What is the absolute value of -7 3/5?

To determine the absolute value of -7 3/5, we need to understand what absolute value means and how it applies to this specific case. The absolute value of a number represents its distance from zero on a number line, regardless of whether the number is positive or negative.

To calculate the absolute value of a mixed number like -7 3/5, we convert it to an improper fraction first. Thus, -7 3/5 can be written as (-7 * 5 + 3)/5, which simplifies to -38/5. Applying the absolute value concept, we disregard the sign and consider only the magnitude. Therefore, the absolute value is 38/5.

FAQs

Q1: What does the absolute value of a number represent?

The absolute value of a number represents its distance from zero on a number line, regardless of its sign.

Q2: How can you calculate the absolute value of a mixed number?

To calculate the absolute value of a mixed number, convert it to an improper fraction, ignore the sign, and determine the magnitude.

Q3: How do you convert a mixed number to an improper fraction?

To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction, add the numerator, and place the result over the original denominator.

Q4: What is the importance of disregarding the sign when finding the absolute value?

Disregarding the sign ensures that we only consider the magnitude or distance from zero, as the absolute value represents.

Q5: Is the absolute value of any negative number always positive?

Yes, the absolute value of any negative number is always positive. It reflects the magnitude or distance from zero, regardless of the sign.

Q6: What is the absolute value of 0?

The absolute value of 0 is 0 itself since it lies exactly at the origin of the number line.

Q7: Is the absolute value of a positive number the same as the number itself?

Yes, since a positive number already reflects the distance from zero, its absolute value is equal to the number itself.

Q8: Can the absolute value of a fraction be a mixed number?

No, the absolute value of a fraction cannot be a mixed number. It is always expressed as an improper fraction or a terminating decimal.

Q9: How would the absolute value of a negative number be written as a math expression?

The expression for the absolute value of a negative number involves enclosing the number within vertical bars or applying the absolute function, e.g., | -3 | or abs(-3).

Q10: Is the absolute value of a number always greater than or equal to zero?

Yes, since the absolute value represents a distance, it is always equal to or greater than zero. Thus, it can never be negative.

Q11: Can the absolute value of a number be a decimal or fraction?

Yes, the absolute value of a number can be a decimal or fraction. It depends on the nature of the number being considered.

Q12: Does the absolute value of a number affect its operations?

When performing operations on numbers, the absolute value does not affect addition, subtraction, and multiplication, but it may impact division and comparisons, depending on the context.

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