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### Course: Arithmetic > Unit 4

Lesson 5: Equivalent fractions# Equivalent fraction models

Use same-sized wholes to show equivalent fractions.

## Want to join the conversation?

- So you simply need to multiply by 2 and you get an equivalent fraction? am I right?(9 votes)
- You're on the right track. When you multiply both the numerator (top number) and the denominator (bottom number) by the same number, you get an equivalent fraction. But remember, it's not always by 2. You can actually multiply by any number, as long as you multiply the numerator and denominator by the
**same number**.

For example, if you start with 1/2, you can multiply both the numerator and denominator by 3 to get 3/6, which is equivalent.

You'll learn this more in-depth later when multiplying fractions is discussed, but this works because in the example above we are actually multiplying by 3/3, which is equal to 1, and anything multiplied by 1 is equal to itself.(19 votes)

- wait so lets say that the hexagon is a pizza and you took 2 slices of pizza away. so, can you just say they the denominator is 3 because you have 3 left and the numerator is 2 because you took two away?(3 votes)
- No, but you're close!

If you took away the two slices you're left with 4 slices. Not 3.

If we start with a pizza that has 6 slices (the hexagon) and we take away 2 slices that means we still have 4/6 of the pizza left.

It's 4 because that's how many we have left, and it's 6 because that's how many slices we need to have a whole pizza.

Now the 2/3.

If we consider a simpler fraction like 1/2, how many slices of the hexagon do we need for there to be half of a pizza? It'd be 3 slices, or 3/6!

That's why we say that 3/6 and 1/2 are EQUIVALENT!

It's the same with the 4/6 and 2/3. 4 out of 6 is 2/3 of the hexagon.(6 votes)

- Can you do equivalent fractions without drawing models? If so, can you tell me how to do it? (Sometimes I forget strategies)(2 votes)
- Yes, you can use equivalent fractions without drawing models! Just multiply/divide the numerator and denominator by the same number. For example:

70/200 is an equivalent fraction of:

7/20, 140/400, 280/800, .......

Anyhow, just multiply/divide the numerator and denominator by the same number! Hope this helps(5 votes)

- Why do fractions with different numbers equal each other, like 4/6 and 2/3?(133 votes)
- If you simplify 4/6 by dividing the numerator and denominator by 2, you will get 2/3.(83 votes)

- people im ten watch this in ten yeas and say hey hes 20 now trust me it will make you think(5 votes)
- do you thik 200 400 -500 =34(1 vote)

- denominator=bottom numerator=top right??(2 votes)
- here is a way to remember denominator downstairs, numerator north (north is upwards)(5 votes)

- how does he do it so fast(5 votes)
- what so fast? his math?(0 votes)

- two or more fractions that have the same values but appears different are called equivalent fractions. Or, Two or more fractions that name the same part of a whole are called equivalent fractions. Equivalent fractions always represent the same point on the numbers line.(3 votes)
- how do fractions help you in life(3 votes)
- Why do fractions with different numbers equal each other, like 4/6 and 2/3?(2 votes)
- Well both represent a piece of a whole number, two fractions are the same when they represent the same piece:

Imagine a cake divided in 6 pieces, then you take 4 of those 6, you just took a little bit more than half of the cake.

If you divide the same cake in 3 pieces, and then you take 2 of those 3, you just took a little bit more than half of the cake!

In both cases you took the same amout of the cake, 4/6 of the cake, is the same as 2/3 of the cake. Both are exactly the same little more than half of the cake.(2 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.