Hey, guys.
Welcome to Algebra I.
Today we're gonna get started
translating expressions.
You've actually been
translating expressions
since elementary school,
but I bet you didn't realize
that you were.

(Describer) She activates a screen which has the word "six".

I bet when you see that word,
I bet you know
it means this number.

(Describer) She writes 6.

You just translated
an expression
from verbal to numeric.
Look at that next number.

(Describer) 11.

I bet you know
that it means this word.

(Describer) She writes.

You just translated
an expression
from numeric to verbal.
Look at that last one,
"Twelve more than a number."
That's when we step it up
to Algebra I.
How exactly do you translate
something like that?
You've got to know key words
and what they're telling you
you need to do.
When you see
plus, and, sum,
increased by,
greater than, more than,
all of those phrases
are telling you to add.
If you run into a problem,
for example,
"Three more than number,"
you see "more than" in there.
That's telling me I'm gonna be
adding two things together.
In algebra, when we don't know
what something is,
we assign it a variable.
Pick any letter in the alphabet.
Normally, we use x.
Three more than some number,
and I don't know
what that number is.
I can represent that
as 3 plus x.
I have some value
that I'm unsure of,
and I'm increasing it by 3.
Now, there's another way you
could write that expression.
If you remember
from middle school,
you can add numbers
in any order that you want.
Right now I have 3 plus x.
I could've also written it
as x plus 3. Either one is fine.
They're both acceptable.
Let's take a look at some more.
"Subtract, less, minus,
difference of."
I bet you knew
from the first word
that those were telling you
to subtract.
When you see something
like two less five,
it sounds a little awkward.
Just swap out "less"
and think "subtract" instead.
So, 2 subtract 5.
2 subtract 5.
You just represented that verbal
expression as something numeric.
Let's keep going.
"Less than, subtracted from."
Those also mean subtract.
So, two less than five.
I have a value of 5,
and I need 2 less than that.
So, 5 subtract 2.
That's exactly
what that means numerically.
I have some value of 5,
and I need 2 less than that.
"Product, times, multiply by."
Those are all telling you
to multiply, and in algebra,
we use the dot symbol
to show that we're multiplying.
So, 7 times a number.
7 times a number.
That's showing me the product
of 7 and some value of x.
If you want, you can
completely disregard the dot
and just write 7x.
Both of those expressions
are telling you
you're multiplying 7 times x.
Let's keep going.
"Quotient, divided by."
I bet you knew those were
telling you to divide.
An example like, "The quotient
of a number and nine."
You have some number that you
don't know the value of,
and you're dividing it by 9.
In Algebra 1--
in all math classes--
it's easier if you use
the horizontal fraction bar
and not the slanted one.
As you keep going through
the course, you'll learn why.
It makes some problems
difficult to read.
From now, go ahead and use
that horizontal bar
when you're dividing.
Okay. Now it's your turn.
Look at these examples.
Pause the tape and try and see
if you can get through these.
You'll never know for sure
if you got it
till you try it yourself.
Then press play,
and we'll check our answers.

(female describer)
Title: Match.

(Describer) Title: Match. In one column are five verbal expressions. In the other are five algebraic expressions.
In the verbal column:
Number One: Five more than a number
Number Two: A number divided by five
Number Three: The product of five and a number
Number Four: Five less a number
Number Five: Five less than a number
In the algebraic column:
Letter A: 5 minus x
Letter B: x over 5
Letter C: x minus 5
Letter D: x plus 5
Letter E: 5x

In one column
are five verbal expressions.
In the other
are five algebraic expressions.
In the verbal column,
number one:
Five more than a number.
Number two:
A number divided by five.
Number three: The product
of five and a number.
Number four:
Five less a number.
Number five:
Five less than a number.
In the algebraic column,
letter A: 5 minus x.
Letter B: x over 5.
Letter C: x minus 5.
Letter D: x plus 5.
Letter E: 5x.

(instructor)
Let's go over these.
"Five more than a number."
Did you catch that "more than"?
That's telling you
you need to add.
That has to be D.
I'm adding 5 to a number
I don't know the value of.

(Describer) X plus 5

"A number divided by 5."
So, "divided by."
I'm looking for division.
Straight across.
That one's B.

(Describer) X over 5.

"The product
of five and a number."
So, "product."
I know I'm multiplying,
so look for your multiplication.
That one's E.

(Describer) 5x

"Five less a number."
Remember we said
that was the one
that sounded awkward?
So, instead of saying "less,"
just say "subtract."
So, 5 subtract a number.
That one's A.

(Describer) 5 minus x.

