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Why does multiplication or division with a negative number yield a negative answer?
The assertion in the question is not always true. Multiplying (or dividing) 0 by a negative number does not yields 0, not a negative answer.
Leaving that blunder aside, let p and q be positive numbers so that p*q is a positive number.
Then
p*q + p*(-q) = p*[q + (-q)] = p*[q - q] = p*0 = 0
that is p*q + p*(-q) = 0
Thus p*(-q) is the additive opposite of p*q, and so, since p*q is positive, p*(-q) must be negative.
A similar argument works for division.
What else can I help you with?
What are the rules of cubing for negative numbers?
the same as all integer exponents, repeated multiplication the indicated number of times. Negative numbers when cubed yield negative numbers.
Why do negative and negative become positive?
A negative and a negative can yield a positive result in some cases.SubtractionSubtracting a negative number is the same as adding its negative value, which is positive. So if the subtracted number is larger in value, the answer will be positive.(-4) - (-3) = (-4) + 3 = (-1) * the subtracted number was not large enough(-4) - (-8) = (-4) + 8 = 4 *the subtracted number was large enough to yield a positiveMultiplication and DivisionWhenever a negative number and a negative number are multiplied or divided, the negative signs "cancel out" and the result is positive.(-2) x (-3) = 6(-6) / (-3) = 2A multiplication or division involving one negative and one positive will, however, have a negative result.
What is the identity element of division?
The identity element of division is not defined in the same way as it is for addition or multiplication. In the case of addition, the identity element is 0, and for multiplication, it is 1. Division does not have an identity element because there is no number that, when divided by another number, will yield the original number for all cases. Specifically, for a number ( a ), ( a \div b ) does not equal ( a ) for any ( b ) other than 1.
When your multiplying a positive and a negative with the answer be a positive?
When you multiply a positive number by a negative number, the result is always negative, not positive. This is because multiplication can be thought of as repeated addition, and adding a negative value reduces the total. Therefore, the product of a positive and a negative number will never yield a positive result; it will always be negative.
What combination of signed numbers always leads to a positive number?
If I understand the question correctly, the sum of two positive numbers will *always* yield a positive number. The product of two positive or two negative numbers will always yield a positive number. The division of two positive or two negative numbers will always yield a positive number. There are more examples along this line. I am not sure if this is what you wanted to know.
How do you use positive number in a sentence?
A negative number multiplied by a negative number will yield a positive number.
When you take a negative number to an odd power you get a negative answer Why do you get a positive answer when you take an odd number to an even power?
When you raise a negative number to an odd power, the multiplication of an odd number of negative factors results in a negative product. In contrast, raising a negative number to an even power involves multiplying it by itself an even number of times, which pairs up the negative factors to yield a positive product. This is due to the fact that multiplying two negative numbers produces a positive result. Thus, the overall effect of multiplying an even number of negative factors is positive.
What multiplication facts that equals 9?
The multiplication facts that equal 9 are 1 x 9, 3 x 3, and 9 x 1. These combinations demonstrate how the number 9 can be achieved through multiplication. Additionally, negative pairs like -1 x -9 and -3 x -3 also yield 9.
What does negative 3 look like as a quotient?
Negative 3 as a quotient can be expressed as the result of dividing two numbers, such as -6 ÷ 2 or -9 ÷ 3, both of which equal -3. In general, any division where the numerator is a negative number and the denominator is a positive number, or vice versa, will yield a negative quotient. For example, -15 ÷ 5 also equals -3.
What cube be the negative number is always?
The cube of a negative number is always negative. This is because multiplying three negative numbers together results in a negative product. For example, ((-2)^3 = -8). Thus, any negative number cubed will yield a negative result.
What its the identity for multiplicarion of real numbers?
The identity for multiplication of real numbers is the number 1. This means that for any real number ( a ), multiplying it by 1 will yield the same number: ( a \times 1 = a ). This property is fundamental in arithmetic and algebra, as it helps maintain the value of numbers during multiplication.
How do you multiple and divide positive and negative integers?
multiplying and dividing a negative number will "flip" the sign of the other number. So multiplying two negative numbers will produce a positive number. Multiplying one positive and one negative number will produce a negative. And of course two positive numbers yield a positive.
