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### Course: 5th grade (Eureka Math/EngageNY) > Unit 3

Lesson 1: Topic A: Equivalent fractions- Equivalent fractions
- Visualizing equivalent fractions
- Equivalent fractions (fraction models)
- More on equivalent fractions
- Equivalent fractions
- Decomposing a fraction visually
- Decomposing a mixed number
- Decompose fractions
- Writing mixed numbers as improper fractions
- Writing improper fractions as mixed numbers
- Write mixed numbers and improper fractions

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# Equivalent fractions

Learn how equivalent fractions represent the same amount, even with different numerators and denominators. We uses a pizza example to show how 1/2, 2/4, and 4/8 are equivalent, as they all represent the same portion. Created by Sal Khan.

## Want to join the conversation?

- how do you know if its equivalent?(24 votes)
- you have to mulitply 2 on both the deomnater and the numerater(3 votes)

- Do you like pizza?(8 votes)
- Does fractions relate with multiplication and division?(2 votes)
- Yes, they greatly do. Proper and improper fractions by themselves are basically division problems. By only considering the numerator, the "original value" was not being divided.

Mixed fractions, show the quotient as a whole number, with the amount left that could not be "equally shared" as a proper fraction rather than stating it as a remainder.(4 votes)

- what does equivalent mean?like its equal?(3 votes)
- I wonder if you could solve a fraction with only using multipacation and addition?(2 votes)
- You
*could*, in theory. Multiplication is repeated addition, and division is repeated subtraction. However, it's a matter of using the correct tool.

You*could*hammer a screw into a board, but it will work better if you use a drill and screwdriver. ;)(2 votes)

- What does equivalent mean?(2 votes)
- Equivalent means equal

I hope this it's helpful.

Happy learning!(2 votes)

- What is the same as 2/4?(0 votes)
- So I've got a whole pizza here, and let's say that I were to cut it into two equal pieces. Let me cut it right over here into 2 equal pieces. And let's say that I ate one of those 2 equal pieces. So let's say I ate all of this right over here. What fraction of the pizza have I eaten? Well, I took the whole and I divide it into two equal pieces, and then I ate one of those pieces. So I ate 1/2 of the pizza. Now, let's imagine that instead of cutting that pizza into only 2 equal pieces, let's imagine instead that decide to cut it into 4 equal pieces. So let's draw that. So 4 equal pieces. So I could cut once this way and then I could cut it once this way. And so here I have 4 equal pieces. But let's say that I want to eat the same amount of pizza. How many of these 4 equal pieces would I have to eat. I encourage you to pause the video and think about that. Well, I would eat this piece. You could imagine me eating this piece and this piece right over here. I've eaten the same amount of the pizza. Each of these pieces you could imagine got cut into 2 pieces when I cut the whole pizza this way. And so now I have to eat 2 slices of the 4, as opposed to 1 slice of the 2. So I just ate 2 out of the 4 slices. I'm using different numbers here. Here I'm using a 1 in the numerator and 2 in the denominator. Here, I'm using a 2 in the numerator and a 4 in the denominator. These two fractions represent the same quantity. I ate the same amount of pizza. If I eat 2/4 of a pizza, if I eat 2 out of 4 equal pieces, that's the same fraction of the pizza as if I eat 1 out of 2 equal pieces. So we would say that these two things are equivalent fractions. Now let's do another one like this. Instead of just dividing it into 4 equal pieces, let's divide it into 8 equal pieces. So now we could cut once like this. So now we have 2 equal pieces. Cut once like this. Now we have 4 equal pieces. And then divide each of those 4 pieces into 2 pieces. So I'll cut those in-- So let's see. I want to make them equal pieces. Those don't look as equal as I would like. So that looks more equal, and that looks reasonably equal. So now how many equal pieces do I have? I have 8 equal pieces. But let's say I wanted to eat the same fraction of the pizza. So I could eat all of these pieces right over here. Well, how many of those 8 equal pieces have I eaten? Well, I've eaten 1, 2, 3, 4 of those 8 equal pieces. And so once again, this fraction, 4 of 8, or 4/8, is equivalent to 2/4, which is equivalent to 1/2. And you might see a little bit of a pattern here. Going from this scenario to this scenario, I got twice as many equal slices. Because I had twice as many equal slices, I needed to eat two times the number of slices. So I multiply the denominator by 2, and I multiply the numerator by 2. If I multiply the numerator and the denominator by the same number, then I'm not changing what that fraction represents. And you see that over here. Going from 4 slices to 8 slices, I cut every slice, I turned every slice into 2 more slices, so I had twice as many slices. And then if I want to eat the same amount, I have to eat twice as many pieces. So all of these, 1/2, 2/4, four 4/8, and I could keep going. I could do 8/16. I could do 16/32. All of these would be equivalent fractions.(4 votes)

