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# Equivalent fractions

CCSS.Math:

## 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 two equal pieces and let's say that I ate one of those two 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 divided it into two equal I divided it into two equal pieces and then I ate one of those pieces let me and then I ate and then I ate one of those pieces so I ate one half of the pizza now let's imagine that instead of dividing instead of cutting that debt pizza into only two equal pieces let's imagine instead that I decided to cut it into four equal pieces so let's draw that so four equal pieces so cut it I could cut it once this way and then I could cut it once this way and so here I have four equal pieces four equal pieces but let's say that I want to eat the same amount of pizza how many of these four 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 can imagine me eating this piece and this piece right over here I've eaten the same amount of the pizza I just each of these pieces you could imagine got cut into two pieces when I cut the whole pizza this way and so now I have to eat two slices of the four as opposed to one slice of the two so I just ate two out of the four slices so even though these I'm using different numbers here here I'm using a 1/2 and here or one in the numerator a two in the denominator here I'm using a two in the numerator and a four in the denominator these two fractions represent the same quantity I ate the same amount of pizza if I eat two fourths of a pizza if I eat two out of four equal pieces that's the same fraction of the pizza as if I eat one out of two 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 into four equal pieces let's let's divide it into 8 equal pieces eight equal pieces so now we could so now we could cut once like this so now we have two equal pieces cut once like this now we have four equal pieces and then divide each of those four pieces into two pieces so or cut those in so here we have so let's see I want to make them equal pieces so let's not look as equal as I would like so that looks more equal and then that looks reasonably equal so now how many equal pieces do I have I have 8 equal pieces 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 eighths 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 I got twice as many equal slices because I had twice as many equal slices I needed to eat 2 times the number of slices so I multiplied the denominator by 2 and I multiplied the numerator by 2 if I multiply the numerator and the denominator by the same number that 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 twice as twice as many pieces so all of these 1/2 2/4 4 eighths and I could keep going I could do 8 16 so I could do 16 30 seconds all of these would be equivalent fractions