# 6.CI 5-Video 1

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In this video,
we are going to model and solve word problems
in which fractions are multiplied or divided.
A survey showed that 5/6 of the students have played soccer.
1/2 of the students who have played soccer
have also played hockey.
What fraction of the students have played both sports?
Let's begin by modeling all of the students.
And, we can do that
with a single block.
And we'll re-size it, so, we have plenty of space to work.
And, we'll label this block.
And, the label will be
Total Students.
We know that five sixths of the students have played soccer.
To model five sixths,
we have to divide our block into 6 equal parts.
And, we can do that by selecting the block
and using the part slider
to make 6 equal parts.
And, then we can separate the blocks.
To show five sixths of the students visually,
we can make the sixth block a different colour.
And, we can label our 5 blocks as well.
We also know that half of the students who played soccer
have also played hockey.
Well, 5 blocks divided by 2
will be 2 and a half blocks.
So, we can divide the middle block into 2 parts.
And, actually we can do that to all of the blocks,
to make it more clear.
We know that half of 10 blocks is 5 blocks.
And, we can label that on our model.
One half of five sixths, played soccer and hockey.
And, we can make these 5 blocks a different colour
to distinguish them from the rest of the model.
And, now that our model is complete,
we can solve the problem.
The model shows that the fraction of students who played both sports
would be 5
out of
12.
Five
twelfths.
To actually solve this problem,
by computation,
we would need to find
one half
of
five sixths.
That's the same as multiplying
one half
by five sixths.
When you multiply fractions,
you multiply the numerators together.
1 times 5 is 5.
And, then yo multiply the denominators.
2 times 6 is 12.
And, we get the same answer.
Whether you solve it visually
or do the computation,
you get the same answer.
Now, let's try a division problem.
Mrs. Wilson bought a block of clay that weighed 2/3 of a pound.
She cut the block into 3 equal pieces.
What is the weight of each piece?
Let's begin by modeling 1 whole pound.
And, we can do that with a single block.
And, we re-size the block,
so, we have plenty of room to work.
And, we can label the block,
1 pound
of Clay.
We know that Mrs. Wilson bought a block of clay that weighed 2/3 of a pound.
To model two thirds,
we need to divide our block into 3 equal parts.
We can do that by selecting the block,
and using the part slider
to make 2 equal pieces.
And, we can separate the pieces.
To show two thirds more visually,
we'll change the colour of the third piece.
And, we can label
two thirds.
We also know that Mrs. Wilson cut her block of clay
into 3 equal pieces.
So, we want to take these 2 pieces
and change them into 3 equal pieces of equal size.
Or we can do that
by changing each piece into thirds.
So, we'll divide this piece into thirds.
And, this block into thirds.
And, we'll do the same
to this block
to be consistent.
And, now we can see
that 2 pieces together
would be one third
of Mrs. Wilson's block of clay.
Now, to make that more clear visually,
let's change the colour of these 2 pieces.
I'm going to break this section apart,
and then change
the colour.
And, the question asked,
what is the weight of each piece?
So, we want to know
what fraction of the whole,
these 2 pieces represent.
So, let's place a 'question mark' here.
And, now we're ready to solve the problem.
We can solve this very easily
by just looking at the model.
We have 2 blocks
out of a total of 9 blocks.
So, if we think of these 2 blocks as being
a piece of clay,
the weight of that piece of clay would be
two
ninths
of a pound.
We can also use computation to solve this problem.
Mrs. Wilson's original block of clay
weighed two thirds of a pound.
And, then she divided it
into
3 equal pieces.
We want to know the weight of each piece.
So, we want to find out
what two thirds
divided by 3
equals.
To divide a fraction by a whole number,
we can multiply the fraction
by the reciprocal of the whole number
which would be 1 over 3.
And, then to multiply fractions,
we multiply the numerators.
2 times 1 is 2.
And, we multiply the denominators.
3 times 3
is 9.
And, we get the same answer,
two ninths
of a pound.
We've solved the problem.