Which of the following is true about -9?
It is an integer but not a whole number
it is both an integer and a whole number
it is an integer nut not a rational number
it is a whole number but not an integer
It is both an integer and a whole number.
The correct statement is:
It is an integer but not a whole number.
To determine which statement about -9 is true, we need to understand the definitions of integer, whole number, and rational number.
1. Integer: An integer is any positive or negative whole number or zero. It includes both positive whole numbers (1, 2, 3, ...) and negative whole numbers (-1, -2, -3, ...), as well as zero (0).
2. Whole Number: Whole numbers are a subset of integers that includes all positive integers (1, 2, 3, ...) and zero (0). Whole numbers do not include negative integers.
3. Rational Number: A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. Rational numbers include integers, fractions, and terminating or repeating decimals.
Now let's evaluate each statement:
a) It is an integer but not a whole number: This statement is incorrect because -9 is both an integer and a whole number. Therefore, this statement is false.
b) It is both an integer and a whole number: This statement is correct. As explained above, -9 is an integer because it is a negative whole number, and it is also a whole number because it is part of the set of integers that includes negative numbers. Therefore, this statement is true.
c) It is an integer but not a rational number: This statement is incorrect. -9 is an integer and can also be expressed as the quotient of two integers (-9/1). Therefore, -9 is a rational number. Thus, this statement is false.
d) It is a whole number but not an integer: This statement is incorrect. -9 is an integer because it is a negative whole number. Therefore, this statement is false.
In conclusion, the correct statement about -9 is that it is both an integer and a whole number.