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Why is it that multiplying two negative integers gives a positive result but multiplying two positive integers cannot give a negative result?
It is well known that if you multiply a positive number (it doesn't have to be an integer) by another positive number the result is always a positive number.
For example (+2.3) x (+2) = +4.6 Similarly, at school you learn that if you multiply a positive number by a negative number the result is always a negative number.
For example (+19) x (-2) = -38 When you multiply two negative numbers you must get a positive result because of the way negative numbers "work", but why that is so is not usually explained at junior or high school. You learn why as part of learning about complex numbers in higher math at technical college or university. To be very brief, it is all to do with the behaviour of the operator "i". (For more information about it please see the answer to the related question shown below.) Because i2 is defined to be equal to -1 then it follows that i2 x i2 = +1 for the following reason: multiplying something by i2 means "apply the operator i twice" so, if you start with a positive number, multiplying it by i2 makes that positive number into a negative number. If you multiply that negative number by i2 again you make the result into a positive number. Overall you are applying the operator i four times so you can say that i2 x i2 (which is the same as i4) means "apply the operator i four times" and doing that gives a result which is a positive number. For example (-1) x (-2) = +2 could be written as: [(+1) x i2] x [(+2) x i2] = +2 x [(i2 x i2)] = +2 or even as (+1) x i2 x (+2) x i2 = +2 x i4 = +2
What else can I help you with?
Can 1.56 be an integer?
1.56 cannot be an integer, since the set of integers do not include any decimal numbers, only whole numbers, negative or positive (including 0).
What is te square root of -120 to the nearest integers?
The square root of a negative number cannot be expressed with integers. The square root of a negative number is always imaginary.
Is a negative a positive is what?
A Negative plus a positive = a negative because negative and a positive cannot work together Negative + Negative= Positive Positive + Positive = Positive when your dealing with numbers such as : -2 + 2 would equal a negative 4 -2 +-2 would equal a positive 4
Why does the product of an integer multiplied by itself cannot be negative?
There are just three possible cases: Positive integer: positive x positive = positive. Negative integer: negative x negative = positive. Zero: zero x zero = zero.
Why can't you factor negative radical numbers?
You cannot factor negative radical numbers because the square of a number must always be positive. A negative number multiplied by a negative number produces a positive number. So, it is impossible to have a negative radical.
What can you conclude about the signs of two integers whose product is positive and negative?
The product of two integers cannot be "positive and negative".
What are two positive integers that have a sum of -18 and a product of 88?
Two positive integers cannot have a sum which is negative!
Can any negative integer be greater than a positive integer explain?
No, a negative integer cannot be greater than a positive integer. By definition, negative integers are to the left of zero on the number line, while positive integers are to the right. Since all negative integers are less than zero, they are always less than any positive integer. Thus, negative integers are always smaller than positive integers.
can the difference of two positive integers always be negative?
No, the difference of two positive integers cannot always be negative. In fact, the difference will be negative only when the first integer is smaller than the second. If the first integer is greater than or equal to the second, the difference will be zero or positive.
Can integer be negative fractions?
No, integers cannot be negative fractions. Integers are whole numbers that can be positive, negative, or zero, but they do not include fractional or decimal components. Negative fractions, on the other hand, are rational numbers that represent parts of a whole, which is distinct from the definition of integers.
How do you get a pair of negative integers that have the sum of five?
You cannot. The sum of negative integers will be negative.
What is consecutive Negative integers of 440?
Consecutive negative integers that sum to 440 would be integers that are sequentially negative and add up to that positive number. For example, the integers -1, -2, -3, and so forth are negative integers, but their sum cannot reach 440 since they are all negative. If you meant the consecutive negative integers that multiply to give -440, those could be -20 and -22, as they are consecutive and their product is 440.
What characteristic can integers have that whole numbers cannot?
Integers can be negative.
What is the difference between directed number and integers?
Directed numbers have a positive or negative sign associated with them. (The positive sign may be implied). They can be rational fractions (including mixed numbers) or irrational. Integers cannot be fractions or irrational.
What are the common misconceptions of integers?
Common misconceptions about integers include the belief that they only represent positive whole numbers, while in fact, integers encompass both positive and negative whole numbers, as well as zero. Another misconception is that the absolute value of an integer can be negative; however, the absolute value is always non-negative. Additionally, some may think that integers cannot be fractions or decimals, but this is accurate since integers are strictly whole numbers. Lastly, there can be confusion around operations, such as assuming that subtracting a larger integer from a smaller one always results in a positive outcome, when it can produce a negative result.
Is 0.1 a integer?
Integers are whole numbers, either positive or negative. They cannot be fractions or decimal numbers.
Why is the product of of two negative integers always negative?
The question cannot be answered because it is based on the wrong premise that "the product of two negative integers always negative".
