5 6 10 Illustrative Math Grade 5 Unit 6 Lesson 10

hi boys and girls this is Mrs Le Mo again and we're going to be doing today unit 6 lesson 10 all sorts of denominators we're going to find common denominators today how many do you see and how do you see them so notice that there are two blocks here each representing one if everything was filled in right and can think of this as one 1 2 3 4 5 six seven eight eight out of 1 two 3 1 two 3 4 so there are 12 can think of that as eight 12ths but can also think of it as thirs right let me get different pin here this would be 1/3 2/3 and 3/3 so could also think of this as 2/3 could think of this second block here as 1 two 3 out of 3 * 4 is 12 again or could think of it as one out of four right so this would be 1/4 2 fourths 3 fourths and four fours so could think of it also as 14 if were adding these two together it wouldn't make any sense for me to do 2/3 +4 but that would be the same as saying 8 12ths 12ths plus 3 12ths right it would be the same so if these are 12ths and these are 12ths and moved one block here one block there and one block there would have 11 12ths all in one box right because there's my 12th One 8 + 3 is 11 and my denominators are going to stay the same so can think of that in number of different ways couldn't could have counted also could have counted let me get different pin here all of the blue blocks because they're both out of twelves so could have said 1 2 3 four five 6 78 9 9 10 11 11 and they're cut into 12ths so could have seen it that way right each part is 112th and there are 11 colored all right let's see what they ask us about this how does the diagram show 2/3 plus 1/4 we talked about that already this is my one two if thought of about them cut into thirs 2/3 and if cut cut this one into fourths this would be my 1/4th right so that's how the diagram shows that see what else they ask us what is the value of 2/3 plus 11 1/4 well we just figured that out didn't we there are eight out of 12 here 8 9 10 11 so we know that that's 11 12ths we could also just move them over we could also say that this is 2/3 is the same as as 8 12ths and 1/4 is the same as 3 12ths so when I'm thinking about that let's think about that in different way so if this were 2/3 what can do to both the top and the bottom to get 8 12ths right and have to multiply the top and the bottom the numerator and the denominator by the same number to be able to get an equivalent fraction so 2 * 4 is 12 and 3 * 4 I'm sorry 2 * 4 is 8 and 3 * 4 is 12 could do the same thing for this side we could think of it as 1 14 times what is going to give me that 3 12ths well 1 time 3 is three and 4 * 3 is 12 so these two things are equivalent and we showed that in the picture but we could also show it by multiplying be by the numerator and the denominator being the same we know that 3 over3 is the same thing as multiplying by one right so 1/4 Time 1 would be 1/4 but we could choose to use 3 over3 to make it the same denominator same thing over here four over four is the same thing as one so know that 2/3 and 8 12ths are the same all right so now we're going to have to find the value of these Expressions do remember that have to have the same denominator in order to be able to add these so if I'm adding 34s and 78s need them to be the same denominator well can change this into an eighth couldn't don't need to change this into an eth because it's already an eighth and know that four time 2 is 8 so 3 * 2 is 6 remember that that 2 over two is 1 so 34s and 68 are equivalent and now can add 6 + 7 is 138s can leave it as 138s 138s or can say 8 goes into 13 one time one time 8 is 8 with five left over so my left over is going to be my numerator it goes in one whole time with five left over and my denominators always have to stay the same all right and always like to Circle my answers so that my teacher can find them really quickly now I'm going to do 34s plus 46 well can't change four into six so I'm going to have to find denominator that that can change both of them into right that would be the same so 34s plus 46 so I'm going to have to find common denominator well know that can make four of 12 can make six of 12 yeah so can make them both 12ths so what do multiply 34s times to get the denominator to be 12 4 * what is 12 4 * 3 is 12 which means have to multiply the top remember we need this to be one 3 * 3 is nine and need to multiply six * 2 to get 12 so I'm going to multiply four * 2 to get 8 now 9 and 8 12ths again can leave it 17 12ths or can come over to the side and say how many 12 are in 17 there's one whole 12th one whole 12th with how many left over five six seven five 12ths left over five 12ths left over all right now have subtraction problem subtraction problem and still don't have common denominators do so I'm going to really need to think about that one that one I'm going to do let's do that one in black so I'm going to move over here and do that 34s minus 2 FS to remember that have to subtract so what can make four and five what can multiply by to get common denominator so I'm going to set it up for success by going ahead doing this part first because know that these denominators all have to be the same well let's see can't think of multiple of five that would be the same except for 20 because can make that four into 20 can make it at five into 20 and my answer is going to be over 20 so