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Today we're going to go over the
President Rules of arithmetic,

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which allow us to workout
calculations involving brackets,

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powers, division and
multiplication, addition and

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Subtraction, and let us all
arrive at the same answer.

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Then afterwards, we're going to
go on and do calculations

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involving positive and negative

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numbers. And use rules for
addition, subtraction,

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multiplication and division.

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But first, let us look at this

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expression. It's 2 + 4 * 3 - 1
and let us work at night.

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Well, we can work it out first
by moving from left to right,

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and if we do that then we will
add, then multiply and then

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subtract. If we do that, we get
2 + 4, which is 6 times by

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three. Is it T minus one gives
us the answer 17.

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But if we change the order, the
calculation and we use add

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first, then subtract and then

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multiply. What answer do we get?
Well, 2 + 4 is 6. Do they

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subtract next 3 - 1 which is 2
so 6 * 2's answer is 12.

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Or we could multiply first,
then add followed by subtract.

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Well, if we multiply first,
that's 4 * 3, which is 12.

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Do the add 2 + 12 which is 14.

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Then subtract the answer is 13.

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And so on.

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And as you can see, we get
different answers according to

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the order in which we do the
operations, so that's not very

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good. So we need to have a
presidents in which we know the

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order in which we do the

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calculation. The order that most
people use is.

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We do brackets first.

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Followed by powers.

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And then multiplication

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Indovision. Then finally
addition and Subtraction.

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And that's a lot to remember.

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So there's an acronym to allow
you to remember it.

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And that acronym
is barred maths.

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BODMAS.
Be for brackets.

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Oh for powers.

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Date for

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division. An multiplication
for the M.

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And these two go together 'cause
they have the same priority

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Avery Edition. And
As for subtraction.

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And these two go together
because they have the same

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priority. So if you remember Bob

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Maths. FIFA brackets and
Overpowers followed by division

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and multiplication, and then
finally addition and

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Subtraction. If you want to
calculate any expression, use

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that order and you won't go

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wrong. So why don't we
look at some examples?

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Take for example, the first one
that we started off with 2 + 4

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times by 3 - 1. Now using board
maths we should have no problem

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working night this expression we
do the Times first, so it's two

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add 12 - 1 night. The addition
and subtraction of the same

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order of priority. So we work
from left to right. That's 2 +

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12 which is 14 - 1 which is 13.

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Look at this next example.

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Here we've got brackets and
using board mass brackets are

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done first, so 3 + 5 is it,
so our expression becomes two

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times it, which is 16. Can be

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easier. What about the next one
9 - 6? But I've got to add the

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plus one now in this case we've
got the subtract and the ad

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together. So we've got the same
priority. The rule is work from

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left to right, so we say 9 - 6
which is 3 add 1 which is 4.

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The last two involving powers.

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3 + 2 squared while using board
Mars again, we do the squares,

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the powers first 2 squared is 4,
so our expression becomes 3 + 4

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and 3 + 4 is 7.

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And finally this expression.

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3 + 2 all squared. Now we've got
powers, an brackets. But

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remember using board Mads we do
what's inside the brackets

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first, so it's 3 + 2 which is 5.

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And then we have to square the
five which is 25.

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Now in these two last examples
with the got the same numbers.

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And we've got a square, but
you've got two totally

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different answers. And the
reason why is in this one the

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square is for the things
inside the bracket. The 3 + 2,

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whereas in this one this
square relates to just the

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two.

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So remember when you're doing
any calculations which involve

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operations such as brackets,
powers, division,

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multiplication, subtraction and
addition, use board baths and

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you won't go wrong.

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What math means?

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Brackets first, then powers
followed by multiplication and

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division. And then addition to

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Subtraction. And when you have
operations of the same priority.

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He just work from left to right.

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Nothing could be easier.

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And now I will move on to
calculations involving positive

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and negative numbers. Now what
are positive and negative

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numbers? Well, if we take all
the real numbers except 0.

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All real numbers.

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Can be. Either
positive or

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negative, and of
course except 0.

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Now, where are those
numbers? Well, if we

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look on a number line.

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And position 0 all the positive
numbers are to the right.

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And all the negative numbers are
to the left.

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And we represent the numbers on
the number line like this

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positive one, positive 2
positive 3 positive for.

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Positive 5 and so on.

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Negative one negative, two
negative, three negative,

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four negative 5.

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Notice how we've written in
numbers, the positive numbers

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and the negative numbers. We
write positive three like this

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and negative for like this. The
sign of the number is written as

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a superscript. Now we do this.

