First find out what 7/12 + 1/6 is To make it easier turn 1/6 into 2/12 (They are equivalent) So 7/12 + 2/12 = 9/12 (Simplified is 3/4 or 0.75)
Well you dont really need to add 3/4 + 1/10 because the other one is 3/4 and this one is 3/4 PLUS 1/10 so of course this will be larger but ill do the math anyways. You can turn them into decimals since they're friendly numbers you can do it in your head. 3/4 = 0.75 1/10 = 0.1 0.75 + 0.1 = 0.85 As a fraction that would be 17/20 in simplest form.
Ohkay I talked about slide 1 and 2 yesterday sooooo here goes slide 3:
2/5+2/10 is bigger because if you divide 60 by 5 its 12 so i times 12 by 2 (because its 2/5 and one fifth is 12) Ohkay so i got 24 then I didvded 60 by 10 then i got 6 but then i hhad to go 6 times 2 (because 6 is one tenth and 12 is two tenths) so i got 12 then i added 24 and 12 and that got me 36 mins Therefore its 36/60 (60is the denominator becaus ether is 60 mins in a clock)
Next waz easy 1/6 is 10 mins of a clock and 2/3 is 20 nmins of a clock so i added 10 and 2 that equals 30 so 30/60 there for 2/5+2/10 is bigger
Slide 4:
ohkay well 7/12 is 35 mins in a clock and 1/6 is 10 mins so thats 45/60
ohaky well the 3/4 is easy thats 45 mins of a clock but 1/10 i had to divide 60by 10 which go tme 6 so 1/10 is 6 mins so i add 45 and 6 that equals 51/60 Therefore 3/4+1/10 is larger
slide 4: I don't know what to say abotu it O__o
Slide 6&7
I talked about slide 6 and 7 yesterday But i was wrong yesterday but know i understand ^__^ YAY me!!!
Slide8:
1/2 of 24 = 12 1/4 of 24 = 6 1/8 of 24 = 3 1/3 of 24 = 8
Ohkay tell you the truth i copied down the answer at school for the first 3 Then I figured out that 1/3 of 24 = 8 because 24 divided by 3 equals eight i just take 24 and divide it by the numerator
Ummm....Slide 9,10 and 11 i dont really understand but i'll try latah Because its time to eat ^__^
1st slide 1/2 + 2/4 and 1/6 + 3/6 1/2 of 60 minutes is 30 minutes 2/4 of 60 minutes is 15 minutes add 15 minutes to 30 minutes = 45 minutes...so its 45/60 because 45 is the equal ## and 60 is the equal of minutes.
1/6 of 60 minutes is 10 minutes 3/6 of 60 minutes is 30 minutes because 10 minutes is 1/6 of 60 minutes so you just have to multiply 10 to 3 = 30 add 10 to 30 you get 40 minutes.... so its 40/60 because 40 is the equal ## and 60 is the equal of minutes.
then you just have to compare 45/60 and 40/60. 45/61 is larger because 45 is a higher number than 40/60.... you don't have to compare the denominators because they have the same numbers.
1/2 of 24=12 (u get this by dividing 24 by 2) 1/4 of 24=6(u get this by dividing 12 by 2) 1/8 of 24=3(u get this by dividing 6 by 2) 1/3 of 24=8(24 divided by 3 is 8(numerator divided by denominator)) A simple way to do it is divide the denominator by the whole. an eg. is 24(the whole)and 3(the denominator) equals 8(which is the answer)
2/5 + 2/10 is bigger than 1/6 + 2/3 by 6 minutes. 2/5 shown on a clock is 24 minutes and 2/10 shown on a clock is 12 minutes. I divided 60 by 5, so i did 12x2 because it is 2/5. Also because 1/5 = 12 and you just double the numerator. Then i divided the clock into 10 sections and that gave me six minutes in each section which gave me twelve minutes altogether. MY answer altogether was 36 minutes out of 60 minutes.
2/5+2/10 is bigger because I divided 60 by 5 and its 12 so then i times 12 by 2 because 2 is the numerator and then i got 24 then I divided 60 by 10 and got a 6 and then times 6 by 2 because 2 is the numerator again. so i got 12. then i added 24 and 12 and that got me 36 mins And the fraction i got is 36/60
Next, i got 1/6 is 10 mins of a clock and 2/3 is 20 mins of a clock so i added 10 and 20 and got 30 so 30/60 So that means that 2/5 + 2/10 is bigger
Ok, well i answered some of these in my comment for yesterdays. So i guess do the rest?
