Final answer:
The correct methods to find the product of factors are by multiplying the factors directly or using the factor-label method for unit conversions. Adding, subtracting, or dividing factors do not result in the product.
Step-by-step explanation:
The question is asking about ways to find the product of factors in a multiplication problem. Two correct methods to break apart the factors and find the product are: multiplying the factors together and using the factor-label method for unit conversion. The first option, adding the factors and multiplying by another factor, or subtracting one factor from another are not methods to find the product of two numbers. Similarly, dividing one factor by the other gives the quotient, not the product. When multiplying, you can multiply the numerators (top numbers) together and the denominators (bottom numbers) together if you are working with fractions, simplifying if necessary. For unit conversions, the factor-label method involves multiplying by conversion factors that are equal to 1 to change units without changing the numerical value.
To correctly employ the factor-label method in computations beyond simple unit conversions, ensure that the labels (units) cancel out appropriately. This involves constructing conversion factors by dividing one quantity into both sides which then allows for the desired unit in the result. It is also possible to multiply both sides of an equation by the same factor to simplify calculations involving integers. When you multiply by a conversion factor, you're essentially multiplying by 1.