Answer:
estimated product: 84
first-level error-corrected estimate: 85 1/8
Step-by-step explanation:
To estimate the product, you can round each number to the nearest integer, then multiply those integers. That product would be 12 times 7 equals 84. This estimate can be estimated to be slightly lower than the actual product.
estimate: 12×7 = 84
actual product: 99/8×55/8 = 5445/64 = 85 5/64
_____
Additional comment
Often, when you make an estimate, you would also like to estimate its error. Here, the actual product is ...
(12 +3/8)(7 -1/8) = (12)(7) +(3/8)(7) - (12)(1/8) -(3/8)(1/8)
The initial estimate is the first term of this sum: 12(7) = 84.
The error can be estimated to be (3/8)(7) -12(1/8) = (21 -12)/8 = 9/8. That is, the value 84 is low by approximately 9/8. Even that approximate error has an error. That error is too high by (3/8)(1/8) = 3/64, meaning the actual product, with errors accounted for, is 84 +1 8/64 -3/64 = 85 5/64.
