Final answer:
To estimate the product of 8 1/6 and 1 7/8 using compatible numbers, round them to the nearest whole numbers (8 and 2 respectively) and then multiply to get an estimated result of 16.
Step-by-step explanation:
To estimate the quotient of 8 1/6 multiplied by 1 7/8 using compatible numbers, we would look for numbers close to these that are easier to work with.
Firstly, 8 1/6 can be approximated to 8, since 1/6 is close to 0. Similarly, 1 7/8 can be rounded to 2, as 7/8 is close to 1.
Now, using these compatible numbers, we multiply 8 by 2 to get an estimated product of 16. This method is based on understanding that multiplication and division can be simplified by using numbers that are easier to calculate mentally.
Understanding the concept of reciprocal numbers can also help with such estimations. For instance, knowing that dividing by 8 is the same as multiplying by its reciprocal (1/8), which is "1.25-like", can simplify calculations.