Reciprocal of a Mixed Number

U02_L2_T3_we1 Reciprocal of a Mixed Number

Find the reciprocal of 2 and 4/5.

So if we want to invert this fraction,
we have to write it

as a pure fraction first, or
as an improper fraction.

Right now, it's just a mixed number.

So let's just write it as an improper fraction.

So 2 and 4/5, if we write it as
an improper fraction,

it's still going to be over 5, but
the numerator is now going to

be 5 times 2 plus 4, and that's
because 2 is 10/5, or 2 times 5 fifths.

So let's write it like that.

So it's going to be 2 times 5 plus 4.

2 times 5 is 10.

10/5 is the same thing as 2, and
then the 4/5 is this 4/5 right there.

So this is going to be equal
to 2 times 5 is 10

plus 4 is 14: 14/5.

So these are equivalent fractions.

This is written as a mixed number.

This is written as an improper fraction.

It's improper because the
numerator is bigger than the denominator.

Now we want to find the reciprocal.

When you find the reciprocal, you just
switch the numerator and the denominator.

You just flip the fraction.

So if you want to take the reciprocal.
Let me do this in a new color.

If we want to take the
reciprocal of this, we just

swap the 5 and the 14.

So this is going to be: instead of 14/5,
it's going to be 5/14.

And we're done!