Slide 1* 1/4 + 2/4 OR 1/6 + 3/6 There are a few ways to do this. First find out what 1/4 is out of 60 because there are 60 minutes on the clock counted by 5 min and there is a marker for every 5 minutes, so there are 12 markers. Anyway we find out 1/4 first because its simple and its a unit fraction. you can look at the clock and just divide it into four equal pieces. OR divide 12 by the denominator to find out what marker it goes on ( this stratagy only works with unit fractions ).So now we know that 1/4 goes on the 3 which is 15 minutes, since the other fraction is 2/4 you can just double you answer for 1/4 and then add the both of them together like so. 15min+30min=45 So we get 45 minutes for 1/4 and 2/4. now we can just repeat the stratageys that we used earlier with the unit fraction. So if we do that, then we should find out that 1/6 goes on the marker 2 which is 10 minutes. Now we just multiply that 3 times to get 3/6. So we get a total of 40 minutes for 1/6 and 3/6. So that means 1/4 + 2/4 is larger than 1/6 + 3/6
Slide 2* 5/12 + 1/12 OR 1/3 + 1/12 Well to compare these we need to figure out what they are. Like i said earlier using the markers on a clock for every 5 minutes, we can count 5 of them to find out that 5/12 is 25 minutes out of an hour. Or we can multiply the numerator by 5 to find out how many minutes the fraction stands for ( can only be done when the denominator is 12 like in this senario ). So now we do the same for the 1/12, and from that we get 5 minutes, Making a total of 30 minutes out of 60. Now for 1/3 and 1/12. You can find out 1/3 by dividing the 12 markers on the clock by 3 to get you 4 which is the mark for 1/3 of the clock. So 1/3 is 25 minutes. 1/12 is of course 5 minutes like we have figured out a billion timesn making the total 25 minutes out of 60. So 5/12 + 1/12 is larger than 1/3 + 1/12.
Slide 3* 2/5 + 2/10 OR 1/6 +2/3 So 2/5 was kind of a ugly number for me to deal with at this point so i skipped that for now and did 2/10 first because its more friendly to me. So for 2/10, i jsut divided the number of markers by the denominator, ( 12/10= 0.12 = 12 minutes) and found out that it was on the second marker on the clock and 2 smaller marks making it 12 minutes for 1/10. Since its 2/10 i just multiplied it by 2 to get my answer for this one of 24 minutes. Then I went back to 2/5 because i can jsut divide what i got for 2/10 by two to get my answer. So then the answer would be 12 minutes! if i were to do it and involve mroe of my thinking for nothing, i would've did the same thing with 2/10, but the reason i didnt do this one was because i was to lazy to think and calculate 12/5 or to get out a calculator and do that. ANYWAY, the answer for that would be 36 minutes. Now for 1/6 + 2/3. For 1/6 we can divide the 12 by 6 and we get 2, so its 10 minutes long. For 2/3 we do the same thing, but end up with 4, so thats 20 minutes for 1/3. Since we have 2 we multiply 20 by 2 and get 40 minutes for 2/3. In total for 1/6 + 2/3 we have 50 minutes out of 60 so that makes it larger than 2/5 + 2/10.
Slide 4* 7/12 + 1/6 OR 3/4 + 1/10 Using what i did earlier, from whats further up on this comment and past comments AND from my pappers and scribbler. I got 35 minutes for 7/12 because if you multiply the 7 by 5, you get your minutes since you already know what marker it is on since the markers is equal to the denominator. for 1/6 you can divide the markers by the denominator to find out the marker its on so this is 10 minutes. Total for this is 45 minutes. The next one is 3/4 + 1/10. So 3/4 is simply gotten by dividing the 12 by the denominator to get the mark or place or it. its 3 in this case so we have 15 min for 1/4, we have 3/4 so we multiply this by 3 to get 9 marks or 45 minutes. Now dividing again but this time to get the minutes for 1/10 like we did earlier. We got 0.12 by dividing 12 by 10 so each 1/10 of an hour is 12 minutes. Adding those together you get 57 minutes in total making this larger than 7/12 + 1/6.
Slide 5* People Subs 1 3/4 =3/4 2 6/4 =1 2/4 3 9/4 =2 1/4 4 12/4 =3 5 15/4 =3 3/4 6 18/4 =4 2/4 7 21/4 =5 1/4 8 24/4 =6 9 27/4 =6 3/4 10 30/4 =7 2/4 11 33/4 =8 1/4 12 36/4 =9 13 39/4 =9 3/4 14 42/4 =10 2/4 15 45/4 =11 1/4 16 48/4 =12 17 51/4 =12 3/4 18 54/4 =13 2/4 19 57/4 =14 1/4 20 60/4 =15 21 63/4 =15 3/4 22 66/4 =16 2/4 23 69/4 =17 1/4 24 72/4 =18 25 75/4 =18 3/4 26 78/4 =19 2/4 27 81/4 =20 1/4 28 84/4 =21 29 87/4 =21 3/4 30 90/4 =22 2/4 That line shows all of the posible answers to that from 1-30 people.This looks like this because each person gets 3/4 of a sub so theres a pattern of the numerator increasing by 3.
Slide6* 4 goes into 9 is the same as . . . 9 divided by 4 and 9/4, when your dividing, your trying to see how many times a number goes into a number, in this case, how many times 4 goes into 9. It's also the same as 9/4 because that's what it would look like as a fraction.
Slide7* 4 Goes into 9 is not . . . 2 1/4 because that's what the answer would be and not the question. The question is 4 goes into 9 and that is 9 divide by 4.
Slide8* 1/2 of 24 = 12 1/4 of 24 = 6 1/8 of 24 = 3 1/3 of 24 = 8 The pattern here is that it keeps halving itself. 1/4 is just half of 1/2 and so is 6 the half of 12. But for the 1/3 of 24, i divided the 24 by 3 and got 8 because Fractions Represent Division. I could have also looked at the clock thing that we did and just doubled my answer of it being on the 4th marker and gotten 8.
Slide9 and 10* This is just that ratio table thingy we did. Sooo lets just have a look back there instead of me rewriting it and making this longer . . .