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To help our understanding so
that we don't confuse the sign

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of the number with addition and

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Subtraction. But of course with

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practice. We drop this and we
just use the normal standard

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notation. But for this
session I'm going to use the

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superscripts just to help
our understanding.

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But what about calculations
involving positive and negative

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numbers? What about addition,
subtraction, multiplication and

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division? Well, I would take
some examples. If I take these

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two examples, negative four at

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positive 5. And.

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Positive for. Subtract

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positive 9. If I have
those two calculations, what do

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they work out to be well?

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In the first instance, we can
use a number line to help us

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evaluate them. And we have to
remember that using a number

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line addition means you kind on
in that direction, and

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subtraction means you kind back
in that direction.

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So using those two little rules
will calculate this expression

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and then this.

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So take this one to begin with
negative 4. Add positive five.

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Start at negative, 4 on the

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number line. And kind on
five 12345, so it negative

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4 add positive 5 gives
me the answer positive one.

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For the other example, we've got
a subtraction, so we started

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positive four, and we subtract

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positive 9. To start a positive

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for. And kind

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back 91234.
56789 so

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positive for

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subtract. Positive 9 gives
you negative 5.

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It could be simpler.

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Now, to simplify matters a
little bit further, it really is

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a fast to keep writing all these

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signs. And because positive
numbers are the numbers that we

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usually use in calculations, we
drop them. We dropped the sign.

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So positive 5 can be written is
just five, and we know that

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positive one is equal to 1 and
positive 9 has 9.

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And it's understood by everyone
that where you have numbers with

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no sign written there then they
are positive numbers.

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And I'm going to use that.

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In all my calculations following

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on. But if you notice in
this calculation and in this

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one. We've added and
subtracted positive numbers.

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But how do we add and subtract

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negative numbers? Well, try and
generate an easy route.

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Going to look at some patterns
of both addition and Subtraction

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and will start with addition.

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And we'll start with something
that we know.

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If we start with 5 + 2,
we know that is 7.

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And then I'm going to write a
sequence of calculations which

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follow on from this.

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5 at one.

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Is equal to 65. Add zero
is equal to 5.

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Notice in this sequence of
addition the answers decreased

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by one. As the numbers that we
add decreased by one.

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So if we follow the pattern.

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We take 5 add negative one
because negative one is 0.

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Subtract 1 is one less than
zero, then it must equal for. If

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we continue the pattern on.

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And five add negative, two must
equal 3 and five ad.

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Negative three must equal
two and five add negative.

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Four must equal 1.

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Not if we look at these

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additions. These additions of
negative numbers we can actually

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write these calculations as
subtractions of positive

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numbers, so 5 add negative, one
would be the same as five

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subtract 1 and you get the same

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answer for. Similarly, 5 add
negative two can be written as

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five subtract 2 and you get the
answer 35 add negative. Three

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can be written as five, subtract

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3. Give me the answer 2 and

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then 5. Add negative four is
the same as five. Subtract

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4, which is one.

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So when we have the addition
of negative numbers.

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That's the same as
the subtraction of

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the positive number.

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So I had these two examples.

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It at negative 10.

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And negative 9 at

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negative 5. Using that

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room. Hi, we calculate

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the answer. Now we take it add
negative 10. That's the same as

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it subtract 10.

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I'm thinking about the number
line. He started it and you go

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back 10. So you go back to 0
and then another two you get

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to the answer negative 2.

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And with this example.

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Negative nine and negative five.
We can rewrite that as negative

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9 subtract 5 again. Visualizing
it on the number line start at

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negative 9. And you go
back five, go back five so your

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land at negative 14.

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So when we have the addition of
negative numbers, it's always

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easier to change them into
subtraction of positive numbers.

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But the one thing that we
haven't done is the subtraction

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of negative numbers.

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So again, I'd like to use a
pattern to help us workout the

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rule that we're going to use.

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If we start off with what we

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know. 4 subtract 2 is 2.

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So 4 subtract 1 is
3 and four subtract 0

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is for.

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Notice in this sequence of
Subtractions, the answers are

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going up by one.

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As the numbers that we're
subtracting decreased by one.

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So if we continue the pattern in
the calculations, the next

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calculation would be 4. Subtract
negative one and the answer will

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be 5. You add one on to the
four to make 5, and four

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00:15:53,780 --> 00:15:55,190
subtract negative 2.

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Will be 6 and four. Subtract
negative. Three would be 7.

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And four subtract
negative four is it?

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Now again. If we look
at these subtractions

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of negative numbers.

