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

Explanation:For a real number a, a + 0 = a.  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:

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

This is false, because:

For any number there exists a number such that

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

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

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

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

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

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.

whole numbers, fractions, radical

step-by-step explanation:

whole numbers are counting numbers.

fraction is a part of a whole, includes decimal.

radical, those that uses radical signs