ARITHMETIC tricks

ARITHMETIC tricks you could implement int he MCAT

Key things that I have found hurt people are:

Powers of ten: This is helped by decimal hopping and labeling numbers with "increased by factor of 10" or "decreased by factor of 100". It comes down to paying attention really.

Ratios: These are made easiest by making denominators easy to deal with. Also, if a ratio is hard to calculate as written, flip it and see if it is easier the other way. We somehow emotionally deal with bigger-over-smaller ratios better than smaller-over-bigger ratios.

Fractions and Equivalent Decimal-based Value: Learn the correlation between fractions and decimals 1/4 = .25, 1/5 = .2, etc... These can prove EXTREMELY useful on the exam.

There are many more strategies and techniques, but these are generally the big three for most people. A little practice goes a long, long way.

The funny thing I've found is that the supposedly more difficult math skills like logs, square roots of complex numbers, and exponential decay/growth are typically easier for people than basic division, fractions, and multiplication.

One of my favorite tricks is Left Add Right Subtract. This refers to exponents, for example, if you move the decimal point to the left one, you need to add one to the exponent. If you move the decimal point to the right one, you need to subtract one from the exponent.

1 x 10^5, move left one decimal point to the left and you got .1 x 10^6

I hope this helps.

Here's an invaluable one that we use to help our students. Its a process more than a trick, but the end result is the trig function value of every important angle on the MCAT. Is seems long when written out, but its completely brainless and takes about 15 seconds to write down (tutorial anyone?)

1. create a table with 3 columns, one for angle, one for sin, one for cos.
2. write in the most important angles on the mcat in the left column: 0, 30, 45, 60, 90
3. in each cell in the sin and cos columns, put in "/2". Essentially every value has a 2 in the denominator.
4. now put a square root sign with nothing inside of it in the numerator of each cell fraction.
5. now start counting from the top. in the sin of 0, put a 0 inside the sqrt, in the sin of 30, put a 1 inside the sqrt, 45 gets 2, 60 gets 3, 90 gets 4. If you did it right, the sin of 0 should show up as sqrt 0 / 2, which is 0. sin 90 should show up as sqrt 4 / 2, which is 1.
6. do the same, but in reverse, for the cos column, cos 90 is (sqrt 0)/2, etc.

Like I said, it looks much worse written out than if you just create the table. Using this you'll have an elegant way to pull up the sin and cos of any important angle on the mcat.
I love that table! It works wonderfully...and you'll have it memorized if you use it enough.

Another good one is just simply becoming comfortable with scientific notation.

This one is more just practice than anything. The basic rule is that you can add exponents of scientific notation and multiply the number in front, and, you can change the sign of exponents on the bottom and move them to the top.

Here is one. It might be a little much for the mcat, but it is cool nonetheless. It's the Babylonian Method (old school).

To calculate the square root of a number:

First guess roughly what you think it would be (number less than 1 guess bigger, for a number greater than 1 guess smaller)

Then divide your guess into the square root number.

Now take your answer and add it to your guess and divide by 2. Presto, you should be very close to the real number.

so for example:

sqrt of .78 = Guess .85

.78
-----= ~.9
.85

.85+.9
-------= ~.87 And this should be your answer (or close enough)
2

The real answer using a calculator is: 0.866 or rounded .87!!

Also, Berkeley Review has a great method for decimal and fraction conversions. This is straight from their stoichiometry chapter.

If you memorize common fractions and decimals, you can mutiply and divide fractions by quickly converting an easy denominator. I've memorized the decimal values of the all fractions from ½ to 1/12 and just wrote them down in a little table. I'd list them here, but it's a little too much time. lol it's the one time you can prob use a calculator for the next however many months!


Ex) 18/66=?
18/66=3/11----->>> 1/11 = 0.091; 3/11=
3 x (1/11)=
3 x (.091)=.273


Ex2) to estimate 11/12,
*1/12=.083


11/12--->(12-1)/12--->12/12 - 1/12----->1- (1/12)--->1-(0.083)=.917

Although not really MCAT related, my favorite math trick is when you multiply two number, multi-digit in the from XA and X(10-A) (i.e 23x27, 35x35, 41x49), or in other words the ones digits add up to 10 and the rest of the digits are the same. So first multiply the ones digits normally and write that down. Then, add one to the rest of the digits and multiple those4 together and place them in front of the two digits you wrote down eariler.

and by the way if the ones digits are 1 and 9 you wriet down 09.

For exapmple 23x27

One digits - 3x7 = 21
add on to rest and multiply 3x2 = 6
place both halves together and 23x27= 621
and it works for every single case.

Oh and when multiplying two numbers (that are relativly reasonable) together without brute forcing it is to multplie two numbers taht are close to it and then add on the diffference. Say 52x18, you could do 50x18 (which can bee done in your head) then add 36, or 20x52 (which is also preety simple) minus 104. not too bad really.

You can use 0kazak1's method...but the fastest way to do 48*52 would be to to rewrite it as:

48*52 = (50-2)(50+2) = 50^2 - 2^2 = 2496.

If two numbers are close together, both even or both odd (so that their average is an integer), you can use this method if you know the square of the average.

Bu t if you do the second way you could do 50x48=2400 + 96 (48x2)
or 50x52= 2600 - 104 which would give you the same thing. or up above works too, but if you get good at