Final answer:
To estimate the product of −29 and −2/7, you use compatible numbers and approximate −2/7 as −1/4. Multiplying −29 by −0.25 gives us −7.25. So, the estimate is positive 7 1/4, which is option C.
Step-by-step explanation:
The question requires us to estimate the product of −29 and −2/7 by using compatible numbers. Compatible numbers are those that are easy to compute with, typically rounded or simplified versions of the original numbers that make mental arithmetic simpler.
First, we approximate −2/7 to −1/4, which is a compatible number. We know that −1/4 is the same as −0.25, so multiplying −29 by −0.25 will give us an estimate. Mathematically:
−29 × −0.25 = 29 × 0.25
Next, 29 × 0.25 is the same as 29/4, which gives us 7.25. Thus, we have −7.25 as the product, but since the original numbers were negative, the actual estimate is positive 7.25.
Therefore, the answer is C. 7 1/4.