Final answer:
The product of 3 and (-1 1/2) is found by converting the mixed number to an improper fraction (-3/2) and then multiplying it by 3, which results in -9/2 or -4.5 as a decimal. The correct answer is a) -4.5.
Step-by-step explanation:
To find the product of 3 and (-1 1/2), we first need to convert the mixed number to an improper fraction. The mixed number -1 1/2 can be written as -3/2 because -1 is the same as -2/2, and adding the fractional part of 1/2 gives us -3/2 in total. To find the product, we multiply 3 by -3/2:
3 x (-3/2) = -9/2
As a decimal, -9/2 is equivalent to -4.5. Therefore, using the number line to find this product would show a point at -4.5, confirming that the correct answer is option a) -4.5.
Remember that when multiplying two numbers with opposite signs, the result will always have a negative sign as per the multiplication rules for signs (rule 7).