Name: Common Maths Mistakes (Part 1 of 4)
Uploaded: 2016-07-22T17:52:53.000Z
Duration: 17 min 1 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Future simple

Welcome to the first of four videos which will go through

some common mistakes that people make in algebraic manipulation

and working with numbers. I've called it a "baker's dozen"

because there are thirteen separate topics covered in the course of these

This first video covers what can loosely be called

"reading the recipe correctly", that is can you

understand the mathematics that's being asked of you when it's presented

in the form of a question and there are three typical things that can

cause trouble under this heading. Making sure that you use powers,

if you attempt to divide by zero. Let's look at the first one

see fairly commonly when people are using algebra is this one.

"Minus a squared" does not actually turn out to be

"-a multiplied by itself". Now to see that,

using some simple numbers. Here we have -3 in brackets

and we are squaring it. Now it's pretty clear that what we're being asked to do

is square the item that's right next to the power of two

The brackets are indicating that it's the number -3.

multiplied together make a plus so we end up with

It is tempting to think that the minus is attached to the 3

and therefore we are still squaring the number -3

that's right next to the power of 2 and therefor that's the only part

to get squared. So dealing with that we have a minus sign

which will, of course, produce -9. Now what's important

is having some kind of strategy, using your other knowledge of mathematics,

when you run into it. Now, in this case what I think it would help

understand how to apply the power correctly to a negative number

a point on the number line, but think of it as a product:

is going to produce the number -3. So in this case if you replace the "-3"

easy to make the mistake of squaring the -1

because now it looks like the -1 is separate from the 3,

the 3 squared and that's the right way to interpret it.

So now it's pretty clear that it's only the 3 that's getting squared

and we'll get the correct answer. So what we doing here is using

some other knowledge we have about the way numerical manipulation works

to help us overcome a potential problem we might be having

interpreting some mathematical notation, because of course "-3"

and "-1 multiplied by 3" a mathematically the same thing.

So they should obey the appropriate rules.

four little questions. What you might like to do at this point is

pause the video, have a bit of a think about which one of those

four statements is correct. It might be all of them, it might be none of them.

Have a bit of a think and then restart the video to

of problems that are similar to the previous set. Note this time that we're

raising all these numbers to the power of 3. So feel free to

pause the video and have a think about those ones as well.

baker's dozen is what happens when you have a power of 0.

mistake to make. When we first learn about powers we learned about

whole number powers like 2 (squaring) or 3

(raising to the power 3, or cubing). Whole number powers

are pretty straightforward but when we start dealing with

powers of 1, 0, negative powers, fractional powers

we have to trade a little more carefully, because their interpretation is a bit

is to think about index laws that are more familiar to us.

that says a raised to the power m divided by the same base, a,

the difference between the numerator and denominator powers.

Even if you aren't particularly familiar with that formula,

or that shortcut if you like, a good idea

underneath the shortcut. So here we have a simple example:

6 raised to the power 5 divided by 6 raised to the power 2.

five 6's on the top line of the fraction multiplied together and

two on the bottom. Now if we saw it like that we might naturally

realize that there are some cancellations possible, that is

two the 6's on the top line cancel two on the bottom.

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Common Maths Mistakes (Part 1 of 4)

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