Translating words into algebraic expressions

Uploaded by videosbyjulieharland on 18.05.2011

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We'll be translating verbal
into algebraic expressions
so there's some terms we need
to know.
The first one is sum.
When you see the sum
that refers to addition
so when you see this word sum
it means we're going
to be adding.
Okay, sum is the same thing
as adding.
So we read this,
the sum of a number
and 6 makes sense,
if you have a sum you've got
two things.
So the two things we have,
so you've got a number and 6.
Usually it's separated
by that word and, okay?
So what do we call the number?
Well let's just use
a variable.
I'm gonna use n for a number.
So we could write n,
that's one part of the sum
and 6 is the other part
of the sum.
So that's how we would write
the sum of a number and 6.
What about the difference
of a number and 2?
Difference refers
to subtraction
so when you see the word
difference it means we
are subtracting.
And again notice this is
of a number and 2.
The two parts are separated
by that word
and so whatever comes first
you'll put before the minus
sign and what comes
after the word
and is what you
would subtract.
That's how you would
differentiate what comes first
and what comes second.
So again, let's just use n
again to represent the number,
it has to be a variable,
and 2.
So n minus 2 is how we would
write the difference
of a number in 2.
Alright next one, the product
of a number and 5,
product means multiplication
so when you see the word
product you have to associate
that with multiplying.
We've got a number and 5
so how would we write a number
and 5 multiplied together?
Well you could say n times 5,
Often you would write this
as 5 times n.
And the most simplified way
of writing it is you know
when you have a dot between it
and you have a variable
and a number you can just put
it together
and write it as 5n.
Now you could also put a
parenthesis around the n
or a parenthesis around the 5
or a parenthesis
around both of them.
There's more
than these three ways
to show a product
but 5 n is probably the
simplest way
of writing this answer
so that would be the product
of a number and 5.
The last one will be the
quotient or ratio.
Both of those words
represent subtraction.
Both quotient
and ratio mean division
but we usually don't write the
division sign
when we are doing algebra
so a more common way
of writing this answer,
again we're separating a
number and 4
so those are the two things,
you could of course say the
number is n, n divided by 4
and it doesn't matter whether
it says quotient or ratio,
both of them mean the
same thing.
That represents division
so whatever comes first goes
before the division sign
so we have a number and 4,
those are the two things.
I forgot to circle it up here,
here we go.
So the more common way
of writing this is
as a fraction
so we say the quotient
of a number divided by,
we use the fraction bar,
and 4.
So this is the way we usually
want to write our answers
when we are doing algebra
so when we're working
with variables.
So we've got the sum
of a number and 6 and plus 6.
The difference of a number
and 2, n minus 2.
The product of a number
and 5 is 5n.
It looks funny to put n5.
We always put the coefficient,
the number part,
in front of the variable.
And the last is the quotient
or the ratio
of a number and 4.
The way we write that is n
over 4 so whatever comes first
you put in the numerator
and what comes second, and 4,
that's what goes
in the denominator.
Alright there are a lot
of ways of expressing
subtraction and there's a lot
of little nuances here.
Let's look at these,
6 more than a number,
that refers
to addition cause we're doing
more than something
so we're going to add it
so if it says 6 more
than a number, think of 6 more
than your age.
Well you have to know your age
and then you would add 6
to it.
So in this case 6 more
than a number means you start
with the number
so we have a number
and then we're gonna do 6 more
than that so we're going
to add 6 to it.
Now the question is could you
write 6 plus n?
Certainly because n plus 6
does happen
to be the same thing
as 6 plus n.
But these next three are
and it's gonna make a
difference what comes first
before the minus sign
and what comes
after the minus sign.
So look at this first one,
7 less than a number.
So one technique is thinking
about how you would answer
this question,
7 less than my age,
how would you get that answer?
You would take your age
and then you would subtract 7
from it.
So instead of starting
with an age we're gonna start
with a number, okay,
and then we're gonna subtract
7 from it.
So this is tricky.
It's not 7 minus n. What it's
saying is 7 less
than a number means you have
to start with a number
and then subtract 7 from it.
Now look at this third one,
it's not the same.
It says 7,
oops it is the same.
I didn't mean
to put less than.
I meant to put 7 less
a number.
A little bit different.
Seven less a number,
well first
of all most people don't talk
that way but you might see
this once in a while.
Seven less a number means we
start with 7 less a number
means we take away
that number.
So this is 7 minus n,
that's pretty tricky.
What's the difference?
It doesn't have
that word less than.
So again for this one 7 less
than a number,
if you're not sure how
to do it, put
in something you would know
like your age
and then do the same thing
using a number as opposed
to your age.
Seven less a number,
that's like saying 7 less 2.
You mean you start with 7,
subtract 2.
And how about this last one,
9 decreased by a number.
It means I've got to start
with 9 and then I'm gonna
decrease it so I have
to take something away from it
and I'm gonna take away the
number, again I'll call it n.
These are pretty tricky,
the ones for subtraction.
So you can see we have the
word difference,
which means subtraction
but here's some other ways
that subtraction might
come up.
You also might see minus
or you might see subtracted
from, decreased by, is here,
etcetera, there's a few more
that might pop up.
By the way,
these are all
just expressions.
They're not equations.
We're not solving
for anything.
We're just writing
an expression.
Notice there's no verb.
Six more than a number,
7 less than a number,
No verb. It's not going
to be an equation.
There's going
to be no equal sign.
We're simply writing an
expression from English
into mathematical symbols.
Let's try doing some
that are used
for multiplication.
Alright first one here,
twice a number,
what does that mean?
Twice a number just means 2
times the number
so we're gonna use n
for the number,
2 times the number you would
just write as 2n.
Now this next one I'm putting
two things together.
It says 3 times a number,
well what would that be?
That would be 3n.
Okay 3 times a number
subtracted from 10.
Okay, so what are you gonna
start with?
Three times the number
or the number 10?
Well you're subtracting
from 10 so that means you've
got to start off with 10
and then you're gonna subtract
something from it
and what are you
gonna subtract?
Three times a number,
that would be 3n.
So there are a couple examples
where we've got multiplication
in the mix
and the second one also has
the subtraction.
Okay try these two
on your own.
Put the video on pause and see
if you could write this
as an expression.
Go ahead and let the number be
n. Okay so what do we have?
Five added to the product of 9
and a number.
So we're adding 5 to something
so I have to do this
part first.
The product, remember,
means multiplication
and what are the two parts?
I've got 9 and a number.
So how do I write the product
of 9 and a number?
I do 9 times n which is 9n.
And then it says I'm gonna add
5 to that so then I add 5.
That's what you should get.
Alright, excellent.
Six less than the quotient
of a number and 4 so 6 less
than something means I'm gonna
take away 6 from something.
So I know I'm gonna subtract 6
from something,
now I've gotta figure
out what I'm subtracting
it from.
What am I subtracting 6 from?
The quotient,
okay remember what the
quotient means,
we write that as a fraction,
fraction bar
and we have the number and 4
so we'll put n
in the numerator,
cause that comes before the
word and, so in the 4
in the denominator
so we've got n over 4 minus 6.
So now we've written 6 less
of the quotient
of the number and 4.
[ Silence ]
>>Please visit my website
where you can view all
of my videos
which are organized by topic.