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# Equivalent fraction word problem example 3

Video transcript

You and your friends
are making name cards to assign seats for dinner. You each are given an
identical strip of blank paper and begin coloring parts
of it with crayons. You start with blue,
or you start with blue. Your friend Micah starts off
with green, Joelle starts with the red, Holden
starts with pink, And Kate starts with purple. After one color is
used, whose strip has the same part of its
area colored as yours? So let's look at my
strip right over here. It has how many equal sections? 1, 2, 3, 4, 5, 6 equal sections. And how many of them
have been colored blue? Well, let's see. 1, 2, 3, 4 of my equal sections
have been colored blue. So I need to figure out
which of these other folks have colored exactly
4/6 of their strip blue. Or another way of thinking
about it, I want to say, whoever has an equivalent
fraction colored, not blue, colored whatever
their color might be. So let's first look at
Micah, or "Mee-kah." So he's got 3 equal sections. He's got 3 equal sections,
and he's colored, he's colored 2 of
them, 2 of them green. Now is 4/6 and 2/3
the same thing? Well, he has 3 equal sections. I had 6. If I were to group each
of these into groups of 2, so if I were to divide
by 2, let me do that. If I were divide by 2, so
I'm going to group this into groups of 2. Then I would have 1, 2-- so I
have 1, 2, 3 equal sections. And then if I were to group the
blue strips into groups of 2, then I would have
1, 2 of them that have actually been colored blue. So if I divide both the
numerator and the denominator by 2, I get 2/3, which is the
exact same fraction as Micah. Another way to
think about it, is if you divide each of
Micah's sections into 2. So if you divide this into 2,
this into 2, and this into 2. Well, then how many total
sections does he have? Well, he had 3,
now each of those 3 have been divided into 2. So we can multiply
by 2 to get 6. So this is multiplying by 2. And each of the 2
in green, there now each of those sections have
now been divided into 2. So you can multiply by 2
as well, and you get 4. So 2/3 and 4/6 are
the same thing. So Micah has colored in the
same amount that I have. Now let's see whether any
of these other fractions are the same. So Joelle has colored
in 4, has colored in 4 out of 1, 2, 3, 4, 5, 6, 7. 4 out of 7. So it's not clear to me that we
can somehow multiply or divide the numerator and the
denominator here-- remember it has to
be by the same number in order to not change the
value of the fraction-- to somehow make
that equal to 4/6. She's colored in
the same number, but the size of each of
her strips is different. So 4/7 is definitely
different than 4/6. So we can rule Joelle out. Holden has colored in 3 out of
5 sections, 3 out of 5 sections. Once again, not obvious
that I can multiply both the numerator and the
denominator 3/5 times something to get you to 4/6, so
these aren't equivalent. And then Kate has colored
in, Kate has colored in 1, 2, 3, 4, 5, 6, 7, 8. 8 out of 11. And once again, I could try
to get a numerator up here, 4, I could divide by 2. But then if I divide by
2 in the denominator, I'm going to get
something strange. I'm going to get 4
over 11 divided by 2, which 11 divided
by 2 is like 5.5. So this is clearly not
the same thing as 4/6. We'll have rule
this out as well. So Micah and I have
colored in the same amount.