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

Lesson 8: Equivalent fractions 2

# 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?
• you have to mulitply 2 on both the deomnater and the numerater
• Do you like pizza?
• Does fractions relate with multiplication and division?
• 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.
• What is the same as 2/4?
• 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.
• 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?
• 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
(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
• I need help I do not understand
(1 vote)
• he divided a pizza into two equal parts and converted it to fractions as he divided it into two equal parts. Then he wanted to eat an equal amount of pizza, so he ate half of it to get the same amount of pizza.
Like the half of two is one. Then he divided it into four equal parts. Like a quarter of four is 1. So, to make it half he ate half of it which means 2/4. Then he divided it into 8 equal pieces. To get it as a half he ate 4 pieces which means the fraction is 4/8. Now as you look closely you will see that the fraction is half of the pizza. He is trying to tell that these fractions are equal and called as equivalent fraction