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What calculation would be easier
to do using the numbers but

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still arriving at the same
answer when I think it's quite

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obvious. For this one, it's for

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AD one. And that gives us the
answer 5. The numbers of the

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same, but the operation and
assign are different.

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For this one it before add 2 and
that will give us 6.

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For this one it before at three,
and that will give us 7.

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And finally, for ad for which
will give us it.

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So.

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If we look at our pattern, we
can see that when you've got the

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subtraction of a negative
number, that's the same as the

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addition of a positive number.

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So we'll use that room to
workout these calculations if we

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take it, subtract negative 10.

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And negative 6 subtract

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negative 13. What answers do
we get if we use our room where

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we change the subtraction to
addition of a positive number?

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So is it plus 10? What could be
easier? That's 18.

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This one you've got negative 6
add 13 slightly harder, but not

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too difficult. They give
negative 6 and the number line

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00:17:53,172 --> 00:17:59,880
and go forward kind on 13. He
kind on 6 and then another

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Seven. So the answer is positive
7 written like that.

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So how can we combine all these
rooms together in a nice, easy

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way for you to remember? Well,
this is one way.

244
00:18:18,870 --> 00:18:24,788
If the operation in the sign are
the same like this.

245
00:18:25,920 --> 00:18:26,790
Sam

246
00:18:28,170 --> 00:18:31,980
The calculation works like
an addition.

247
00:18:33,450 --> 00:18:36,550
Off a positive number.

248
00:18:40,960 --> 00:18:46,252
If the operation and assign are
different like this.

249
00:18:48,350 --> 00:18:50,999
Then the operation.

250
00:18:51,750 --> 00:18:55,718
Works like this subtraction.

251
00:18:55,940 --> 00:18:59,808
Off a positive number.

252
00:19:00,920 --> 00:19:05,683
Now, if you remember those two
Golden rules, then the addition

253
00:19:05,683 --> 00:19:10,013
and subtraction of positive and
negative numbers is dead easy.

254
00:19:10,830 --> 00:19:14,950
Now we've talked about addition
and subtraction of positive and

255
00:19:14,950 --> 00:19:17,010
negative numbers, but wanna bite

256
00:19:17,010 --> 00:19:22,532
multiplication Indovision. Well,
we start with what we know. We

257
00:19:22,532 --> 00:19:28,131
know how to multiply and divide
positive numbers. We know that

258
00:19:28,131 --> 00:19:31,185
five times by 5 is 25.

259
00:19:32,060 --> 00:19:35,972
An 5 / 5 is one

260
00:19:35,972 --> 00:19:41,060
dead easy. But what about
the multiplication division

261
00:19:41,060 --> 00:19:42,515
of negative numbers?

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00:19:43,540 --> 00:19:48,204
Well, I'll use patterns the way
I did before. In addition,

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00:19:48,204 --> 00:19:53,288
Subtraction. And I'll start off
with this calculation and

264
00:19:53,288 --> 00:19:57,056
continue doing a sequence of
multiplications that involve

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00:19:57,056 --> 00:20:03,179
negative numbers, and we'll see
if we can get a rule coming out

266
00:20:03,179 --> 00:20:05,534
from the pattern in the

267
00:20:05,534 --> 00:20:09,904
calculations. For the next
calculation here, I'll say this

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00:20:09,904 --> 00:20:11,994
is 5 times by 4.

269
00:20:12,780 --> 00:20:14,688
And we know that is 20.

270
00:20:15,420 --> 00:20:22,756
Five times by 3:15,
five times two is

271
00:20:22,756 --> 00:20:28,892
10. 5 * 1
is 5 and 5

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00:20:28,892 --> 00:20:31,556
* 0 is not.

273
00:20:32,850 --> 00:20:37,729
I notice in these
multiplications the answers.

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00:20:38,300 --> 00:20:43,184
Are going down by 5 as the
number that we times by

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00:20:43,184 --> 00:20:44,405
decreases by one.

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00:20:45,220 --> 00:20:50,620
So the next calculation in the
sequence would be 5 times by

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00:20:50,620 --> 00:20:54,740
negative one. And if we use the
pattern that have just stated.

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00:20:55,430 --> 00:21:00,916
We subtract 5 from zero as we
subtract 5 from zero, we get

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00:21:00,916 --> 00:21:05,980
negative 5. The next calculation
would be 5 times by negative 2.

280
00:21:07,270 --> 00:21:11,477
Negative 5 subtract
5 is negative 10.

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00:21:12,720 --> 00:21:15,070
Five times by negative 3.

