Select true or false for each statement. for a real number a, a + 0 = a. for a real number a, a + (-a) = 1. for a real numbers a and b, | a - b | = | b - a |. for real numbers a, b, and c, a + (b ∙ c) = (a + b)(a + c). for rational numbers a and b when b ≠ 0, is always a rational number.

For a real number a, a + 0 = a.  TRUE

For a real number a, a + (-a) = 1.  FALSE

For a real numbers a and b, | a - b | = | b - a |.  TRUE

For real numbers a, b, and c, a + (b ∙ c) = (a + b)(a + c).  FALSE

For rational numbers a and b when b ≠ 0, is always a rational number. TRUE

This comes from the identity property for addition that tells us that zero added to any number is the number itself. So the number in this case is , so it is true that:

This is false, because:

For any number there exists a number such that

This is a property of absolute value. The absolute value means remove the negative for the number, so it is true that:

This is false. By using distributive property we get that:

A rational number is a number made by two integers and written in the form:

Given that are rational, then the result of dividing them is also a rational number.