MATHS
TRICKS GUESSTIMATION (FULL GUIDE)
GUESSTIMATION | MATHS
TRICKS "GUESSTIMATION" So far, he has been
perfecting the mental techniques necessary to discover the exact answers to
math problems with the aid of MATHS
TRICKS formulas.
However, often, all you'll want is a rough estimate. Let’s say you are receiving quotes from different lenders to refinance your home. Everything really the need at this stage of information gathering is a rough estimate of what your monthly payments will be. Or say you are paying a restaurant bill with a group of friends and you do not want to include the account of each person to the penny. The MATHS TRICKS guesstimation methods.
GUESSTIMATION GUIDE FOR YOU
CHAPTER 5
However, often, all you'll want is a rough estimate. Let’s say you are receiving quotes from different lenders to refinance your home. Everything really the need at this stage of information gathering is a rough estimate of what your monthly payments will be. Or say you are paying a restaurant bill with a group of friends and you do not want to include the account of each person to the penny. The MATHS TRICKS guesstimation methods.
Described in this MATHS TRICKS GUESSTIMATION chapter will make these two tasks and
much more equal to them, easier. Addition, subtraction, division, and
multiplication lend themselves to MATHS
TRICKS guesstimation. As usual, he will do his calculations from left to
right according to with the help of MATHS TRICKS.
MATHS
TRICKS ADDITION GUESSTIMATION
MATHS TRICKS formulas also provide you Guesstimation.
Guesstimation is also a good technique to make your life easier when the
numbers of Problems are too long to remember the trick is to round the original
numbers up or down:
Notice that we round the first
number to the nearest thousand and Second number above since the exact answer
is 14.186, our relative error is only 186/14186 or 1.3% if you want to be more
exact, instead of rounding to the nearest thousand, Round to the nearest
hundred:
The answer is only 14 off of the exact answer, an error of less than .1%. This is
What I call a good guess!
Test a 5-digit sum problem,
rounding to the nearest hundred:
Rounding to the nearest
hundred, our response will always be disabled in less than 100. If the answer is
greater than 10,000, your estimate will be within 1%.
Now let's try something
wild:
If you
round to the nearest million, you get a response of 31 million, off by
approximately 285,000. Not bad, but you can do it better by rounding to the
nearest hundred thousand, as we have shown in the column on the right. In this MATHS TRICKS case, you go
only for 15,000, which is terribly close when it comes to numbers up to the third digit of the largest number (here the hundred thousand digits), your
estimate will always be within 1% of the precise answer. If you can calculate
exactly these smaller problems, you can Guesstimate the answer to any addition
problem.
GUESSTIMATING AT THE SUPERMARKET
Let's
try an example of the real world. Have you ever gone to the store and asked
yourself?
What
will be the total before the teller calls him? To estimate the total, my
The technique consists of rounding the prices to the nearest 500. For example,
while the cashier is adding the numbers shown below to the left, I mentally add
the numbers are shown in the
Right:
My final figure is usually within a dollar of the exact answer.
Subtraction Guesstimation
The way
to estimate the answers to the MATHS TRICKS
subtraction problems are the same: you round to the nearest thousand or hundred
digits, preferably the latter:
You can see that
rounding to the nearest thousand leaves you with a pretty good answer a little outside
the brand. When rounding to the second digit (hundreds, in the example), you’re
the answer will usually be within 3% of the exact answer. For this problem,
your answer is off for only 52, a relative error of 2%. If you round to the 3rd
digit, the relative error
In general, be below
1%. For example:
By
rounding the numbers to the third digit instead of the second digit, Improve
the accuracy of the estimate by a significant amount. The first estimate is off.
By approximately 1.3%, while the second estimate is only approximately 0.16%.
MATHS TRICKS DIVISION GUESSTIMATION
The first step in estimating the
response to a division problem is to determine the magnitude of the response:
Now the next step is to
round the largest numbers to the nearest thousand and Change the 57,870 to
58,000. Divide 6 into 58 is simple. The answer is 9 with a reminder. But the
most important component in this problem is where to place the 9. For example,
multiplying 6 x 90 yields 540, while multiplying 6 x 900 yields 5400, both of
which are too small. But 6 x 9000 = 54,000, which is quite close to the reply.
This tells you that the answer is 9 thousand and something. You can estimate
only what is that something subtracting first 58 - 54 = 4. At this point, you
could bring lower the 0 and divide 6 into 40, and so on. But if you are on your
fingers you will notice. That dividing 6 into 4 gives you 4/6 2/3 = .667. You
already know that the answer is 9 thousand something, now you're in a position
to guess 9667. In fact, the real answer is 9645- Very close!
Here is an astronomical
calculation for you. How many seconds does the light take?
To get from the sun to
the earth? Well, light travels at 186,282 miles per second, and the sun is (on
average) 92,960,130 miles away:
I doubt you are
particularly anxious to try this problem by hand. Fortunately, it is relatively
easy to guess an answer. First, simplify the problem:
Now it
divides 186 into 930, which gives 5 with no remainder. Then lift
The two
zeros he eliminated from 93,000 and voila, his answer is 500 seconds. The exact
answer is 499.02 seconds, so this is a very respectable estimate.