Slide11* LAAAAAAAAAAAAAST ONE!!!!!! Peeeeps Subs 48 = 144/4 = 36 60 = 180/4 = 40 2/4 120 = 360/4 = 90 Well heres another line up of the numbers and the subs. I got the first one with 48 peeps by doubling the answers from 16 but i realized that that was wrong when i checked my answer over. I realized this when i looked at the ones that ended in 8 and found out that they all ended in a 4 so i thought something was wrong when i found that problem.So i found another easier way to figure this out, multiply the number by 3 and get the improper fraction, it works everytime. But then i just realized that half of 48 was 24 . . . so i just totally blanked out. THE REAL ANSWER this time I'm TOTALLY SURE. The real answer is 144/4 or 36 subs and i got that by doing what i did to the other number that i thought was half, i multiplied the answer by two to get this answer. The multiplying by 3 works too but i just wanted to point this out. Now for 60, i got 180/4 or 40 and a half subs by multiplying the answers from half of 60 peeps which is 30. And for 120 i did the exact same things except i couldnt multiply by two, so i found 12 and and added 0's which is just multiplying by 10. I did that because 120 is 12 but 10 times more, so whatever that was i just did the same thing to get the subs equal to the peeps.
THIS TOOK 2 hours!!!!! i guess boredom can kill a guy. . . Anyway since i know this is going to be long . . . TAKE THAT ROMULO!!! haha try beating MY book =P Have a good night?
1/4 of 24 is 6 because we know that 12 is half of 24 so we just half 12(=6)
1/8 of 24 is 3 because we know that half of 24 is 12 and half of 12 is 6 so we just simply half it.
1/3 of 24 is 8 because 8 goes into 24 3 times.
A simple way of doing all that is using a calculator (eg. denominator/the number ex.24/3) or just half the answer from the other one each time the even denominator goes up by 2.
For today I'll be commenting on all of them. Oh Snap another big book!
Slide 1 (1/4+2/4 vs 1/6+3/6):
Part 1 The firt thing you do is add 1/4 abd 2/4. Since they have the same denominator you can turn it to 3/4 just by adding them, but now you have to find out what 3/4 of a clock is. So what you do is divide the clock into 4 equal pieces. For each piece it will equal a time of 15 minutes. Since th fraction is 3/4 all you do now is multiply 15 by and you get 45 minutes. So that means 1/4 + 2/4= 45 minutes out of 60 minutes.
Part 2 Now what you do is find out what 1/6 + 3/6 equals. So since there denominators are the you can multiply both numerators and denominators by two an you get:
1x2= 2 6x2= 12 So 1/6 turns to 2/12.
Now you have to do the same thing for 3/6.
3x2= 6 6x2= 12 So 3/6 turns to 6/12. So you new fractions are 2/12+6/12
I multiplied them to make it easier since a clock has 12 marks and for each mark it equals 5 minutes. So 2x5= 10 and 6x5=30. So 30+10= 40 minutes. Now it shows that 1/6 + 3/6= 40 minutes.
Part 3 Now that you know what each fraction equalls all you do is compare to see which one is more. 1/4 + 2/4= 45 1/6 + 3/6= 40
45>40 which means that 1/4 + 2/4 is bigger than 1/6 + 3/6. Slide 2
Slide 3 The patterns I see are that the peeps are going up by 1 each time and the top is adding 3 to the numerator each time while the denominator stays at 4 if you're doing it as an improper fraction. If you're doing it was a mixed fraction It's like youre adding 0.75 each time. For example 1peep 3/4= 0.75
2peeps 1 and 1/2= 1.50
3peeps 2 and 1/4= 2.25
See what I mean It's like you're adding 0.75 each time. For the 11th sub you'll need 33/4. I got that since the pattern is multiply the number of people by 3 and thats the numerator while the denominator is 4 every time this is only if you're using the improper version way. If you're using the mixed fraction way the answer for the 11th one would be 8 and 1/4. I got that by multiplying 0.75 by 11 and getting 8.25 which is 8 and 1/4 as a fraction.
Slide 2 Part 1 The first thing you do is add 5/12 to 1/12. Sice they have the same denominator you can turn it to 6/12 just by adding them. Now just find out how much of a clock that is. So you just have to cut 60 into half and you get 30 mins. So 5/12 + 1/12= 6/12 = 30mins out of 60.
Part 2 Now what you do is add 1/3 to 1/12. To make it easier turn 1/3 to 4/12. You get that by multiplying the numerator and denominator by 3. So since 4/12 and 1/12 have the same denominator just add them up and get 5/12. Now just multiply 5 by 5 and get 25. I got that since each mark is 5mins. So 1/3 + 1/12= 25mins
Part 3 Now just compare 5/12 + 1/12= 30 mins 1/3 + 1/12= 25 mins 30>25 which means 5/12 + 1/12 is bigger
Slide 3 (2/5+2/10 VS 1/6+2/3) -Part 1 The first thing you do is add 2/3 to 2/10. Since 2/5 has a different denominator than 2/10, you have to multiply the numerator and denominator by 2 and you get 4/10. I turned it to 4/10 to make it easier to add now that there denominators are the same. So now you just add them up and you get 6/10. Now you have to find out how much a 1/10 of 60 is. To get a 1/10 you have to divide 60 into 10 equal pieces. Each equal piece equals 6mins. So you just multiply 6 by 6 and you get 36. So that shows that 2/5 + 2/10= 36mins
-Part 2 Now you have to find out what 1/6 + 2 /3 is. To make it easier so that they have the same denominator just multiply the numerator and denominator of 2/3 by 2 and you get 4/6. It's easier now because they have the same denominator so all you have to do is add them up. 1/6 + 4/6= 5/6 Now you have to find out what a sixth of a clock is. So just divide 60 into 6 equal pieces and you get 10 minutes each piece. Now just multiply 10 by 5 and you get 50 minutes out of 60minutes. So that shows that 1/6+2/3=50 mins out of 60 mins.
