Additive opposites MUST have the same absolute values.
The absolute value is always non-negative. So, the absolute values of zero and positive integers are the same as the numbers. However, the absolute values of negative integers are their additive inverses or additive opposites (or positive equivalents).Thus, for example, abs(-3) = +3
Yes.
No, an integer and its absolute value are not always opposites. The absolute value of an integer is always non-negative, while the integer itself can be negative, zero, or positive. For example, the integer -5 has an absolute value of 5, which are opposites, but the integer 0 has an absolute value of 0, making them the same. Thus, they are only opposites when the integer is negative.
Different.
X and Y have the same absolute value because the opposite of a number doesn't change its distance from zero. The absolute value of a number represents its distance from zero on the number line, and since X and Y are opposites, they have the same distance from zero.
All numbers have opposites that are the same as their absolute values.
The absolute value of the answer is the difference between the absolute values of the two numbers and the sign associated with it is the same as that of the number with the greater absolute value.
The absolute value is always non-negative. So, the absolute values of zero and positive integers are the same as the numbers. However, the absolute values of negative integers are their additive inverses or additive opposites (or positive equivalents).Thus, for example, abs(-3) = +3
yes
Yes.
Different.
X and Y have the same absolute value because the opposite of a number doesn't change its distance from zero. The absolute value of a number represents its distance from zero on the number line, and since X and Y are opposites, they have the same distance from zero.
Two numbers that are the same distance from zero on a number line are called "opposites." For example, +5 and -5 are opposites, as they are equidistant from zero but lie on opposite sides of it. They have the same absolute value but different signs.
A positive and negative number with the same magnitude (value) will have their absolute values equal.
If the signs are the same, add the absolute values and keep the sign. If the signs are different, subtract the lesser absolute value from the greater absolute value and keep the sign of the number with the greater absolute value.
Adding integers, if they have the same sign, add their absolute values and keep the same sign. Subtracting, change the sign of the 2nd number and the add using rules of addition. Multiplying and dividing, Divide the absolute values, if the signs are the same the answer is positive, if the signs are different the answer is negative.
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