MATHS TRICKS MULTIPLICATION GUESSTIMATION
You can
use the same MATHS TRICKS formula/techniques to estimate your answers
MATHS TRICKS Multiplication problems for example,
Rounding to the nearest
multiple of 10 simplifies the problem considerably, but you're still out by
252, or around 5%. You can do better if you round both numbers the same amount but in opposite directions. That is, if you round 88 by increasing 2, you must
also decrease 54 by 2:
Instead of a
multiplication problem of 1 per l, you now have a problem of 2 per l, which it
should be easy enough for you to do it. Your guesstimation is disabled by only
1.5%.When you estimate the answer to multiplication problems rounding the higher
number above and lower number below, your estimate will be a little low. Yes, round the larger number down and the smaller number upward so that the numbers
are closer, your estimate will be a bit high. The greater the amount by which
Rounding up or down, the higher your estimate will be outside the exact answer.
For example:
Since the numbers are
closer after rounding them, your estimate it’s a bit tall
Since the numbers are
further apart, the estimated response is too low, although again, not for a
long time you can see that this method of guessing multiplication works quite
well. Also, keep in mind that this problem is only 67 'and that our approach is
only the first step of the square techniques. Let's see another MATHS TRICKS example:
We note that the approximation is more accurate when the original numbers they are very close try
to estimate a multiplication problem of 3 x 2:
By round 63 to 60 and
728 to 731, you create a multiplication of 3 per l problem, which puts its
estimate within 2004 of the exact answer, an error of 4.3%.
Now try to guess the
following 3 by 3 problem:
You will notice that
although you round both numbers up and down in 8, your guesstimate is disabled
in more than 1000. That's because the problem of multiplication is greater and
the size of the rounding number is larger, so the resulting estimate will be
reduced by a greater quantity. But the relative error is still less than 1%. How
high can you get with this system for stimulating multiplication problems? As
high as you want. You just need to know the names of the big numbers. Thousand
one thousand is one million, and one billion is one billion. Knowing these
names and
Numbers, try this in
size:
As
before, the goal is to round the numbers to simpler numbers, such as
29,000,000
and 14,000. Lowering the 0 for now, this is just a multiplication of 2 by 2
Problems: 29 x 14 = 406 (29 x 14 = 29 x 7 x 2 = 203 x 2 = 406). Therefore the
answer is
Approximately
406 billion, since one billion is one billion.
MOD SUMS (CASTING OUT 9'S)
Sometimes,
when I do my calculations on paper, I verify my answer with a method call
1"Mod sums" (because it is based on the elegant mathematics of
modular arithmetic).With the method of sums mod, you add the digits of each
number until you stay with a single digit. For example, to calculate the mod
sum of 4328, add 4 + 3 + 2 + 8 =17. Then add the digits of 17 to get 1 + 7 = 8.
Therefore, the sum of the mod of 4328 is 8. For the in the following problem,
the mod sums of each number are calculated as follows:
As illustrated above, the next
step is to add all the sums of mod (8 + 2 + 8 +).
1 + 5 + 5). This produces 29,
which adds to 11, which in turn adds up to 2.
Note that the mod the sum of
8651, its original total of the original digits, is also 2. This is not a coincidence!
If you have calculated the answer and the mod sums correctly, your final mod
sums should be the same. If they are different, you have definitely made a
mistake somewhere. There's a 1 out of 9 chances that the mod sums coincide
accidentally. If there is an error then this method will detect it 8 times out
of 9.
The sum mod method is more
commonly known to mathematicians and
The counters like "eject
9s" because the sum of the mod of a number turns out to be equal to the rest
obtained when the number is divided by 9. In the case of the answer up -8651 -
the sum of the mod was 2. If you divide 8651 by 9, the answer is 961 with rest of
2. In other words, if you throw 9 out of 8651 a total of 961 times, you'll have
it has a remainder of 2. There is a small exception to this. The sum of the
digits of any the multiple of 9 is also a multiple of 9. Therefore, if a number
is a multiple of 9, you will have a mod sum of 9, even if it has a remainder of
0.
You can also use mod sums to
check your answers to subtraction problems. The key is to subtract the mod sums
you reach and then compare that number with the mod. Sum of your answer.
There is an extra turn.
If the difference in the sums of the mod is a negative number or 0, add 9. For
example:
You can check your
answers to multiplication problems with the mod sum. The method by multiplying the
mod sums of the two numbers and calculating the result sum mod of the number.
Compare this number with the mod sum of the answer. They should match. For
example:
If the
mod sums do not match, he made a mistake. This method will detect errors, on
average, 8 times out of 9.
MATHS TRICKS |GUESSTIMATION EXERCISES
Go
through the following exercises for guesstimation mathematics; then check your
Answers
and calculations with ours in the back of the book.
Exercises:
Addition Guesstimation of MATHS TRICKS
Round
these numbers up or down and see how close you can get to the exact answer.
Mentally calculate the
total for the next column of price numbers by rounding to 500 closest:
Exercises:
Subtraction Guesstimation of MATHS TRICKS
Estimate the following
subtraction problems by rounding to the second or third digit.
Exercises:
Guesstimation Division. Adjust the numbers in a way that allows you to estimate
the next division problems.
Exercises: MATHS TRICKS guesstimation
Multiplication Adjust the numbers in a way that allows you to estimate the next
multiplication problems.
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