Leah here from leah4sci.com/MCAT and in this video I will show you how to do more advanced
Multiplication and Division when you have multiple digits or multiple decimal spaces
in your equation. In my last video I showed you a simple trick
on how to multiply and divide numbers that have a factor of 10 by moving the decimal
to the right or the left. This trick can be taken a step further for more advanced questions
such as this one. "An elephant bumps a stone weighing 89 grams
giving it an initial acceleration of 200 meters per second squared 200 m/s^2). With how much
force did the elephant hit the stone?" At first glance it seems to be an easy question
if only you had a calculator. I'll show you how to solve the question then we'll break
down Math trick. With any question like this, you have to look beyond the story and find
the numbers that you're going to calculate. In this case we are given 89 grams and 213
meters per second squared. In my physics videos I'll break down the kinematic equations showing
you how exactly when to use each formula. For now, let's just focus on the Math. We're
looking for Force is equals to Mass and Acceleration (F=ma). So looks like a simple plugin but
be careful. Force has units of kilograms meter second squared (km/s^2) and here we're given
grams so we first have to convert. I'm only writing up the conversion because I want you
to see what I'm doing but try to get comfortable doing this in your head.
We have 89 grams and we want to convert to kilograms. We know that 1 kg is equals to
1000 g and we set it up as 1 kg/1000 g allowing me to cancel out grams. In my last video I
showed you the trick, when you're dividing a thousand that has 3 zeros, you simply take
the decimal and move it back 3 spaces. This gives me a new and usable number 0.089kg.
Now I have the appropriate units, I can plug them in. 0.089kg x 213m/s^2, we know the units
are good because Force is kilogram meter per second squared (kgm/s^2), now let's do the
Math; 0.089 x 213 looks complicated, so let's start by simplifying. 89 is close to 90 so
we'll change this number to 0.090, 213 is very close to 200 so we'll round that down,
so we've simplified the question. But we still have the issue of numbers that we can't necessarily
do in our head. So here's what I'm doing to do, I'll take the first number and multiply
it by a hundred (0.090x100), I'll take the second number divided by a hundred (200/100),
this gives me 9x2 which I can certainly do on my head and the answer is it's 18 N. Punching
this in a calculator, I got the answer 18.957 which on the MCAT it's just close enough.
So let's break down this trick going through series of step by step exercises. You already
know that any number times 10 means that you move the decimal one space to the right and
any number divided by 10 means that you move the decimal one space to the left. There's
another trick at work here; the second trick is multiplying a number by 1. Ninety Seven
times one is Ninety Seven (97x1=97). A hundred times one is a hundred (100x1=100). Multiplying
the number by 1 doesn't change the number. But the trick is being able to multiply by
1 when you see the number differently. For example, one over one is one (1/1=1), two
over two is not two but still one (2/2=1), thirty three over thirty three is one (33/33=1),
a green duck divided by a green duck is still one. And the idea here is, that it doesn't
matter what form your number takes, as long as it's the same above and below the divisor,
the answer is still 1. So for example if I take twenty times one over one is twenty three
(23 x 1/1 = 23). Twenty three times Four point Six Seven divided by Four point Six Seven
is still 23 (23 x 4.67/4.67=23) because I am simply multiplying 23 by 1. Okay, so let's
take this one step further. If I have the equation 4 x 6 x 1/1, the answer is just 4x6.
We're not actually solving that, I just wanna show you that the identity doesn't change.
Now if I take 4 x 6 and I multiply it by 10/10, it's still just 4x6. When you're multiplying
and dividing, you can move the numbers around because the order of operations doesn't matter
within multiplication and division, so watch. If I have 4 x 6 x 10/10 that's still 4x6 because
I have 10 divided by 10, that's 10/10. I can also write it as 4 x 6 x 10 x 1/10, one more
time I have times 10 divided by 10 and I can even write it as 4/10 x 6 x 10 . This is the
key; notice that I took the two numbers that I initially started with and I took 1 and
multiplied it by 10, the other to divide by 10, that still gives me 4x6. Now let's try
an application on this. Let's take a number that you can probably
do in your head, let's say I ask you to calculate 2 x 20. Two times twenty is just twenty and
twenty which is forty (2x20=40). So let's prove that using this trick still gives us
40. If I take the numbers Two times Twenty and then do times 10 and divided by 10 (2x10x20/10)
I still should have the answer 40, let's prove it. 2 x 10 means we move the decimal one space
to the right giving me 20, 20 divided by 10 means we move the decimal to the right giving
me 2. I have 20 x2 which is still 40. Let's try something even more complicated.
Let's take the number 0.05 x 400. This is something that you may come across and can
necessarily do it from your head but what if now instead of times 10 divided by 10 we
try times a hundred divided by a hundred. What I am trying to do and how we choose where
to put the multiplication and where to put the division is take the big number and make
it smaller and take the smaller number and make it bigger. Specifically, I'm trying to
get rid of the decimal because let's face it, decimals are confusing. So if I take the
point zero five (0.05) and I multiply that by a hundred, to make that fair, we have to
take the 400 and divided by 100 because this way I have times a hundred divided by a hundred
and that means I'm not changing the total identity of the question. 0.05 times 100,
100 has two zeros that's why I move the decimal two spaces to the right giving me 5. Look
at 400 divided by a hundred, 100 hundred has two zeros and because we're dividing, we move
the decimals two spaces to the left, that gives me 4. Now I don't know about you but
0.05 x 400 is difficult, 5x4 is not, it's just 20. So what we did here is instead of
writing it up the long way, don't even write this up. On your MCAT just mentally move the
decimal to the right for the small number, to the left for the big number by the same
number of space, so watch me do this without even writing times a hundred divided by a
hundred. Here's how I would look at it if this was an MCAT question. 0.05 is too small,
I move the decimal 2 spaces to the right. To make up for that, I move the big decimal
2 spaces to the left. 5x4 as we already said is 20.
Now let's go back to the initial question that we look at. We had 0.090 x 200, look
at what we did. We move the decimal from 0.090 two spaces to the right, giving me 9, we move
the decimal 200 two spaces to the left, giving me 2 and without any long and detailed calculation
we know that 9 times 2 is 18 and that's how we quickly got our answer.
Be sure to join me in the next video where I show you how to apply a similar trick when
it comes to negative and positive exponents. Are you stuck on a specific MCAT topic? I
offer Private Online Tutoring where I focus on your needs to strengthen your individual
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