"Five less than a number."
Either process of elimination,
you know that one is C,
or you really did translate it.
There we go, x minus 5.
Let's step up
our operations a bit.
See if we can handle these.
Anytime you see
"to the power of,"
that is a signal
there's an exponent involved.
Look at that example.
"A number
to the power of five."
I don't know my value,
but I'm gonna raise it
to the fifth power.
So, I'll write x,
and then my exponent's 5.
Some value I'm unsure of.
I've raised to the fifth power.
Let's keep going.
"Squared to the power of two
to the second power."
This is still telling me
I have an exponent,
but in this case,
the exponent is 2.
Anytime you see phrases
like that,
your exponent is gonna be 2.
A number squared.
"Squared" is telling me 2.
I've got x to the second power.
Let's keep going.
"Cubed to the power of three
to the third power."
All right, got an exponent.
And I bet you figured it out
that in this case
that exponent's 3.
A number to the third power.
Don't know what that number is,
so that's my variable
that I'm gonna raise
to the third power.
Okay?
We got a few for you to try.
Pause me again.
Give yourself a shot at these.
Then we'll check our answers.

(describer)
Number one: A number
to the second power.

(Describer) Number One: A number to the second power
Number Two: A number cubed
Number Three: A number to the power of four

Number two:
A number cubed.
Number three:
A number to the power of four.

(instructor)
Okay. "A number
to the second power."
Let's see what you got.
Gonna have to switch
to my pointer tool.
All right,
x-squared for that one.
"A number cubed."
X-cubed for that one.
"A number
to the power of four."
X to the 4th power
for that one.
Let's keep going.
Let me get my pen back.
Okay. "One-half of a number."
I know nobody likes fractions.
We see them and say,
"What do I do?"
You can't avoid them in math,
so learn to handle them.
Eventually,
they won't bother you.
So, "one-half of a number."
That "of" is telling me
I've got to multiply.
I'm taking one half of
some value that I don't know.
So, I've got 1/2 times a number.
Don't know what that number is.
I'm calling it x.
If you feel fancy, you could
also represent this this way:
x divided by 2.
Because multiplying
a number by 1/2
is the same as
dividing it by 2.
Whichever one you want to write,
they're both acceptable.
Let's keep going.
"Three-fourths of a number."
Different fraction,
but it's the same idea.
I've got 3/4 times a number.
Or, in this case,
if you want to write it
differently,
you could represent that
as 3x divided by 4.
They're both acceptable.
It's a matter of
which one you want to write.
Let's keep moving.
"Twice a number."
This one isn't a fraction,
but it's a little funky.
I want to make sure you can
handle it. "Twice a number."
You're multiplying it by 2.
Whatever number that is,
I multiply it by 2.
I could represent that as 2x,
and you've translated
that expression.
Let's take a look at these.
Go ahead and pause.
Try this,
see how you work it out.
Then we'll get back together
and we'll check our answers.

(describer)
Number one:
Four-fifths of a number.

(Describer) Number One: Four-fifths of a number
Number Two: One-third of a number
Number Three: Triple a number

Number two:
One-third of a number.
Number three: Triple a number.

(instructor)
Let's see how you did.
So, "four-fifths of a number."
Either you wrote
4 divided by 5 times x,
or 4x divided by 5.
Either one is fine.
"One-third of a number."
Either one of those are fine.
1/3 times x or x divided by 3.
And triple a number: 3 times x.
Okay. Let's keep going.
"Three times the sum
of five and a number."
That sounds like a mouthful,
but we'll break it down,
and then it won't be so bad.
"Three times the sum
of five and a number."
Handle this part first.
Let me get my pen back.
You want to handle that sum
of five and a number.
Throw back to middle school
a bit, order of operations.
You remember whatever was in
the parentheses you'd do first?
Same idea here.
Because I want to handle that
sum of five and a number first,
I'm gonna put it
in parentheses.
So, the sum--I know I'm adding--
of 5 and a number.
And then I need
three times that sum.
So, three times the sum
of five and a number,
and you've translated
that expression.
Let's keep going.
Get the pointer tool back.
All right.
"One-half the product
of six and seven."
It sounds like a lot again,
but let's do
exactly what we did before.
We're gonna start with
the second half of that first,
that product of 6 and 7.
In this case,
I'm gonna put my dot.
Because I'm multiplying,
and if I don't show that dot,
it's gonna look like 67.
You don't want to take
the product.
Don't multiply
6 and 7 together.
Represent it just like you did:
6 times 7.
Then I have
one-half of that product.
I know I'm gonna be multiplying
by one-half out front.
All right?
Not too bad.
A couple for you to try.
So, press pause.
Then we'll get back together
and check our answers.

(Describer) Number One: Four times the product of nine and a number
Number Two: One-fourth the sum of three and a seven

(describer)
Number one: Four times the
product of nine and a number.
Number two: One-fourth
the sum of three and a seven.

(instructor)
Okay.
"Four times the product
of 9 and a number."
You've got your 9 times x
in parentheses,
and you're multiplying it
by four.
"One-fourth the sum
of three and a seven."
You're adding 3 plus 7,
and then 1/4 times that.

(Describer) Three plus seven is in parentheses.

All right.
Okay.
So, you've had some practice
translating expressions.
I hope you got comfortable
working with fractions.
And I bet you now
are feeling more comfortable
with all of this altogether.
See you next time.

(Describer) Accessibility provided by the US Department of Education.