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Here is a proof.
Let a and b be any two real numbers. Consider the number x defined as
x = ab + (-a)(b) + (-a)(-b).
We can write this out differently as
x = ab + (-a)[ (b) + (-b) ]
Then, by factoring out -a , we find that x= ab + (-a)(0) = ab + 0 = ab.
Also,
x = [ a + (-a) ]b + (-a)(-b)
And by factoring out b, we find that x=0 * b + (-a)(-b) = 0 + (-a)(-b) = (-a)(-b).
Therefore x = ab and x = (-a)(-b)
Then, by the transitivity of equality, we have
ab = (-a)(-b).
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The quotient of a negative integer and a positive integer is?
The quotient of a positive integer by a negative is always negative. Say this to yourself a couple times: "MULTIPLICATION: minus times minus is plus (negative x negative = positive).....minus times plus is minus (negative x positive = negative).....plus times plus is plus (positive x positive = positive) DIVISION: minus divi minus is plus (negative ÷ negative = positive)......minus divi plus is minus (negative ÷ positive = negative).....plus divi plus is plus (positive ÷ positive = positive)"
When a negative number is cubed is it negative or a positive number?
I think that it's a negative number, as a negative times a negative is a positive, and a positive times a negative is a negative, but I could be wrong. (DUN-DUN--DUUUUUN...)
How can we predict the sign of the product or quotient of sign numbers?
positive times positive equals positive negative times negative equals positive positive times negative equals negative Substitute "divided by" for "times" in the previous sentences and they are still true.
Why is the product of a positive integer and a negative integer a negative integer?
I honestly don't know :D but heres something to help you "MULTIPLICATION: minus times minus is plus (negative x negative = positive).....minus times plus is minus (negative x positive = negative).....plus times plus is plus (positive x positive = positive) DIVISION: minus divi minus is plus (negative ÷ negative = positive)......minus divi plus is minus (negative ÷ positive = negative).....plus divi plus is plus (positive ÷ positive = positive)"
Is it possible for the product of two consecutive integers to be negative?
No, a negative times a negative would be a positive and a positive times a positive would also be positive, and anything multiplied by zero would still be zero
What are rules in dividing integers?
negative times negative = positive positive times positive = positive negative times positive = negative positive times negative = negative
Negative times a positive equals?
positive times negative equals negative. positive times positive equals positive. negative times negative equals positive
What are the negative and positive rules in math?
A negative times a negative equals a positive A negative times a positive equals a negative A positive times a positive equals a positive
A negative times or divided by a positive equals a?
A Negative times or divided by a Positive equals a Negative A Negative times or divided by a Negative gives a Positive A Positive times or divided by a Negative gives a Negative A Positive times or Divided by a Positive gives a Positive Zero is neither Positive or Negative so anything times Zero is not Positive or Negative.
Is a negative times a positive a negative?
A negative times a positive is a negative.
Is a negative divided by a negative the same as a positive times a positive?
Well a negative times a negative equals a positive while as a positive times a positive equals a positive.
Would a positive multiplied by a negative be a positive?
No. A positive times a negative is always negative. A negative times a negative is always a positive.
What is a positive times a negative?
It is a negative. Always remember this: -A positive times a positive equals a negative -A negative times a negative equals a positive -A negative times a positive equals a negative *This works ONLY for addition and multiplication I hope this info helped you! :)
Is a negative divided by a negative a positive number?
negative times negative is positive negative divided by a negative is a postive negative times a positive is a negative negative divided by a positive is a negative
Positive times a negitive?
A negative times a negative equals a positive
What is a negitaive times a positive?
A negative number times a positive number will give you a negative product.A negative number times a positive number will give you a negative product.A negative number times a positive number will give you a negative product.A negative number times a positive number will give you a negative product.
What is a negative times a positive and will it be negative or positive?
It will be a negative.
