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If the product of two numbers is positive then the two numbers must both be positive?
No! If one number is negative and the positive is greater than it's interval (positive version [e.g. the interval of -6 is 6]), then the product will very well be positive. In theory, of course. Sorry, tenth grader speaking...
Small error here; product is the result of multiplication. The answer above is correct for a sum, but not a product.
The rule for a product is even simpler than for a sum :- If the two numbers have the same signs (both positive or both negative) then the result will be positive. If the numbers have different signs the result will be negative.
What else can I help you with?
Is the product of an even number of negative numbers positive?
Yes because the product of each pair of negative numbers must be positive.
If the quotient of two numbers is positive then both numbers must be positive?
Yes, but not always because the quotient of two negative numbers will be positive as for example -6/-2 = 3
Is the product of two positive mixed numbers ever less then 1?
No. A mixed number must be greater than 1, and two numbers that are greater than one that are multiplied together end up being greater that either number by itself.
What two numbers multiply to get 30 and add to get 1?
31
If the product of two numbers are even then the two numbers must both be even?
No. If you have an odd number (for example 5) and an even number (say 2) and you multiply them together, you will get an even number (10). Therefore, just because the product of two numbers are even does not make both the numbers being multiplied together even (although at least one must be).
If two positive numbers sum to N what must the numbers be so that their product is maximum?
Both must be the positive square root of N.
Is the product of an even number of negative numbers positive?
Yes because the product of each pair of negative numbers must be positive.
What is the product of two numbers is zero?
One or both of the numbers must be zero.
If the quotient of two numbers is positive then both numbers must be positive?
Yes, but not always because the quotient of two negative numbers will be positive as for example -6/-2 = 3
How would you Explain how you would decide whether the product of three numbers is positive or negative?
If all three numbers are positive then the product obviously has to be positive. If TWO of the three numbers are negative, then the product is also positive. But if exactly ONE of the three numbers is negative or if all THREE are negative, then the product must be negative. In general, a product of numbers is negative if an ODD NUMBER of the terms is negative.
Is the product of two positive mixed numbers ever less then 1?
No. A mixed number must be greater than 1, and two numbers that are greater than one that are multiplied together end up being greater that either number by itself.
Find a counterexample to show that the conjecture is false?
if the qoutient of two numbers is positive, then both numbers must be a rectangle.
If the product of two numbers is even then the two numbers must be even?
At least one of the two numbers has to be even, but both can be even.
What two numbers multipled together equal1728 and add together equal 2?
1730
Explain Why the product of two nonzero absolute values is always a positive number?
The absolute value of a number is its distance from zero on the number line, so it is always non-negative. When you multiply two nonzero absolute values, you are essentially multiplying two non-negative numbers together. In multiplication, a positive number multiplied by a positive number always results in a positive number, hence the product of two nonzero absolute values is always positive.
What two numbers multiply to get 30 and add to get 1?
31
If the product of two numbers are even then the two numbers must both be even?
No. If you have an odd number (for example 5) and an even number (say 2) and you multiply them together, you will get an even number (10). Therefore, just because the product of two numbers are even does not make both the numbers being multiplied together even (although at least one must be).
