Translating words to Equations


Uploaded by videosbyjulieharland on 18.05.2011

Transcript:
>>Hi, this is Julie Harland
and I'm your math gal.
Please visit my website
at yourmathgal.com
where you could search for any
of my videos organized
by topic.
We're going
to translate sentences
into algebraic equations
or inequalities.
So we'll start with this one,
7 less than a number is 10.
Now what makes this a sentence
is it has this verb, is,
and usually that's what
separates an expression
from an equation.
So when you see the word is
that's kind of breaking
up where the equals sign
will be.
So we're going
to have the left side
of the equation,
which will be 7 less
than a number,
and the right side
which will be the number 10.
So is, that's
where the equal sign is.
Now we just look before the
word is and we've got what?
Seven less than a number
so that means we're
subtracting 7 from a number
so let's call the number n.
So N minus 7 will be 7 less
than a number on the left side
and then on the right side
both the equal sign
after the word is is just the
number 10.
And now we've just translated
7 less than a number is 10
into an equation.
Now if we were trying
to solve this,
usually you would define
your variables.
In other words you would say
I'm gonna let n be the number
that, in this video we're just
going to keep using n,
let that be the number.
So where it says a number
we're just gonna use the
letter n. You could use x, c,
a, any letter you want.
I like n for number.
Alright why don't you try this
one on your own
by putting the video on pause
and seeing
if you can figure it out.
Okay again we're gonna see
that we've got
that word is there,
5 more than a number is,
those are equal,
is twice a number.
That breaks up so left side
of the equation
with the right side
of the equation.
Alright so I've got the word
is, that's gonna be our equals
so we've got 5 more
than a number.
Okay, 5 more
than something means I'm
adding 5 to something
and I'm gonna add it
to the number and we decided
to use n for the number.
Alright now I've got the left
side of the equal sign
and then what
about on the right hand side?
We've got twice the number,
that means 2 times the number
or 2n.
Hopefully you got that.
Alright let's look
at this one, 4 is not equal
to the product of 2 and 3.
Hmm, a little tricky.
You see that word is again
but it's this whole part
that goes together,
4 is not equal so instead
of an equal sign we're gonna
use a not equal sign.
What's a not equal sign
look like?
Well, that's what an equal
sign looks like.
That's what a not equal sign
looks like.
You just put a slash
through it, not equal.
So now we've got the left side
of the equation is just the
number 4.
So we have 4 on the left side,
4 is not equal to
and on the right hand side we
have the product of 2 and 3.
Alright product
means multiplication.
So the product of 2
and 3 means we're gonna
multiply 2 times 3.
So we can just say 2 times 3
with a dot
or you could put a 2
parenthesis 3
to denote multiplication
and this makes sense.
Hopefully everybody,
4 is not equal to 6,
right cause 4
and 6 aren't the same number.
Notice there was no variable
in this one.
That's okay.
So this is still just taking a
statement and writing it using
the symbols.
In this case all the symbols
were just numbers
and the not equal sign.
Alright the sum of a number
in 8 is less than 14.
Again you see this word is
but you kind of have to look
at the context.
It says is less
than something.
So this time instead of is,
which would be equal,
we have is less than.
This symbol is written
like this, is less than.
So again we've broken
up what comes before
that is the sum of the number
in 8 and the sum, remember,
means addition.
So a number, we'll use n
and the other part of it is 8
so n plus 8 is less than,
right, what's
on the other side
of the equal sign, I'm sorry,
of the less than symbol, 14.
So now we've just translated
this sentence
into an inequality.
Both of these
on this page are called
inequalities
because they don't have just
an equal sign.
We've got a not equal sign
and we have a less
than symbol.
So these are called
inequalities as opposed
to equations
but they're still
algebraic inequalities.
I guess this first one is
actually just numerical,
there's no algebra.
So it's just an inequality
with numbers.
Alright here are a couple
for you to try on your own
and then we'll check them
so put the video on pause
and try these two.
Alright the first one,
4 decreased
by twice a number is 1 more
than the number.
Okay we've got just is this
time so that's gonna separate
the two parts.
So first we've got 4 decreased
by twice a number, hmm,
4 decreased by,
alright so I've got to start
with the number 4
and then I'm gonna decrease it
so I have to subtract
something from that.
What is it gonna be?
I'm subtracting twice a
number, that's 2 times n
so I write 2n.
And I've got is,
there's my equal.
Alright now we've got,
right hand side,
1 more than the number.
Alright 1 more
than something is I'm adding 1
to something.
What am I adding it to?
Whatever that number is,
same number,
n. So I've got 4 minus 2n
equals n plus 1.
So all we're doing
is translating.
We're not worrying
about what n is.
Alright and let's see this
last one, 3 times a number is
greater than or equal to 9,
hmm, tricky.
So I've got,
this whole part is greater
than or equal to,
that's this symbol,
greater than or equal to.
Alright so on the left hand
side of that I've got 3 times
the number,
on the right hand side I've
got 9.
So on the left hand side 3
times the number can be
written as 3n,
cause we're using n
to represent the number.
On the right side we've just
got the number 9
so now we've written 3n is
greater than or equal to 9.
So that's just a little
introduction
to translating some sentences
into equations
or inequalities.
Where there's an equal sign
it's an equation.
When you've got greater than
or a less than symbol or a not
to equal symbol,
then we're talking
about an inequality.
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