- If 1/2 is the same as 2/4 then aren't you just adding?

then 2/4 would be the same as 4/6 right?(3 votes)- it is correct because you multiplied it by 3 and it could get multiplied by two or more it would still be equvilint.

for example times 1/2 by 3 it would be equal to 3/6(0 votes)

- i'm just beginning fractions i don't understand please help!!(1 vote)
- You just did a fraction in your information you said you like to practice Kahn academy for forty minutes to a hour and a half one half is a fraction think of fractions like this you have one hole piece and 1/2 is half of that piece add another half and you have one hole same thing with 1/4 you have 1 out of four parts add three more parts and you have one hole or four fourths hope this helped(2 votes)

- I am having a hard time with Equivalent fractions please help me!(0 votes)
- Sooo, lets say your fraction is 3/6. The equivalent is 2x more than that. Multiply 2 to 3/6 and you'll get 6/12. That means 6/12 is a equivalent fraction to 3/6.

You don't multiply 2 by the numerator, 3, and switch the multiplied by 3 for the denomatior, keep it the same number, like 2 for each place.(5 votes)

## Video transcript

So I've got a whole
pizza here, and let's say that I were to cut it
into two equal pieces. Let me cut it right over
here into 2 equal pieces. And let's say that I ate
one of those 2 equal pieces. So let's say I ate all
of this right over here. What fraction of the
pizza have I eaten? Well, I took the
whole and I divide it into two equal pieces, and
then I ate one of those pieces. So I ate 1/2 of the pizza. Now, let's imagine that instead
of cutting that pizza into only 2 equal pieces,
let's imagine instead that decide to cut it
into 4 equal pieces. So let's draw that. So 4 equal pieces. So I could cut once
this way and then I could cut it once this way. And so here I have
4 equal pieces. But let's say that I want to
eat the same amount of pizza. How many of these 4 equal
pieces would I have to eat. I encourage you to pause the
video and think about that. Well, I would eat this piece. You could imagine me eating
this piece and this piece right over here. I've eaten the same
amount of the pizza. Each of these pieces you could
imagine got cut into 2 pieces when I cut the whole
pizza this way. And so now I have to
eat 2 slices of the 4, as opposed to 1 slice of the 2. So I just ate 2 out
of the 4 slices. I'm using different
numbers here. Here I'm using a
1 in the numerator and 2 in the denominator. Here, I'm using a
2 in the numerator and a 4 in the denominator. These two fractions
represent the same quantity. I ate the same amount of pizza. If I eat 2/4 of a pizza, if I
eat 2 out of 4 equal pieces, that's the same
fraction of the pizza as if I eat 1 out
of 2 equal pieces. So we would say that
these two things are equivalent fractions. Now let's do another
one like this. Instead of just dividing
it into 4 equal pieces, let's divide it
into 8 equal pieces. So now we could
cut once like this. So now we have 2 equal pieces. Cut once like this. Now we have 4 equal pieces. And then divide each of
those 4 pieces into 2 pieces. So I'll cut those
in-- So let's see. I want to make
them equal pieces. Those don't look as
equal as I would like. So that looks more equal, and
that looks reasonably equal. So now how many equal
pieces do I have? I have 8 equal pieces. But let's say I wanted to eat
the same fraction of the pizza. So I could eat all of these
pieces right over here. Well, how many of those 8
equal pieces have I eaten? Well, I've eaten 1, 2, 3,
4 of those 8 equal pieces. And so once again, this
fraction, 4 of 8, or 4/8, is equivalent to 2/4,
which is equivalent to 1/2. And you might see a little
bit of a pattern here. Going from this scenario
to this scenario, I got twice as
many equal slices. Because I had twice
as many equal slices, I needed to eat two times
the number of slices. So I multiply the
denominator by 2, and I multiply the
numerator by 2. If I multiply the numerator
and the denominator by the same number,
then I'm not changing what that fraction represents. And you see that over here. Going from 4 slices to 8
slices, I cut every slice, I turned every slice
into 2 more slices, so I had twice as many slices. And then if I want to
eat the same amount, I have to eat twice
as many pieces. So all of these, 1/2, 2/4, four
4/8, and I could keep going. I could do 8/16. I could do 16/32. All of these would be
equivalent fractions.