to make four 20 I'm going to multiply it times five and 3 * 5 is 15 to make the five of 20 I'm going to multiply that times four so 2 * 4 is 8 and remember I'm subtracting so 15 minus 8 believe is 7 7 20ths so here we can write that up here too or could just circle my work 7 20ths all right okay so let's see what they ask us to do next it says how did you find the value of three 34s + 46 I'm so glad didn't erase my work so here's this problem right oops let me get my pencil back 34s where is that one three plus here we go this one here 34s plus 46 how did find the value knew that could make four of 12 and six of 12 so that's what did multiplied 34 * 3 over 3 and got 9 12ths remember I'm multiplying it times value of one because 2 over 2 is 1 and 3 over 3 is 1 okay knew that both four and six were factors of 12 and knew that four and six are factors of 24 as well could have used 24 could have said four time six so if we would have done that our number would have been equivalent to this but different all right let's go ahead and erase some of this so we talked about when we made the common denominator we talked about making it 12 what if we did make it 24 so 34s + 46 and how did come up with the number 24 well 4 * 6 is 24 so know that those will be equivalent fractions right 4 * 6 so that's going to be 4 * 6 is 24 so that's going to be 16 4 * 6 is 24 so that's going to be 18 and 18 + 16 know this is going to be over 24 that's 14 is going to be 34 over 24 that is equivalent to the answer that we got before which was 7 17 12ths so that's going to be the same as 17 12ths and how do know that because if divided if divide the top and the bottom sorry about that by the same number will get 17 12ths so 24 divided by what is 12 24 divided 2 is 12 and then 34 / 2 is 17 so know that these two are equivalent because I'm dividing by one right two over two is one and so these two things are equivalent could have chose to use the common denominator of 12 or 24 to solve that problem all right and it's asking how did you use the common denom to found the sum found the equivalent expressions with 12 or 24 as common denominator and then could add the fractions since they had the same denominator which means I'm just adding numerators the denominators are staying the same okay in the next activity we're going to see general strategy for finding common denominator for two fractions so let's go ahead and look at this multiply denominators here is Lynn's strategy for finding the value of two fths plus 49ths know that 5 * 9 is common denominator so I'll use that so she's multiplying to find the common denominator does Lynn's strategy for finding common denominator work so let's try that so two fths plus 4 9ths and she said she's going to say that the common denominator is going to be 5 time 9 which is 45 so that means have to multiply this times and this times so it's going to be 18 going to do the same thing for this my common denominator is going to be 45 so I'm going to multiply this times 5 and this times 5 9 * 5 is 45 4 * 5 is 20 and get 38 fifths 38 out of 45 not fifths 45ths should say so does that work yeah think it does right can find it out by multiplying the two denominators together so that's one strategy that can use find the value of each expression using the method that makes sense to you all right so 38s and 1 15 so can think of all the multiples of eight and five and find common one or can multiply five and eight think I'm going to start with that strategy so 38 need pen plus5 and so if multiplied eight and five know that my common denominator is going to be 40 so ask myself what do multiply eight times to get 40 multiply it times five so that means I'm going to multiply the numerators together and get 15 so now I'm going to multiply 5 * 8 to get 40 so that means I'm going to have to multiply 1 * 8 which is 8 and now since have all 40ths can add 15 and8 5 + 8 know is 13 so that's 23 4ths okay so my next problem that I'm going to do I'm going to choose different color so you guys can see so this was go back to and put now I'm going to do and is subtraction problem so 710 minus 23 so when think about the denominators think about the multiples of three don't see any ones that are going to end in zero so let's multiply right so it's 3 9 3 69 12 15 18 all the way way until we get to 3 * 9 which is 27 so I'm going to have to multiply them together so know that 3 * 10 is 30 so both of my denominators are going to end up being 30 so to get this to be 30 I'm going to multiply the top and the bottom times three to get this to be 30 I'm going to multiply the top and the bottom times 10 2 * 10 is 20 so now can subtract and get 130th so when lay out my problems like this my teacher can see all of my thinking right and each step that it took me to get to the part where subtracted or added so it's important that you show all of your work when you're doing these types of problems all right so I'm going to choose let's see I'm going to choose this color for let's see if we can fit it in there maybe should choose different one let's see let's do this darker one let's see if that works so now I'm going to do 7even over 20 plus 41 over 5050 all right so this one's going to be little bit difficult because have really high numbers right so could go through all the 20s and see if hit 50 know that if multiply two times something can't get five so I'm