- Hi, my name is Josh Udy.
I'm the Elementary
Mathematics Curriculum Manager
for Houston Independent School District.
In this video, I will be representing
and solving the addition of fractions
including mixed numbers with
unlike or unequal denominators
using an open number line.
Let me begin by reading the problem.
Here, I have Jacob's shape.
You can see it's an isosceles trapezoid
because each of these legs
are five-sixth inches,
the base at the bottom
is two and a half inches,
and the base at the top
is one and a half inches.
In order to add these fractions,
I will be using an open number line.
I want to mark off where zero is,
and then I need to think about
how I want to add these
fractions together.
Knowing that I can use the
commutative property of addition,
it doesn't matter which fractions
I choose to represent first,
and since two and a half is the greatest
and it's easy to represent,
I'll show that first.
One, two, I'll mark three,
and then I'll show a half.
So I'm going to show that the length here
is 2 and 1/2 inches long for the first base.
Next, I'm going to add in 1 and a 1/2 inches.
So I already have a half inch there,
and now I just need to add one more inch.
So this represents one and a half inches
for the second base.
Now I need to add in both 5/6 inch parts.
So here I'll make a mark for my next inch,
and because it's broken into
sixth,
the denominator is six,
I know I need to draw interval marks
so that there are six in between this.
1, 2, 3, 4, 5 marks will make sixths,
and I know that one side
is five of those six.
One, two, three, four, five out of six.
This represents 5/6 for one of the legs.
I'll call that leg one.
Now I need to add in my last leg,
which is also sixths.
I'll show a six here for one more inch,
and I'll break it into sixths.
Now I need to add 5/6 inches more.
I already have 1/6 of an inch right here.
So I just need to add 1, 2, 3, 4,
5/6 inches for leg two.
Here, I can see that my total perimeter length
is five inches and 1/6, 2/6, 3/6,
4/6 inches.
So I know that Jacob's trapezoid
has a perimeter of five
and one, two, three, four,
four-sixth inches.
While the answer of five
and four-sixth inches
is mathematically correct,
you will want to have
your students simplify
the fractional part of
your answer, four-sixths.
I'll show this using an open number line.
In order to show this,
I first need to represent
one inch on my number line.
I know that I'm trying to represent the fraction 4/6,
so I'll want to partition this into sixths.
I know that I have four-sixths,
so I can shade that.
1/6, 2/6, 3/6, 4/6.
In order to simplify this fraction,
students need to see that
they can partition the distance
between zero to one into
a different number of equal parts.
I could actually make halves
by showing 3/6 and 3/6,
but that doesn't simplify
the orange shaded part nicely.
So I know I could try to group by two,
and when I do that,
I see thirds.
This means that
this distance is one-third,
this distance is another third,
and this distance is a third-third.
I have 4/6 or 1/3,
2/3.
This means that the perimeter is
equal to 5 and 2/3 inches.
It's important here
that students understand
that 5 and 4/6
inches is the exact same
as 5 and 2/3 inches.
(bright music)
