How to solve one-step equations with fractions and decimals | 6th grade | Khan Academy

- [Voiceover] Let's give
ourselves some practice

solving equations.

So let's say we had
the equation 1/3 plus A

is equal to 5/3.

What is the A that makes
this equation true?

If I had 1/3 plus this
A, what does A need to be

in order for 1/3 plus
that to be equal to 5/3?

So there's a bunch of
different ways of doing this,

and this is one of the fun
things about equations is

there's no exactly one right way to do it.

But let's think about
what at least I think

might be the simplest way.

And before I work through
anything, you should always try to

pause the video, and do it on your own.

So what I like to think
about is can I have just my A

on one side of the equation?

And since it's already
on the left-hand side,

let's see if I can keep
it on the left-hand side,

but get rid of this 1/3 somehow.

Well the easiest was I can
think of getting rid of

this 1/3 is to subtract
1/3 from the left-hand

side of the equation.

Now I can't just do that from the

left-hand side of the equation.

If 1/3 plus A is equal to 5/3,

and if I just subtract 1/3
from the left-hand side,

then they're not going
to be equal anymore.

Then this thing is going to be 1/3 less,

which this thing isn't going to change.

So then this thing on
the left would become

less than 5/3.

So in order to hold the
equality, whatever I do on the

left-hand side I have to do on
the right-hand side as well.

So I have to subtract 1/3 from both sides.

And if I do that, then
on the left-hand side,

1/3 minus 1/3, that's the whole reason why

I subtracted 1/3 was
to get rid of the 1/3,

and I am left with A is
equal to 5/3 minus 1/3,

5/3 minus 1/3,

minus 1/3, and what is
that going to be equal to?

I have five of something,
in this case I have 5/3,

and I'm gonna subtract 1/3.

So I'm gonna be left with 4/3.

So I could write A is equal to 4/3.

And you could check to
make sure that works.

1/3 plus 4/3 is indeed equal to 5/3.

Let's do another one of these.

So let's say that we have
the equation K minus eight

is equal to 11.8.

So once again I wanna solve for K.

I wanna have just a K
on the left-hand side.

I don't want this subtracting
this eight right over here.

So in order to get rid of
this eight, let's add eight

on the left-hand side.

And of course, if I do
it on the left-hand side,

I have to do it on the
right-hand side as well.

So we're gonna add eight to both sides.

The left-hand side, you
are substracting eight

and then you're adding eight.

That's just going to cancel out,

and you're just going to be left with K.

And on the right-hand
side, 11.8 plus eight.

Well, 11 plus eight is 19,
so it's going to be 19.8.

And we're done, and once again,
what's neat about equations,

you can always check to see
if you got the right answer.

19.8 minus eight is 11.8.

Let's do another one,
this is too much fun.

Alright, so let's say that
I had 5/13 is equal to

T minus 6/13.

Alright, this is interesting
'cause now I have my variable

on the right-hand side.

But let's just leave it there.

Let's just see if we can
solve for T by getting rid of

everything else on the right-hand side.

And like we've done in the
past, if I'm subtracting 6/13,

so why don't I just add it?

Why don't I just add 6/13?

I can't just do that
on the right-hand side.

Then the two sides won't be equal anymore,

so I gotta do it on the
left-hand side if I wanna

hold the equality.

So what happens?

So what happens?

On the left-hand side I have,

let me give myself a
little bit more space,

I have 5/13 plus 6/13,

plus 6/13 are equal to,

are equal to...

Well, I was subtracting
6/13, now I add 6/13.

Those are just going to add to zero.

6/13 minus 6/13 is just
zero, so you're left with T.

So T is equal to this.

If I have 5/13 and I add to that 6/13,

well I'm gonna have 11/13.

So this is going to be
11/13 is equal to T,

or I could write that
the other way around.

I could write T is equal to 11/13.