-Part 3 Now just compare the fractions to see which is bigger 2/5 + 2/10= 36mins 1/6 + 2/3 = 50mins
50mins>36mins which means 1/6 + 2/3 is the larger fraction between the two.
Slide 4 Part 1 The first thing you do is add 7/12 to 1/6. Since they have different denominators you have to make them equal. You make them equal by multiplying the numerator and denominator of 1//6 by 2. 1/6 turns to 2/12. Now that they have the same denominator just add them up. 7/12 + 2/12= 9/12. Now find out what 9/12 of a clock is. Since a clock has 12 marks and each equals 5, just mulyiply 9 by 5 and you get 45 minutes. 7/12 + 1/6= 45 mins
Part 2 Now for these fractions you can make them equal but it'll be a big fraction and we don't want that. So first you'll have to find what 1/4 of a clock is. So divide the clock into 4 equal pieces. Each piece you slice it into equals 15. So just multiply 15 by 3 since you'r fraction is 3/4 and not 1/4 and you got 45. We can tell already that this fraction is bigger but I'll finishing explaining anyways. Now just find out how much 1/10 of a clock is. So just divide the clock into 10 equal pieces and find out how much time each piece is. You get 12 mins since 60 divided by 10 and you get 6. Now add them up and you got 51. So 3/4 + 1/10= 51 mins out of 60.
Part 3 Now compare! 7/12 + 1/6= 45 mins 3/4 + 1/10= 51 mins 51>45 Therefore 3/4 + 1/10 is bigger.
Slide 5 The patterns I see are that the peeps are going up by 1 each time and the top is adding 3 to the numerator each time while the denominator stays at 4 if you're doing it as an improper fraction. If you're doing it was a mixed fraction It's like youre adding 0.75 each time. For example 1peep 3/4= 0.75
2peeps 1 and 1/2= 1.50
3peeps 2 and 1/4= 2.25
See what I mean It's like you're adding 0.75 each time. For the 11th sub you'll need 33/4. I got that since the pattern is multiply the number of people by 3 and thats the numerator while the denominator is 4 every time this is only if you're using the improper version way. If you're using the mixed fraction way the answer for the 11th one would be 8 and 1/4. I got that by multiplying 0.75 by 11 and getting 8.25 which is 8 and 1/4 as a fraction.
Slide 6 4 goes into 9 is the same as 9 divided by 4 and 9/4 when your dividing your trying to see how much a number goes into a number, in this case how many times 4 goes into 9. It's also the same as 9/4 because that's what it looks like as a fraction. It's also the same as 9 in da house and 4 comes a knockin'
Slide 7 4 goes into 9 is not 4 divided by 9 and 4/9. Or 4 in da house and 9 comes a knockin'. This is basically the opposite of slide 6.
Slide 8 1/2 of 24 = 12 (Chop 24 in half and you get 12) 1/4 of 24 = 6 (Chop 24 in half then cut it into half again) 1/8 of 24 = 3 (Chop 24 in half then in half again then in half again) 1/3 of 24 = 8 (Just chop 24 into 3 equal pieces)
The pattern here is you're basically chopping them in half every time.
Slide 11 Since you probably have filled out your charts all the way to the 3rd row this should be easy.
120 people For 120 people you would need 90 subs. I got that just by looking at how many subs go into 12 and that's 9. It's easy because 120 is just 12 multiplied by 10. So all you had to do was multiply 9 by 10 and you get 90. Easy as that.
60 people For 60 people you would need 45 subs. I got that just by looking at how many subs goes into 6 and that's 4 and 1/2. It's easy because 60 is just 6 multiplied by 10. So all you do is multiply 4 and 1/2 by 10 and you get 45.
48 people For 48 people you would need 36 subs. I got that just by looking at how many subs goes into 24 and that's 18. It's easy because 48 is just 24 multiplied by 2. Soo just multiply 18 by 2 and you get 36.
Formula The second way is a formula I made up. It's number of people divided by 4 times three. It works. I'll show you.
120 divided by 4= 30 40 times 3 = 90
60 divided by 4 = 15 15 times 3 = 45
48 divided by 4 = 12 12 times 3 = 36
See it works on all of them.
Wow it took me like forever to finish. I was even drinking coffee since it took so long and I needed to stay awake of boredom. Wow again because I can't beleive I did all the slides, but some were easy because I did a few yesterday and I just had to copy and paste some.
1/4+2/4 is greater than 1/6+3/6 because... 1/4 on the clock would equal 15 mins. and 2/4 on the clock would equal 30 mins. when you add that together 15mins+30mins you get 45 mins.
and for the 1/6 on a clock would equal 10 mins and 3/6 out of and hour would equal 30 mins... added together 10mins.+30mins you get 40 mins. ..... so for the first anwser 45/60.. 60 because thats what it is out of on the clock (60 mins) and the second one 40/60.
