Equivalent fractions

welcome to my presentation on equivalent fractions so equivalent fractions are essentially what they sound like there are two fractions that although they use different numbers they actually represent the same thing let me show you an example let's say I had the fraction mmm 1/2 why isn't it writing make sure I get the right color here to add the fraction 1 over 2 so graphically if we were to draw that if I had a pie and I were to cut it into two pieces that's the denominator there two and then if I were to eat one of the two pieces I would have eaten one half of this pie makes sense nothing nothing too complicated there well what if instead of dividing the pie into two pieces let me just draw that same pie again instead of draw it divided in two pieces what if I divided that pie into four pieces so here in the denominator I have a possibility of total of 4 pi four pieces in the pie well and instead of eating one piece this time I actually ate two of the four pieces so I ate two out of four pieces or a two fourths of the pie well if we look at these two pictures we can see that that I've eaten the same amount of the pie so these fractions are the same thing if someone told you that they ate one half of a pie or if they told you that they ate two fourths of a pie it turns out that they ate the same amount of pie so that's why we're saying those two fractions are equivalent another way if we actually had let's do another one let's say and that pie is quite ugly but aha let's assume it's the same type of pie let's say we divided that pie into eight pieces and now instead of eating - we ate four of those eight pieces so we ate four out of eight pieces well we still ended up eating the same amount of the pie we ate half of the pie so we see that one half will equal two forts and that equals four eight now do you see a pattern here if we just look at the numerical relationships between 1/2 2/4 and 4:8 well to go from 1/2 to 2/4 we multiplied the denominator the denominator just as a review is the the number on the bottom of the fraction we multiply the denominator by 2 and when you multiply the denominator by 2 we also multiply the numerator by 2 we did the same thing here and that makes sense because well if if I double the number of pieces in the pie then I have to eat twice as many pieces to eat the same amount of pie let's see let's let's let's do some more examples of equivalent fractions and hopefully it'll it'll hit the point home let me erase this why isn't it letting me erase something is okay let me see erase let me just a regular Mouse okay good good good sorry for that so let's say I had the fraction 3 over 5 well by the same principle as long as we multiply the numerator and the denominator the numerator and the denominator by the same numbers we'll get an equivalent fraction so if we multiply the numerator times 7 and the denominator times 7 we'll get 21 because 3 times 7 is 21 over 35 and so 3/5 and 21 over 35 are equivalent fractions and we essentially and I don't know if you already know how to multiply fractions but all we did is we multiplied 3/5 times 7 over 7 to get 21 over 35 and if you look at this what we're doing here isn't magic 7 over 7 well what's 7 over 7 if I had 7 pieces in a pie and I were to eat 7 of them I ate the whole pie right so 7 over 7 this is the same thing as 1 so all we essentially said is well 3 fifths and we multiplied it times 1 and that's which is the same thing as 7 over 7 boy this thing is messing up same thing stems it and that's how we got 21 over 35 so it's interesting all we did is multiply the number by 1 and we know that any number times 1 is still that number and all we did is we figured out a different way of writing 21 over 35 so let's say if I were to let's start with a fraction 5 over 12 and I wanted to write that with the denominator let's I want to write that with the denominator 36 well to go from 12 to 36 what do we have to multiply by well 12 goes into 36 3 times so if we multiply the denominator by 3 we also have to multiply the numerator by 3 times 3 we get 15 so we get 15 over 36 is the same thing as 5 over 12 and just going to our original example all that's saying is if I had a pie with 12 pieces and I ate five of them let's say I did that and then you had a pie the same size pie you had a pie with 36 pieces and you ate 15 of them then we actually ate the same amount of pie