Final answer:
When a whole number greater than 1 is multiplied by another whole number, the result is larger because multiplication is repeated addition. Positive numbers multiplied together result in a larger positive number, while a negative and positive number multiplied result in a negative. Raising a number to a power is also a form of multiplication leading to larger numbers.
Step-by-step explanation:
The statement "When you multiply a whole number by a whole number the result is a larger number" is generally true for whole numbers greater than 1. This is because multiplication is essentially an operation involving the addition of a number to itself a certain number of times. For instance, 2 multiplied by 3 (2x3) is the same as adding 2 to itself 3 times (2+2+2), which results in 6. With each multiplication, the number grows because you are repeatedly adding the number to itself.
Multiplication rules for the sign of numbers also impact the result. When two positive numbers are multiplied together, the result is always a positive number and typically larger than both of the original numbers unless one is 1. For example, (-4) multiplied by (-3) (-4x-3) results in 12, another positive number. On the other hand, when a positive and a negative number are multiplied, such as (-3) multiplied by 2 or 4 multiplied by (-4), the result is a negative number, indicating a difference in magnitude but not necessarily an increased 'size' in terms of absolute value.
The process of integer powers, such as raising a number to a power (like 4³), is related to multiplication. The power indicates how many times the number is multiplied by itself, potentially resulting in a much larger number.