SO... 1/4+2/4 is greater than 1/6+3/6.
p.s it really helped when i got to understand the clock thing.
18 comments:
2/5+2/10 and 1/6+2/3
2/5= 60 divided by 5=12 12=12=24 minutes
2/10= 60 divied by 10=6 6+6=12 minutes
24+12=36/60
1/6+2/3
1/6=60 divided by6=10 minutes
2/3= 60 divided by3=20 20 +20 =40
40+10=50/60
1/6+2/3 is bigger because it is 50 and the othe rone is 36. you also have to cut the pieces larger for the 1/6 ans2/3 making it larger
Slide #4
7/12+1/6
There are 5 minutes in every 1/12 so 5*7=35. 1/6 is 0 minutes because there are 6 10 minutes in an hour so 35+10=45 minutes. 45/60
3/4+1/10
3/4 of an hour is 45 minutes and 1/10 of and hour is 6 minuts because there are 10 6 minutes in an hour so the answeris 51/60
7/12 + 1/6 ~ 3/4 + 1/10
First find out what 7/12 + 1/6 is
To make it easier turn 1/6 into 2/12 (They are equivalent)
So 7/12 + 2/12 = 9/12 (Simplified is 3/4 or 0.75)
Well you dont really need to add
3/4 + 1/10 because the other one is 3/4 and this one
is 3/4 PLUS 1/10 so of course this will be larger but ill do the
math anyways.
You can turn them into decimals since they're friendly numbers you can do it in your head.
3/4 = 0.75
1/10 = 0.1
0.75 + 0.1 = 0.85
As a fraction that would be 17/20 in simplest form.
SO!
7/12 + 1/6 < 3/4 + 1/10
Ohkay I talked about slide 1 and 2 yesterday
sooooo here goes
slide 3:
2/5+2/10 is bigger because
if you divide 60 by 5 its 12 so i times 12 by 2
(because its 2/5 and one fifth is 12)
Ohkay so i got 24
then I didvded 60 by 10
then i got 6
but then i hhad to go 6 times 2
(because 6 is one tenth and 12 is two tenths)
so i got 12
then i added 24 and 12 and that got me 36 mins
Therefore its 36/60
(60is the denominator becaus ether is 60 mins in a clock)
Next waz easy
1/6 is 10 mins of a clock
and 2/3 is 20 nmins of a clock
so i added 10 and 2
that equals 30
so 30/60
there for 2/5+2/10 is bigger
Slide 4:
ohkay well 7/12 is 35 mins in a clock
and 1/6 is 10 mins
so thats 45/60
ohaky well the 3/4 is easy thats 45 mins of a clock
but 1/10 i had to divide 60by 10
which go tme 6
so 1/10 is 6 mins
so i add 45 and 6 that equals 51/60
Therefore 3/4+1/10 is larger
slide 4:
I don't know what to say abotu it O__o
Slide 6&7
I talked about slide 6 and 7 yesterday
But i was wrong yesterday
but know i understand ^__^ YAY me!!!
Slide8:
1/2 of 24 = 12
1/4 of 24 = 6
1/8 of 24 = 3
1/3 of 24 = 8
Ohkay tell you the truth i copied down the answer at school for the first 3
Then I figured out that 1/3 of 24 = 8 because
24 divided by 3 equals eight
i just take 24 and divide it by the numerator
Ummm....Slide 9,10 and 11 i dont really understand but i'll try latah
Because its time to eat ^__^
`chantel
~xoxo~xoxo~
^__^
O.o
Slide 4:
7/12 + 1/6 > 3/4 + 1/10
7/12 of a clock is 35 mintues. because the block is already spit into 12 peices.
1/6 is 10 mintues because if you cut a clock into 6 peices and shade in 1 piece only makes 10 mintutes
35+10=45 MINUTES
____________________________
3/4 of a clock is cut into for and shaded into 3 it makes 45 min.
1/10 of a clock cut into 10 with one shaded in makes6 minutes
45+6= 51 min.
45/60 or 51/60 50 is larger. because they have the same denomanator so the have to compare it with the numerator which 51 is bigger! yay..
☺☻♥♂♦♣♠•◘○ -- jasmine
Slide 3:
2/5+2/10 and 1/6+2/3
1) 2/5+2/10 is greater because 2/5 of the clock equals 24 minutes, and 2/10 of the clock equals 12 minutes
2/5+2/10= 36 minutes !
1/6 of a clock equals 10 minutes, and 2/3 of the clock equals 20 minutes
1/6+2/3=30 minutes
Slide 4:
7/12+1/6 and 3/4+1/10
on a clock 7/12 equals 35 minutes, and 1/6 of the clock equals 10 minutes. 7/12+1/6=45 minutes !
3/4+1/10 is greater because 0n the clock 3/4 is equal to 45 minutes, and 1/10 equals 6 minutes.
45+6=51 minutes.!
-marina! :)
1st slide
1/2 + 2/4 and 1/6 + 3/6
1/2 of 60 minutes is 30 minutes
2/4 of 60 minutes is 15 minutes
add 15 minutes to 30 minutes = 45 minutes...so its 45/60 because 45 is the equal ## and 60 is the equal of minutes.