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00:21:15,920 --> 00:21:19,685
Negative 10 subtract 5 negative

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00:21:19,685 --> 00:21:26,504
15. Will do just one more just
to see if we can spot the

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00:21:26,504 --> 00:21:30,784
pattern and the pattern is
working five times negative 4.

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00:21:31,550 --> 00:21:35,528
Take negative 15 and subtract 5.
That's negative 20.

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00:21:37,170 --> 00:21:39,108
So look at.

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00:21:39,740 --> 00:21:41,864
Our multiplications by a

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00:21:41,864 --> 00:21:48,818
negative number. We get
a negative number answer.

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00:21:49,490 --> 00:21:54,350
So when we multiply a negative
sorry, a negative by a positive.

290
00:21:56,040 --> 00:21:58,800
Will always get a
negative answer.

291
00:21:59,940 --> 00:22:04,857
And vice versa if we multiply a
negative by a positive.

292
00:22:05,810 --> 00:22:07,278
Will get a negative.

293
00:22:08,290 --> 00:22:11,174
So if I give you these two

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00:22:11,174 --> 00:22:15,770
examples. 6 times by
negative 5.

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00:22:17,120 --> 00:22:21,432
Steady, easy to workout. The
answer you just multiply the six

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00:22:21,432 --> 00:22:26,528
by the five to get 30. The signs
are different. Remember this is

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00:22:26,528 --> 00:22:31,232
positive 6 times by negative 5
the two signs are different, so

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00:22:31,232 --> 00:22:33,584
the answer is a negative number

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00:22:33,584 --> 00:22:40,694
negative 30. If we take
negative four times by three.

300
00:22:41,260 --> 00:22:44,570
Multipliers normal 3/4 or 12.

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00:22:45,500 --> 00:22:48,900
And then take into account
the signs. This is a

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00:22:48,900 --> 00:22:51,620
negative. This is a
positive. 2 signs different.

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00:22:51,620 --> 00:22:53,320
So the answer is negative.

304
00:22:54,610 --> 00:22:56,650
And the same goes for division.

305
00:22:58,020 --> 00:23:04,380
And we can just double check
that by looking at these two

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00:23:04,380 --> 00:23:08,620
calculations. Negative 30
divided by positive six must

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00:23:08,620 --> 00:23:10,210
equal negative 5.

308
00:23:11,490 --> 00:23:16,638
And negative 12 divided by
positive three must equal

309
00:23:16,638 --> 00:23:17,782
negative 4.

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00:23:19,700 --> 00:23:24,364
So when the signs are different
and you multiply positive and

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00:23:24,364 --> 00:23:28,604
negative numbers together in
pairs, the answer will always be

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00:23:28,604 --> 00:23:29,876
a negative number.

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00:23:31,010 --> 00:23:37,544
But we haven't finished just
yet. What if you multiply and

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00:23:37,544 --> 00:23:39,920
divide by negative numbers?

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00:23:40,480 --> 00:23:41,878
What happens there?

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00:23:42,680 --> 00:23:46,200
Well, again, I'm going to use
patterns. I like using patterns

317
00:23:46,200 --> 00:23:50,040
because it gives me a bit of
confidence that I'm doing things

318
00:23:50,040 --> 00:23:54,520
correctly and I always start off
with things that I know. So if I

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00:23:54,520 --> 00:23:57,400
start off with negative five
times by positive 4.

320
00:23:58,140 --> 00:24:02,412
I know the answer is negative 20
because the signs are different

321
00:24:02,412 --> 00:24:04,548
and 5 * 4 is 20.

322
00:24:05,080 --> 00:24:10,820
Next one in the sequence
negative five times by three.

323
00:24:10,820 --> 00:24:17,708
That will give us negative 15
negative 5 * 2 negative, ten

324
00:24:17,708 --> 00:24:24,596
negative 5 * 1 is negative,
five negative 5 * 0 is

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00:24:24,596 --> 00:24:26,318
equal to 0.

326
00:24:27,940 --> 00:24:29,100
Now look at the pattern.

327
00:24:30,620 --> 00:24:35,573
Is a bit like a dejavu. We've
done this before. Look at the

328
00:24:35,573 --> 00:24:40,145
answers. You can see that we
are increasing by 5 each time

329
00:24:40,145 --> 00:24:44,717
as we multiply by one less
each time. That seems a bit

330
00:24:44,717 --> 00:24:46,622
odd, but stay with Maine.

331
00:24:47,970 --> 00:24:52,910
The next multiplication, if we
keep the pattern in the

332
00:24:52,910 --> 00:24:57,850
calculations, the same would be
negative five times by negative

333
00:24:57,850 --> 00:25:03,140
one. And according to our
pattern, that will equal 5 more

334
00:25:03,140 --> 00:25:05,834
than zero, which is positive 5.

