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Simplifying fractions

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hello this is mr. Baker and this is another one of our videos on mathematical techniques that we've been developing in class today we're going to be focusing on simplifying fractions before we discuss simplifying fractions it's better to start with it with a definition of what equivalent fractions are equivalent fractions are fractions that equal  simplest the simplest form of a fraction could be thought of as a special type of equivalent fraction one definition of simplest form would be the equivalent fraction with the lowest denominator another definition is that the simplest warm is the fraction that uses the fewest pieces IE having the smallest numerator and just for some review we can remember that the new where's the number on top of a fraction which tells us how many pieces were focusing on and the denominator is the number on the bottom of the fraction which tells us how many pieces we have in when we first introduced this concept in class we as with as with most Concepts try to use a visual tool to make the IDM more concrete the visual tool in this case is a sheet of what we call fraction strips as you can see fraction strips splay the same length being broken into several different fractions to half's 3/3 for Force 5/5 on and on way to 12:12  we first use this tool again to make the idea more concrete and to help us notice pattern with fractions that are equivalent to each other the way that we use this tool  is we find the fraction that were focusing with focusing on excuse me for example let's look at  6 tents I would find the tents on my fraction strips I would count out 1 2 3 4 5 6 tenths and line up the edge of another sheet of paper right on the edge of the 6/10 then I'm going to use the is the paper to see if there any other fractions which touched the edge of the paper and thus are the exact same length as 6/10 if I go down I can see that for example 3/5 is equivalent to 6/10 now of course students are not always going to have this visual tool with them yes one has been sent home and yes they have one in class however we need to use this as a bridge to build understanding of how to find equivalent and simpler fractions clue using mathematical relationships as opposed to a visual prompt in our work we have noticed that for instance 6/10 and 3/5  art equivalent also that 6/8 and 3/4 are equivalent using these two examples we can see that there were theirs Nation ship mathematically not just visually between the two fractions this relationship is a is one word that can be solved by division or displayed by division so for example both 6 and 10 can be divided by the same number  they can't B / 26 / 2 equals 310 / 2 of course equals 5 and so we can see that not only are these fractions equivalent visually but that there is a proportional relationship between these again the same relationship is displayed with 6/8 in 3/4  I can divide both the numerator and the denominator by the same number now in this case it does happen to be two again and again we see that 6 / 2 is 3 + 8 / 2 is 4 the general strategy that were attempting to develop in class is looking at a fraction  determining what number we can divide both the numerator and the denominator by  of course all numbers can be divided by 1 but as we see dividing by one does not change the fraction so dividing by one not help us simplify fractions on help us find a simplest form so we will not be focusing on dividing by one of course so given a fraction another example might be 8/12 the students are sing to look at these numbers and think what number can they divide both of them by  no students May recognize that these are even numbers so they can both be divided by 2  if they were 2/2 they would get four sexts well 4/6 is a simpler form it is not the simplest form because 4 and 6 can also be divided by the same number in this case they can both be divided by 2  so we need to divide again until we can no longer divide by any number other than one and that's the case now two and three can only be divided by 1 or themselves but of course we can only do we have to divide both by the same number  since these cannot be divided any further this is the Apple list  forum it has the smallest a nominator of all the equivalent fractions 2/3 4 6 8 12 it also uses the fewest pieces to as opposed to 4 or 8 so here we can see the general strategy  of dividing  both have the fraction by the same number now some students may have good with this same problem 8 out of 12  I noticed that there's old there was a larger number than to that they could divide both numbers by some students May recognize both of these numbers as multiples of four numbers we can get by multiplying by 4 since we can get these numbers by multiplying by for that means we can divided by 4  so in that case if a student were start off recognizing if they could / that larger number for send they would end up at the simplest form quick but either way we can see that the general strategy is to divide both pieces of the fraction by the same number now determining what number 2 / can be challenging  so a few strategies would be trying to divide by  smaller numbers such as to  or three as we saw what's our previous example  dividing by these lower numbers will work but it may involve an extra step along the way another technique which we have not yet developed in class but we'll would be dividing by what we called the greatest common factor this is a technique that really is introduced in fourth grade however some third graders are ready to use this strategy the greatest common factor would be the largest number that we can multiply both the numerator excuse me would be the largest number that we can multiply to get the greater or the denominator for example looking at another fraction  912 a student would realize that they can divide scuse me if they can multiply 9 by 1 and 9 as one times 9 equals 9 or they can x 3 x 3 x 3 equals 9 I don't have to list three twice of course only once so here I have all the numbers that I can divide 9 by again the numbers that we can multiply by to get a number same numbers we can divide that number by  so one night and three are the factors that I can divide 9 by if I were to think about 12 I can multiply 1 times 12 so 1 and 12 or both factors I can multiply to time 6 so 2 and 6 or both factors  I can multiply 3 by 4 as well so three and four factors if I were to look at these two lists of factors the only one that I see that's common between them is 3  so I'm going to use three as the number that I divided by 2 simplify the fraction of course 9/3 is 3 + 12 / is 4  one is the only number that I can divide both three and four by that means that I have now found simplest form so we could say that the simplest form of 9/12 is 3/4 and if I were to go back to our original model  are visual model I can check that that's true I can line my paper up with 9:12 NFI follow the edge of the paper down I see that it lines up  with 3/4 so I know visual and mathematically that these numbers are equivalent now that double-checking may or may not be necessary for all students and may not be necessary very as students develop their understanding of this skill in of this concept however at this beginning stage when we've just introduced the concept that may be helpful for the students to back up their mathematical thinking with this visual thinking so again to review the most important aspect of this technique is that we want to divide both pieces of the ocean by the same number and again that may work the first time or we may have to dividing a long until we get to the simplest form however this technique of always dividing the numerator and the denominator by the same number even if it requires an extra step will always get to the simplest form of a fraction obviously this video is one component of developing this concept in our students but I hope that it's a component that you found helpful thank

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