1/6 of 60 minutes is 10 minutes
3/6 of 60 minutes is 30 minutes
because 10 minutes is 1/6 of 60 minutes so you just have to multiply 10 to 3 = 30
add 10 to 30 you get 40 minutes....
so its 40/60 because 40 is the equal ## and 60 is the equal of minutes.
then you just have to compare 45/60 and 40/60. 45/61 is larger because 45 is a higher number than 40/60.... you don't have to compare the denominators because they have the same numbers.
1/2 of 24=12 (u get this by dividing 24 by 2)
1/4 of 24=6(u get this by dividing 12 by 2)
1/8 of 24=3(u get this by dividing 6 by 2)
1/3 of 24=8(24 divided by 3 is 8(numerator divided by denominator))
A simple way to do it is divide the denominator by the whole. an eg. is 24(the whole)and 3(the denominator) equals 8(which is the answer)
Slide 3:
2/5 + 2/10 is bigger than 1/6 + 2/3 by 6 minutes. 2/5 shown on a clock is 24 minutes and 2/10 shown on a clock is 12 minutes. I divided 60 by 5, so i did 12x2 because it is 2/5. Also because 1/5 = 12 and you just double the numerator. Then i divided the clock into 10 sections and that gave me six minutes in each section which gave me twelve minutes altogether. MY answer altogether was 36 minutes out of 60 minutes.
2/5+2/10 is bigger because
I divided 60 by 5 and its 12 so then i times 12 by 2
because 2 is the numerator and then
i got 24
then I divided 60 by 10
and got a 6
and then times 6 by 2
because 2 is the numerator again.
so i got 12.
then i added 24 and 12 and that got me 36 mins
And the fraction i got is 36/60
Next, i got 1/6 is 10 mins of a clock
and 2/3 is 20 mins of a clock
so i added 10 and 20
and got 30
so 30/60
So that means that 2/5 + 2/10 is bigger
Ok, well i answered some of these in my comment for yesterdays. So i guess do the rest?
Slide 1* 1/4 + 2/4 OR 1/6 + 3/6
There are a few ways to do this. First find out what 1/4 is out of 60 because there are 60 minutes on the clock counted by 5 min and there is a marker for every 5 minutes, so there are 12 markers. Anyway we find out 1/4 first because its simple and its a unit fraction. you can look at the clock and just divide it into four equal pieces. OR divide 12 by the denominator to find out what marker it goes on ( this stratagy only works with unit fractions ).So now we know that 1/4 goes on the 3 which is 15 minutes, since the other fraction is 2/4 you can just double you answer for 1/4 and then add the both of them together like so.
15min+30min=45
So we get 45 minutes for 1/4 and 2/4.
now we can just repeat the stratageys that we used earlier with the unit fraction. So if we do that, then we should find out that 1/6 goes on the marker 2 which is 10 minutes. Now we just multiply that 3 times to get 3/6.
So we get a total of 40 minutes for 1/6 and 3/6. So that means 1/4 + 2/4 is larger than 1/6 + 3/6
Slide 2* 5/12 + 1/12 OR 1/3 + 1/12
Well to compare these we need to figure out what they are. Like i said earlier using the markers on a clock for every 5 minutes, we can count 5 of them to find out that 5/12 is 25 minutes out of an hour. Or we can multiply the numerator by 5 to find out how many minutes the fraction stands for ( can only be done when the denominator is 12 like in this senario ). So now we do the same for the 1/12, and from that we get 5 minutes, Making a total of 30 minutes out of 60.
Now for 1/3 and 1/12.
You can find out 1/3 by dividing the 12 markers on the clock by 3 to get you 4 which is the mark for 1/3 of the clock. So 1/3 is 25 minutes. 1/12 is of course 5 minutes like we have figured out a billion timesn making the total 25 minutes out of 60. So 5/12 + 1/12 is larger than 1/3 + 1/12.
Slide 3* 2/5 + 2/10 OR 1/6 +2/3
So 2/5 was kind of a ugly number for me to deal with at this point so i skipped that for now and did 2/10 first because its more friendly to me. So for 2/10, i jsut divided the number of markers by the denominator, ( 12/10= 0.12 = 12 minutes) and found out that it was on the second marker on the clock and 2 smaller marks making it 12 minutes for 1/10. Since its 2/10 i just multiplied it by 2 to get my answer for this one of 24 minutes. Then I went back to 2/5 because i can jsut divide what i got for 2/10 by two to get my answer. So then the answer would be 12 minutes! if i were to do it and involve mroe of my thinking for nothing, i would've did the same thing with 2/10, but the reason i didnt do this one was because i was to lazy to think and calculate 12/5 or to get out a calculator and do that. ANYWAY, the answer for that would be 36 minutes.
Now for 1/6 + 2/3.
For 1/6 we can divide the 12 by 6 and we get 2, so its 10 minutes long. For 2/3 we do the same thing, but end up with 4, so thats 20 minutes for 1/3. Since we have 2 we multiply 20 by 2 and get 40 minutes for 2/3. In total for 1/6 + 2/3 we have 50 minutes out of 60 so that makes it larger than 2/5 + 2/10.
Slide 4* 7/12 + 1/6 OR 3/4 + 1/10
Using what i did earlier, from whats further up on this comment and past comments AND from my pappers and scribbler. I got 35 minutes for 7/12 because if you multiply the 7 by 5, you get your minutes since you already know what marker it is on since the markers is equal to the denominator. for 1/6 you can divide the markers by the denominator to find out the marker its on so this is 10 minutes. Total for this is 45 minutes.
