Here's an example. Say need to calculate 43 x 697.
For a very rough estimate, multiply 40 x 700 = 28000. (To get that answer easily - break up, and rearrange, the rounded numbers:
40 x 700 = (4 X 10)(7x100) = (4x7)(10x100) = (28)(1000) = 28000)This "ballpark" of 28000 may be enough to eliminate 2 or more answers!
For a better estimate: You know 28000 is too low, because the 43 was rounded down quite a bit. (Yes, the 697 was rounded up - but not as much as the 43 was decreased.) So we now know we are looking for an answer MORE THAN 28000.
(For those who find math easy, you can even estimate how much more than 28000 I should be looking for. Read on ONLY if you want to know how. The 43 was rounded down to 40. Compare that to the 43 - it was rounded down ROUGHLY not quite 10%, so rounding our ballpark number up by roughly not quite 10% gives 28000 + 2800 - 30800. This is MORE more than the real answer. The correct answer needs to be BETWEEN 28000 and 30800, and these bounds may be enough to single out the answer. The correct answer is 29971.)
Seems complicated, but often to think it through this way. But oftentimes the first ballpark is good enough to pick an answer, and knowing simply if your ballpark is too high or too low can help you choose among answers if you haven't eliminated them all. If you practice and hone your estimation skills now, you could save a lot of work and time on the test - and avoid "careless errors" that crop up on long calculations... Remember - the right answer is right in front of you! Sometimes all you need to do is eliminate all the wrong answers. Skillful estimation can help you do that!
WANT AN EVEN SHORTER SHORT CUT????? LOOK AT THE LAST DIGIT!!!
Remember this great advice -- when doing long multiplication, never do more than you need to!
the LAST digit will come from the 7 x 3. Since 7 x 3 = 21, the correct answer ends in a 1. See how many answers you can eliminate with just that!!! And by ballparking you know the answer is close to (but over) 700 x 40 = 28000, --- AND ends in a 1. How fast was that???