Final answer:
The statements regarding multiplication of numbers with the same or different signs, and division following the same sign rules as multiplication, are true. The commutative property of addition and the rules of raising numbers to a power are also accurately described.
Step-by-step explanation:
The student's question revolves around the mathematical expression (9 + 3) · 4 and statements about the rules of arithmetic operations. Let's address the statements mentioned:
- When two positive numbers multiply, the answer has a positive sign. This statement is true. For example, 2x3 equals 6, which is positive.
- When two negative numbers multiply, the answer also has a positive sign. This statement is true as well. An example is (-4) x (-3) which equals 12.
- When two numbers with opposite signs multiply, the answer has a negative sign. This is true, demonstrated by (-3) x 2 equals -6 and 4 x (-4) equals -16.
- Division follows the same rules for signs as multiplication. This is a true statement. For example, (-2) / (-1) equals 2 and (-2) / 1 equals -2.
Additional concepts that should be correct:
- The commutative property of addition states that A + B = B + A. This is true for ordinary numbers.
- Raising a number to a power, such as 4³, implies multiplying the number by itself the given number of times, e.g., 4 × 4 × 4.
- The power affects everything inside the parentheses, so for (2 × 7)3, the correct expansion would be (23 × 73) and not (2 × 21).