The next one is 3/4 + 1/10.
So 3/4 is simply gotten by dividing the 12 by the denominator to get the mark or place or it. its 3 in this case so we have 15 min for 1/4, we have 3/4 so we multiply this by 3 to get 9 marks or 45 minutes. Now dividing again but this time to get the minutes for 1/10 like we did earlier. We got 0.12 by dividing 12 by 10 so each 1/10 of an hour is 12 minutes.
Adding those together you get 57 minutes in total making this larger than 7/12 + 1/6.
Slide 5*
People Subs
1 3/4 =3/4
2 6/4 =1 2/4
3 9/4 =2 1/4
4 12/4 =3
5 15/4 =3 3/4
6 18/4 =4 2/4
7 21/4 =5 1/4
8 24/4 =6
9 27/4 =6 3/4
10 30/4 =7 2/4
11 33/4 =8 1/4
12 36/4 =9
13 39/4 =9 3/4
14 42/4 =10 2/4
15 45/4 =11 1/4
16 48/4 =12
17 51/4 =12 3/4
18 54/4 =13 2/4
19 57/4 =14 1/4
20 60/4 =15
21 63/4 =15 3/4
22 66/4 =16 2/4
23 69/4 =17 1/4
24 72/4 =18
25 75/4 =18 3/4
26 78/4 =19 2/4
27 81/4 =20 1/4
28 84/4 =21
29 87/4 =21 3/4
30 90/4 =22 2/4
That line shows all of the posible answers to that from 1-30 people.This looks like this because each person gets 3/4 of a sub so theres a pattern of the numerator increasing by 3.
Slide6*
4 goes into 9 is the same as . . .
9 divided by 4 and 9/4, when your dividing, your trying to see how many times a number goes into a number, in this case, how many times 4 goes into 9. It's also the same as 9/4 because that's what it would look like as a fraction.
Slide7*
4 Goes into 9 is not . . .
2 1/4 because that's what the answer would be and not the question. The question is 4 goes into 9 and that is 9 divide by 4.
Slide8*
1/2 of 24 = 12
1/4 of 24 = 6
1/8 of 24 = 3
1/3 of 24 = 8
The pattern here is that it keeps halving itself. 1/4 is just half of 1/2 and so is 6 the half of 12.
But for the 1/3 of 24, i divided the 24 by 3 and got 8 because Fractions Represent Division. I could have also looked at the clock thing that we did and just doubled my answer of it being on the 4th marker and gotten 8.
Slide9 and 10*
This is just that ratio table thingy we did. Sooo lets just have a look back there instead of me rewriting it and making this longer . . .
Slide11* LAAAAAAAAAAAAAST ONE!!!!!!
Peeeeps Subs
48 = 144/4 = 36
60 = 180/4 = 40 2/4
120 = 360/4 = 90
Well heres another line up of the numbers and the subs. I got the first one with 48 peeps by doubling the answers from 16 but i realized that that was wrong when i checked my answer over. I realized this when i looked at the ones that ended in 8 and found out that they all ended in a 4 so i thought something was wrong when i found that problem.So i found another easier way to figure this out, multiply the number by 3 and get the improper fraction, it works everytime. But then i just realized that half of 48 was 24 . . . so i just totally blanked out. THE REAL ANSWER this time I'm TOTALLY SURE. The real answer is 144/4 or 36 subs and i got that by doing what i did to the other number that i thought was half, i multiplied the answer by two to get this answer. The multiplying by 3 works too but i just wanted to point this out.
Now for 60, i got 180/4 or 40 and a half subs by multiplying the answers from half of 60 peeps which is 30.
And for 120 i did the exact same things except i couldnt multiply by two, so i found 12 and and added 0's which is just multiplying by 10. I did that because 120 is 12 but 10 times more, so whatever that was i just did the same thing to get the subs equal to the peeps.
THIS TOOK 2 hours!!!!! i guess boredom can kill a guy. . .
Anyway since i know this is going to be long . . . TAKE THAT ROMULO!!! haha try beating MY book =P
Have a good night?
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5/12 + 1/12 vs. 1/3 + 1/12
5/12 = 25 min on a clock because there are 12 sections on a clock, with 5 min in between
5 x 5 = 25
1/12
1x5 =5
25+5 = 30
1/3 on a clock is 20 min because 1/6 is 10 min and 1/3 is x2 1/6
1/12 is 5
20 + 5 = 25
5/12 + 1/12 > 1/3 + 1/12
- Jordan
1/2 of 24 is 12 because 2 groups of 12 is 24.
1/4 of 24 is 6 because we know that 12 is half of 24 so we just half 12(=6)
1/8 of 24 is 3 because we know that half of 24 is 12 and half of 12 is 6 so we just simply half it.
1/3 of 24 is 8 because 8 goes into 24 3 times.
A simple way of doing all that is using a calculator (eg. denominator/the number ex.24/3)
or just half the answer from the other one each time the even denominator goes up by 2.
For today I'll be commenting on all of them. Oh Snap another big book!
Slide 1 (1/4+2/4 vs 1/6+3/6):
Part 1
The firt thing you do is add 1/4 abd 2/4. Since they have the same denominator you can turn it to 3/4 just by adding them, but now you have to find out what 3/4 of a clock is. So what you do is divide the clock into 4 equal pieces. For each piece it will equal a time of 15 minutes. Since th fraction is 3/4 all you do now is multiply 15 by and you get 45 minutes. So that means 1/4 + 2/4= 45 minutes out of 60 minutes.
