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The sum of absolute values refers to the total obtained by taking the absolute value of each number in a set and then adding those values together. The absolute value of a number is its distance from zero on the number line, regardless of direction, meaning it is always non-negative. For example, for the set {-3, 4, -1}, the sum of absolute values would be |−3| + |4| + |−1| = 3 + 4 + 1 = 8. This concept is often used in mathematics and statistics to analyze data without regard to sign.
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Is the sum of an absolute value is the same of their absolute values?
The sum of the absolute values of two numbers is greater or equal than the absolute values of the sum. It will be equal if both are positive or both are negative; greater if one is positive and one is negative. Try it out with some sample numbers!
Can you use the distributive property in absolute values?
Yes, you can apply the distributive property in expressions involving absolute values, but it's important to consider the properties of absolute values. The distributive property states that ( a(b + c) = ab + ac ), and this can be used with absolute values, such as ( |a(b + c)| = |ab + ac| ). However, the absolute value of a sum is not necessarily equal to the sum of the absolute values, meaning ( |a + b| \neq |a| + |b| ) in general. Thus, careful attention is needed when manipulating expressions involving absolute values.
When is the sum of a positive integer and a negative integer zero?
When the absolute value of the positive integer is the same as the absolute value of the negative one.
Why is the sum of a negative number and a positive number is sometimes positive sometimes negative and sometimes zero?
The sum of a negative number and a positive number can be positive, negative, or zero depending on their absolute values. If the positive number has a greater absolute value than the negative number, the result is positive. Conversely, if the negative number has a greater absolute value, the result is negative. If their absolute values are equal, the sum equals zero.
How can you tell if adding two rational numbers with different is a positive negative or zero?
Consider the absolute values (the numerical values ignoring the signs) of the two numbers. If these are equal then the sum is equal; otherwise the sum takes the sign of which ever number has the larger absolute value.
Is the sum of an absolute value is the same of their absolute values?
The sum of the absolute values of two numbers is greater or equal than the absolute values of the sum. It will be equal if both are positive or both are negative; greater if one is positive and one is negative. Try it out with some sample numbers!
Can you use the distributive property in absolute values?
Yes, you can apply the distributive property in expressions involving absolute values, but it's important to consider the properties of absolute values. The distributive property states that ( a(b + c) = ab + ac ), and this can be used with absolute values, such as ( |a(b + c)| = |ab + ac| ). However, the absolute value of a sum is not necessarily equal to the sum of the absolute values, meaning ( |a + b| \neq |a| + |b| ) in general. Thus, careful attention is needed when manipulating expressions involving absolute values.
What is greater than the number in a pair?
The value of the sum of their absolute values is one possible answer.
How can you decide if the sum of two numbers is positive negative or zero without actually calculating the sum?
The sum of two positive numbers is always positive, and the sum of two negatives is always negative. If you have a positive and a negative number, there sum can be either, so look at the absolute values to decide. For example -3+2=-1. Since all you care about is the sign, look at the absolute value. If the negative number has a greater absolute value, the sum is negative and if the positive number's absolute value, which is the number itself, is bigger, the sum is positive. If the absolute values are equal, the sum is 0.
How can you decide if the sum of two numbers is positive negative or zero without calculating the sum?
The sum of two negative numbers is positive and the sum of two negatives is negative. If you have both positive and negative numbers the sum can be either so look at the absolute value. If the negative number has a greater absolute value, the sum is negative. If the positive number has a greater absolute value the sum is positive. If the absolute values are equal, the sum is zero.
The difference of a negative integer and a positive integer is?
An integer that is equal in magnitude to the sum of their absolute values. Its sign is the same as which of the two numbers you are taking the difference from. For example, for the integers 5 and -7. Their absolute values are 5 and 7 so that the sum of the absolute values is 5+7 = 12. Then 5 - (-7) = +12 and -7 - 5 = -12.
When is the sum of a positive integer and a negative integer zero?
When the absolute value of the positive integer is the same as the absolute value of the negative one.
When is true that absolute value of x plus y equals sum of their individual absolute values?
When 'x' and 'y' both have the same sign.
Why is the sum of a negative number and a positive number is sometimes positive sometimes negative and sometimes zero?
The sum of a negative number and a positive number can be positive, negative, or zero depending on their absolute values. If the positive number has a greater absolute value than the negative number, the result is positive. Conversely, if the negative number has a greater absolute value, the result is negative. If their absolute values are equal, the sum equals zero.
How can you tell if adding two rational numbers with different is a positive negative or zero?
Consider the absolute values (the numerical values ignoring the signs) of the two numbers. If these are equal then the sum is equal; otherwise the sum takes the sign of which ever number has the larger absolute value.
What is triangular inequality of complex number?
The absolute value of the sum of two complex numbers is less than or equal to the sum of their absolute values.
When is the sum of a positive and negative integer negative?
When the absolute value of the positive integer is smaller than the absolute value of the negative one.