going to go ahead and multip them together just like Lyn did 2 * 5 is 10 and then add the zeros so 20 times think can make this 100 and not have to multiply them together right so 20 times 2 4 6 8 10 yeah five and then know that can make this 100 by just doubling it so didn't have to do 20 time 50 that would be really big denominator it would be th000 right so can make this 100 by multiplying times two and then can multiply 41 * 2 as well 7 * 5 know is 35 41 * 2 may have to go over here to my side or can just double it in my head 82 now it's an addition problem so I'm going to add 2 + 5 is 7 and 3 + 8 is 11 and I'm going to keep my denominator so this one became an improper fraction 117 over 100 and would probably leave it improper like that I'm not going to go ahead and and change it all right let's choose different color and do is another subtraction one have to keep that in mind when I'm working this out so 2 9 minus 1 6 so so I'm trying to think know that these are both have factors of three but what number would be good number to make common denominator without having to multiply them together think that could make 6 18 and know can make 9 18 so let's try 18 now there's nothing wrong with multiplying them together you're just going to end up with really big clunky fraction all right so what do multiply nine by to get 18 I'm going to multiply by two so that's going to be four and then I'm going to multiply this by three so that's going to be three and end up with 11 18th 118 there are other ways that you could have done each one of these problems depending on what you did to find the common denominator but my use my my knowledge of factors and all of my math facts to know that know that can make both N9 and 6 18 and knew that 20 would go into 100 and 50 would go into 100 all right we did lot of math there let's see if they what they ask us in the syn synthesis how did you find the volum of 38 plus 1/5 well for that one couldn't think of common denominator so multiplied 5 * 8 to get common denominator of 40 right and then asked myself what do multiply times eight to get 40 that would be five and what do multiply times five to get 40 and that would be eight so that became eight and this became 15 and then added them together and got 8 9 10 11 12 13 23 40s how did your strategy compare the lens well it was the same multiplied the two denominators together to get that common denominator how did you find the value of 710 minus 2/3 the same thing had to multiply couldn't think of multiple of both three and 10 that were the same so multiplied them together same strategy does Len strategy work here too yes how did you find the value of 720th plus 41 50ths well for this one knew that could have multiplied them together but knew that both of them were factors of 100 so just had to figure out what to multiply together to get to 100 each one could have done 100 or could have done th000 are these fractions equivalent yes they are because they could divide this number could divide this number by right the numerator and the denominator for the second one are 10 times the numerator so if divided this by 10 or if multiplied this by 10 would get this fraction if divided it would get this fraction which of these denominators do you prefer prefer the smaller one the 100 one because I'm used to them also like using thousands but didn't have didn't have to think about finding common denominator just took the product of thousand 20 times 20 time 50 so didn't have to think about it for this one it's easier for me to see and it's small or less clunky fraction but had to think about what would multiply 20 times to get 100 and what would multiply 50 times to get 100 all right today we investigated different ways to add and subtract fractions how can we find the value of this expression well we're going to have to find common denominator right for the two fractions so common denominator that used was 18 CU knew could make 9 18 and could make 68 but could have also used 9 * 6 could have also used 36 right 36 is also one could multiply this times four to get 36 and could multiply this time six to get 36 so there was lot of them that we could have used could have used 18 could have used 36 or could have used 54 4 because 9 * 6 is 54 they're all multiples of six and they're all multiples of N9 what do you notice about these common denominators which denominator did you use to help you find the value of 2 9s minus six and why did you choose that one of course choose chose 18 because that was going to make the nicest neest little fraction in the end but could have chosen either one of them and would have had an equivalent fraction all right so now we are at our cool down and we're going to find the sum of four fths plus 27s so five and seven what are some common denominators that could use or common multiples so can't think of any ex so I'm going to go go ahead and multiply them together 7 * 5 is 35 so to make this 35 I'm going to multiply by 7 4 * 7 is 28 to make this 35 I'm going to multiply times 5 7 * 5 is 35 2 * 5 is 10 and I'm adding always check my operation so it's going to be 385th 35ths 38 35ths all right boys and girls that's it for today we did some work with adding and subtracting fractions without common denominators and we found some Trends on how to find common denominators hope to see you again on lesson 11 thank you for joining me