Question

What is the absolute value of 45?

Answer 1

Hint: The absolute value or modulus of any number x, denoted\[\left| x \right|\], is just the non-negative value of x without reference to its sign. Namely, \[\left| x \right| = x\] if x is positive, and \[\left| x \right| = - x\]if x is negative (in which case x is positive), and |0| = 0. Absolute value of any number is also thought of as its distance from zero.

Complete step-by-step solution:
Absolute value of any real number, x is denoted as \[\left| x \right|\].
Thus, according to the question, Absolute value of 45 is \[\left| {45} \right|\].
By definition we know the absolute value of any real number is its positive value, and only the positive value.
Therefore, \[\left| {45} \right|\]is nothing but 45 itself as 45 is a positive number.
From an analytical geometry point of view, the absolute value of any real number is that number's distance from zero along the number line, and more generally the absolute value of the difference of two real numbers is that the distance between them.

Note: Absolute value has properties that are used in generalization of expressions. They are,
$|a| \geqslant 0$, also read as “Absolute values are non-negative”.
$|a| = 0 \Leftarrow \Rightarrow a = 0$, also known as property of positive definitiveness.
$|ab| = |a|{\mkern 1mu} |b|$, called the property of multiplicity.
$|a + b| \leqslant |a| + |b|$, this property is called the “property of subadditivity” and is especially used in triangle inequalities.