Let's analyze each option to verify its validity in the set of whole numbers:
A) [tex]\( 16 \div 4 = 4 \div 16 \)[/tex]
- Division is not a commutative operation. This means that changing the order of the operands does not yield the same result.
- [tex]\( \frac{16}{4} = 4 \)[/tex] (Dividing 16 by 4 equals 4)
- [tex]\( \frac{4}{16} = 0.25 \)[/tex] (Dividing 4 by 16 equals 0.25)
- Since [tex]\(4 \neq 0.25\)[/tex], this statement is false.
B) [tex]\( 16 + 2 = 2 + 16 \)[/tex]
- Addition is a commutative operation. This means that changing the order of the operands does not affect the result.
- [tex]\( 16 + 2 = 18 \)[/tex]
- [tex]\( 2 + 16 = 18 \)[/tex]
- Since [tex]\(18 = 18\)[/tex], this statement is true.
C) [tex]\( 1 - 8 = -7 \)[/tex]
- Subtraction is not a commutative operation, and it also can produce negative results which are not considered whole numbers.
- [tex]\( 1 - 8 = -7 \)[/tex]
- [tex]\(-7\)[/tex] is not a whole number; whole numbers are non-negative integers.
- Therefore, this statement is false.
D) [tex]\( 2 \times -1 = -1 \times 2 \)[/tex]
- Multiplication is a commutative operation, but in the context of whole numbers, we only consider non-negative integers.
- Here, [tex]\( 2 \times -1 = -2 \)[/tex] and [tex]\(-1 \times 2 = -2 \)[/tex], both expressions yield the same result.
- However, [tex]\(-2\)[/tex] is not a whole number.
- Therefore, this statement is false.
After carefully analyzing all the options, the valid operation in the set of whole numbers is:
B) [tex]\( 16 + 2 = 2 + 16 \)[/tex]
