## www.mathcentre.ac.uk/.../Rules%20of%20arithmetic.mp4

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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
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Subtraction, and let us all
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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
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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
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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
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But if we change the order, the
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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,
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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
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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
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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
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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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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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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
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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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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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involving positive and negative
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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
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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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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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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
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that we know.
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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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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
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by one. As the numbers that we
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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
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Negative three must equal
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Four must equal 1.
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Not if we look at these
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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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negative two can be written as
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five subtract 2 and you get the
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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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negative 10. That's the same as
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it subtract 10.
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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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• 14:14 - 14:17
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
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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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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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• 17:12 - 17:17
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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we get if we use our room where
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we change the subtraction to
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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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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.
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If the operation in the sign are
the same like this.
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Sam
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The calculation works like
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Off a positive number.
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If the operation and assign are
different like this.
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Then the operation.
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Works like this subtraction.
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Off a positive number.
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Now, if you remember those two
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and subtraction of positive and
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and subtraction of positive and
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negative numbers, but wanna bite
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multiplication Indovision. Well,
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know how to multiply and divide
positive numbers. We know that
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five times by 5 is 25.
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An 5 / 5 is one
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the multiplication division
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of negative numbers?
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Well, I'll use patterns the way
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Subtraction. And I'll start off
with this calculation and
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continue doing a sequence of
multiplications that involve
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negative numbers, and we'll see
if we can get a rule coming out
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from the pattern in the
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calculations. For the next
calculation here, I'll say this
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is 5 times by 4.
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And we know that is 20.
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Five times by 3:15,
five times two is
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10. 5 * 1
is 5 and 5
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* 0 is not.
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I notice in these
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Are going down by 5 as the
number that we times by
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decreases by one.
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So the next calculation in the
sequence would be 5 times by
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negative one. And if we use the
pattern that have just stated.
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We subtract 5 from zero as we
subtract 5 from zero, we get
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negative 5. The next calculation
would be 5 times by negative 2.
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Negative 5 subtract
5 is negative 10.
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Five times by negative 3.
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Negative 10 subtract 5 negative
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15. Will do just one more just
to see if we can spot the
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pattern and the pattern is
working five times negative 4.
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Take negative 15 and subtract 5.
That's negative 20.
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So look at.
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Our multiplications by a
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negative number. We get
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So when we multiply a negative
sorry, a negative by a positive.
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Will always get a
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And vice versa if we multiply a
negative by a positive.
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Will get a negative.
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So if I give you these two
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examples. 6 times by
negative 5.
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answer you just multiply the six
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by the five to get 30. The signs
are different. Remember this is
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positive 6 times by negative 5
the two signs are different, so
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the answer is a negative number
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negative 30. If we take
negative four times by three.
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Multipliers normal 3/4 or 12.
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And then take into account
the signs. This is a
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negative. This is a
positive. 2 signs different.
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And the same goes for division.
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And we can just double check
that by looking at these two
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calculations. Negative 30
divided by positive six must
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equal negative 5.
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And negative 12 divided by
positive three must equal
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negative 4.
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So when the signs are different
and you multiply positive and
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negative numbers together in
pairs, the answer will always be
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a negative number.
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But we haven't finished just
yet. What if you multiply and
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divide by negative numbers?
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What happens there?
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Well, again, I'm going to use
patterns. I like using patterns
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because it gives me a bit of
confidence that I'm doing things
• 23:50 - 23:55
correctly and I always start off
with things that I know. So if I
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start off with negative five
times by positive 4.
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I know the answer is negative 20
because the signs are different
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and 5 * 4 is 20.
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Next one in the sequence
negative five times by three.
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That will give us negative 15
negative 5 * 2 negative, ten
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negative 5 * 1 is negative,
five negative 5 * 0 is
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equal to 0.
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Now look at the pattern.
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Is a bit like a dejavu. We've
done this before. Look at the
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answers. You can see that we
are increasing by 5 each time
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as we multiply by one less
each time. That seems a bit
• 24:45 - 24:47
odd, but stay with Maine.
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The next multiplication, if we
keep the pattern in the
• 24:53 - 24:58
calculations, the same would be
negative five times by negative
• 24:58 - 25:03
one. And according to our
pattern, that will equal 5 more
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than zero, which is positive 5.
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Negative five times negative 2,
which is the next calculation in
• 25:11 - 25:16
sequence. That would be five
more than five, which is 10.
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Negative five times by negative
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3. Is 15th.
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Negative five times negative
four is 20.
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So. It's really great. See that
when we multiply negative
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numbers together in pairs.
• 25:38 - 25:41
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Negative by negative gives it a
positive negative negative
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positive, negative negative
positive negative negative
• 25:49 - 25:54
easy. So if I had this
• 25:54 - 25:59
calculation negative 6 times by
negative three, you multipliers
• 25:59 - 26:05
normal. 6 * 3 is it teen? And
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via team because it's two
negatives makes the positive.
• 26:10 - 26:16
And the same goes with
• 26:16 - 26:20
negative 9 times by negative
• 26:20 - 26:22
229382. Two negatives.
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The answer is a positive, so
again we get the same answer
• 26:26 - 26:29
it team but different numbers
in the calculation.
• 26:30 - 26:34
But remember where else did we
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When you multiplied 2 positive
• 26:37 - 26:41
numbers together. So if you
multiplied 6 by three, you'll
• 26:41 - 26:46
get it team and when you
multiplied 9 by two you get it
• 26:46 - 26:50
too. So when the signs of
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the same. Then the answer will
be positive whether they are
• 26:55 - 26:58
two negatives be multiplied
together or two positive
• 26:58 - 27:00
numbers being multiplied
together.
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And that's a lot to take
in for multiplication and
• 27:07 - 27:10
division of negative numbers.
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I'd like to summarize that bit
by again using a diagram when
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the signs of the sea.
• 27:19 - 27:27
A positive times by a positive
or a negative times by a
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negative. The
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• 27:34 - 27:41
positive. Is a
positive number when the signs
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are different. I positive
times by a negative or
• 27:48 - 27:52
a negative times by a
• 27:52 - 27:54
• 27:56 - 27:57
Is negative.
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And the same goes the same
rules go if you divide.
• 28:08 - 28:15
So if
• 28:15 - 28:23
these examples.
Negative 6 divided
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by. Negative
2.
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My answer will be do the
division first 6 / 2, which is 3
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and then think about the signs
negative negative signs saying
• 28:39 - 28:41
• 28:42 - 28:49
division negative 12 divided by
• 28:49 - 28:55
positive 3. Do the division is
normal 12 / 3 is for.
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Think of the signs
signs, different
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negative and a
positive. So the
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