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## Arithmetic (all content)

### Course: Arithmetic (all content) > Unit 5

Lesson 6: Equivalent fractions 1# Equivalent fraction models

Use same-sized wholes to show equivalent fractions.

## Want to join the conversation?

- Why do fractions with different numbers equal each other, like 4/6 and 2/3?(126 votes)
- If you simplify 4/6 by dividing the numerator and denominator by 2, you will get 2/3.(75 votes)

- I used to be confused with simplifying fractions too! But here’s an something that helped me, to simplify... you really just divide! Do u know how to divide? I hope so! Cause you really just divide and yeah! Np!(7 votes)

- at1:32your hexagon looked alot like a cube like shape(9 votes)
- It does look like a cube not a hexagon your right noahcald9700!(0 votes)

- Why do fractions with different numbers equal each other, like 4/6 and 2/3?(5 votes)
- Let's say we have two pies, one with 3 slices, and one with 6 slices.

You eat 2 slices of the first and 4 of the second.

If the slices on the second pie are half the size of the first pie, and you eat twice the pieces of the second pie, then you ate the same amount of the second pie as the first pie.(7 votes)

- I don't get one bit of it help(6 votes)
- hey im on agles what if you have a 120 angle what will that count as like acute,right, or obtuse. plz help. thanks(2 votes)
- It is a obtuse because an obtuse angle is more than 90 deegrees and a acute angle is less than 90 deegrees. I hope this helped! (I don't know how to spell deegrees.)(6 votes)

- Than how do you know what to divide or multiply, like 4/6=8/12, this is correct but why is it multiply 2?(4 votes)
- Can you multiply and divide fractions?(4 votes)
- texogon?whats that man?(3 votes)
- How do you exactly cut them into 8 pieces?(2 votes)
- Put them into 4ths and then split those 4ths in half(3 votes)

## Video transcript

- So this hexagon right over here, the whole thing is filled
in with this pink color. So we'll say that this
represents one whole. The whole thing is filled in. Now, what I want you to think about is, which of these other
hexagons have 2/3 filled in? So, our goal is to identify the hexagons that are 2/3 filled in. So, pause the video now. So, I assume you have given
a go at it, you have tried to determine which of
these are 2/3 filled in. Now let's work on this together. So, when you're thinking in
terms of thirds, and here we're thinking in terms of 2/3,
literally two thirds, what we think about is dividing things into three equal sections. Let me see if I can draw
a hexagon fairly well. So, let me draw the hexagon. And I'm going to try to split it up into three equal sections. Whoops, I'm going to try to split it up into three equal sections. So, this is the center of
the hexagon right over here. And so, maybe that's one
of the equal sections. And then if I do one
more line, I split it up into three equal
sections, one, two, three. It's actually kind of
neat the way it's drawn. It looks like a three dimensional cube. But that was not my intent. My intent was to draw a hexagon. So each of these is a third,
actually I could write this. That's one third, that's one
third, and this is one third. But what we care about is two thirds, so two of these one thirds. And so, let me clean this up a little bit. So, I would fill in one of the one thirds and then two of the one thirds. And this right over here,
this hexagon that I've just drawn, now has 2/3 of it filled in. Now, I know what you're thinking. "All right, Sal, that would
have been pretty straightforward "if these were divided into thirds." "But these are not divided into thirds. "Each of these are divided into one, two "three, four, five, six equal pieces. "This is divided into sixths. "How do we figure out how many of the "sixths should be filled in, in order "to have the same thing as 2/3?" Well, I would tell you,
"You, don't worry too much." All we have to do, is we can redraw this or we can do a little bit
of work here to split this into, instead of three equal sections, we can split it into six equal sections. Well, how would we do that? We take each of those three equal sections and then split them
into two equal sections. So, this one right over here, I can split this into two equal sections. This one right over here, I can split into two equal sections. This one right over here, I can split into two equal sections. So, I had three equal sections before, now each of them have been split into two, so now I have six equal sections. So now, they way I've drawn
it, I'm dealing with sixths. And how many sixths represent the same fraction as the 2/3 did? I still have my shaded area. I have one, two, three, four sixths. So, 4/6 is the same thing as 2/3. Or, another way to think
about it, any of these that have four out of
the six equal sections filled in, that means that 2/3 of the sections are filled in. Or I could say 2/3 of
the hexagon is filled in. So, let's just look at these. This one, we have one, well
let me do it in a color that has a little more contrast. So we have one, two, three, four out of the six is filled in. 4/6 are filled in, that's
the same thing as 2/3. So, this one represents 2/3. This one only has two
of the sixths filled in, so it's not 4/6, which has
to be 2/3, this is 2/6. We want 2/3. This one is one, two, three, four. Four of the sixths are filled in. So this is 2/3. So I will put a square around that one. And this one has one, two, three, four of the sixths filled in, so this is 4/6, which we've already figured out is the same thing as 2/3. And we're done.