This online calculator is currently under heavy development. It may or it may NOT work correctly.

You CAN try to use it. You CAN even get the proper results.

However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.

Feel free to send any ideas and comments !

# Addition: sign of sum

The first argument | The second argument | 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 | The second argument | 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 | The second argument | 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 | The second argument | 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 sum of two
- 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$

- subtraction of
**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$

# Tags and links to this website

Tags:

math_operations_signs · signs_of_arithmetic_operations · addition_result_sign · subtraction_result_sign · multiplication_result_sign · division_result_sign · sum_sign · difference_sign · product_sign · quotient_sign

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