335
00:25:06,590 --> 00:25:11,430
Negative five times negative 2,
which is the next calculation in

336
00:25:11,430 --> 00:25:16,270
sequence. That would be five
more than five, which is 10.

337
00:25:16,800 --> 00:25:19,600
Negative five times by negative

338
00:25:19,600 --> 00:25:22,350
3. Is 15th.

339
00:25:23,040 --> 00:25:27,674
Negative five times negative
four is 20.

340
00:25:29,880 --> 00:25:35,801
So. It's really great. See that
when we multiply negative

341
00:25:35,801 --> 00:25:37,917
numbers together in pairs.

342
00:25:38,420 --> 00:25:40,620
We get a positive answer.

343
00:25:41,740 --> 00:25:46,051
Negative by negative gives it a
positive negative negative

344
00:25:46,051 --> 00:25:48,925
positive, negative negative
positive negative negative

345
00:25:48,925 --> 00:25:54,194
positive is not great. Dead
easy. So if I had this

346
00:25:54,194 --> 00:25:58,505
calculation negative 6 times by
negative three, you multipliers

347
00:25:58,505 --> 00:26:04,732
normal. 6 * 3 is it teen? And
the answer is positive positive

348
00:26:04,732 --> 00:26:09,043
via team because it's two
negatives makes the positive.

349
00:26:09,570 --> 00:26:16,370
And the same goes with
this one. If we had

350
00:26:16,370 --> 00:26:19,770
negative 9 times by negative

351
00:26:19,770 --> 00:26:22,040
229382. Two negatives.

352
00:26:22,590 --> 00:26:26,358
The answer is a positive, so
again we get the same answer

353
00:26:26,358 --> 00:26:28,870
it team but different numbers
in the calculation.

354
00:26:29,910 --> 00:26:33,620
But remember where else did we
get a positive answer?

355
00:26:34,600 --> 00:26:37,055
When you multiplied 2 positive

356
00:26:37,055 --> 00:26:41,440
numbers together. So if you
multiplied 6 by three, you'll

357
00:26:41,440 --> 00:26:46,055
get it team and when you
multiplied 9 by two you get it

358
00:26:46,055 --> 00:26:49,725
too. So when the signs of

359
00:26:49,725 --> 00:26:54,935
the same. Then the answer will
be positive whether they are

360
00:26:54,935 --> 00:26:58,095
two negatives be multiplied
together or two positive

361
00:26:58,095 --> 00:26:59,675
numbers being multiplied
together.

362
00:27:00,790 --> 00:27:07,450
And that's a lot to take
in for multiplication and

363
00:27:07,450 --> 00:27:10,114
division of negative numbers.

364
00:27:10,120 --> 00:27:16,060
I'd like to summarize that bit
by again using a diagram when

365
00:27:16,060 --> 00:27:18,535
the signs of the sea.

366
00:27:19,480 --> 00:27:27,328
A positive times by a positive
or a negative times by a

367
00:27:27,328 --> 00:27:30,170
negative. The

368
00:27:30,170 --> 00:27:33,810
answer. Is

369
00:27:33,810 --> 00:27:40,856
positive. Is a
positive number when the signs

370
00:27:40,856 --> 00:27:48,021
are different. I positive
times by a negative or

371
00:27:48,021 --> 00:27:51,536
a negative times by a

372
00:27:51,536 --> 00:27:54,270
positive. The answer.

373
00:27:55,760 --> 00:27:57,460
Is negative.

374
00:28:00,400 --> 00:28:07,154
And the same goes the same
rules go if you divide.

375
00:28:07,950 --> 00:28:15,142
So if
I had

376
00:28:15,142 --> 00:28:22,685
these examples.
Negative 6 divided

377
00:28:22,685 --> 00:28:26,870
by. Negative
2.

378
00:28:28,730 --> 00:28:34,666
My answer will be do the
division first 6 / 2, which is 3

379
00:28:34,666 --> 00:28:38,906
and then think about the signs
negative negative signs saying

380
00:28:38,906 --> 00:28:41,026
so. The answer is positive.

381
00:28:41,960 --> 00:28:49,210
And if we had this
division negative 12 divided by

382
00:28:49,210 --> 00:28:55,130
positive 3. Do the division is
normal 12 / 3 is for.

383
00:28:55,650 --> 00:28:58,314
Think of the signs
signs, different

384
00:28:58,314 --> 00:29:00,978
negative and a
positive. So the

385
00:29:00,978 --> 00:29:02,310
answer is negative.