Part 2
Now what you do is find out what 1/6 + 3/6 equals. So since there denominators are the you can multiply both numerators and denominators by two an you get:
1x2= 2 6x2= 12
So 1/6 turns to 2/12.
Now you have to do the same thing for 3/6.
3x2= 6 6x2= 12
So 3/6 turns to 6/12.
So you new fractions are 2/12+6/12
I multiplied them to make it easier since a clock has 12 marks and for each mark it equals 5 minutes. So 2x5= 10 and 6x5=30.
So 30+10= 40 minutes. Now it shows that 1/6 + 3/6= 40 minutes.
Part 3
Now that you know what each fraction equalls all you do is compare to see which one is more.
1/4 + 2/4= 45
1/6 + 3/6= 40
45>40 which means that 1/4 + 2/4 is bigger than 1/6 + 3/6.
Slide 2
Slide 3
The patterns I see are that the peeps are going up by 1 each time and the top is adding 3 to the numerator each time while the denominator stays at 4 if you're doing it as an improper fraction.
If you're doing it was a mixed fraction It's like youre adding 0.75 each time. For example
1peep 3/4= 0.75
2peeps 1 and 1/2= 1.50
3peeps 2 and 1/4= 2.25
See what I mean It's like you're adding 0.75 each time. For the 11th sub you'll need 33/4. I got that since the pattern is multiply the number of people by 3 and thats the numerator while the denominator is 4 every time this is only if you're using the improper version way.
If you're using the mixed fraction way the answer for the 11th one would be 8 and 1/4. I got that by multiplying 0.75 by 11 and getting 8.25 which is 8 and 1/4 as a fraction.
Slide 2
Part 1
The first thing you do is add 5/12 to 1/12. Sice they have the same denominator you can turn it to 6/12 just by adding them. Now just find out how much of a clock that is. So you just have to cut 60 into half and you get 30 mins.
So 5/12 + 1/12= 6/12 = 30mins out of 60.
Part 2
Now what you do is add 1/3 to 1/12. To make it easier turn 1/3 to 4/12. You get that by multiplying the numerator and denominator by 3. So since 4/12 and 1/12 have the same denominator just add them up and get 5/12. Now just multiply 5 by 5 and get 25. I got that since each mark is 5mins.
So 1/3 + 1/12= 25mins
Part 3
Now just compare
5/12 + 1/12= 30 mins
1/3 + 1/12= 25 mins
30>25 which means 5/12 + 1/12 is bigger
Slide 3 (2/5+2/10 VS 1/6+2/3)
-Part 1
The first thing you do is add 2/3 to 2/10. Since 2/5 has a different denominator than 2/10, you have to multiply the numerator and denominator by 2 and you get 4/10. I turned it to 4/10 to make it easier to add now that there denominators are the same. So now you just add them up and you get 6/10. Now you have to find out how much a 1/10 of 60 is. To get a 1/10 you have to divide 60 into 10 equal pieces. Each equal piece equals 6mins. So you just multiply 6 by 6 and you get 36. So that shows that
2/5 + 2/10= 36mins
-Part 2
Now you have to find out what 1/6 + 2 /3 is. To make it easier so that they have the same denominator just multiply the numerator and denominator of 2/3 by 2 and you get 4/6. It's easier now because they have the same denominator so all you have to do is add them up.
1/6 + 4/6= 5/6
Now you have to find out what a sixth of a clock is. So just divide 60 into 6 equal pieces and you get 10 minutes each piece. Now just multiply 10 by 5 and you get 50 minutes out of 60minutes. So that shows that 1/6+2/3=50 mins out of 60 mins.
-Part 3
Now just compare the fractions to see which is bigger
2/5 + 2/10= 36mins
1/6 + 2/3 = 50mins
50mins>36mins which means 1/6 + 2/3 is the larger fraction between the two.
Slide 4
Part 1
The first thing you do is add 7/12 to 1/6. Since they have different denominators you have to make them equal. You make them equal by multiplying the numerator and denominator of 1//6 by 2. 1/6 turns to 2/12. Now that they have the same denominator just add them up.
7/12 + 2/12= 9/12.
Now find out what 9/12 of a clock is. Since a clock has 12 marks and each equals 5, just mulyiply 9 by 5 and you get 45 minutes.
7/12 + 1/6= 45 mins
Part 2
Now for these fractions you can make them equal but it'll be a big fraction and we don't want that. So first you'll have to find what 1/4 of a clock is. So divide the clock into 4 equal pieces. Each piece you slice it into equals 15. So just multiply 15 by 3 since you'r fraction is 3/4 and not 1/4 and you got 45. We can tell already that this fraction is bigger but I'll finishing explaining anyways.
Now just find out how much 1/10 of a clock is. So just divide the clock into 10 equal pieces and find out how much time each piece is. You get 12 mins since 60 divided by 10 and you get 6. Now add them up and you got 51. So
3/4 + 1/10= 51 mins out of 60.
Part 3
Now compare!
7/12 + 1/6= 45 mins
3/4 + 1/10= 51 mins
51>45
Therefore 3/4 + 1/10 is bigger.
Slide 5
The patterns I see are that the peeps are going up by 1 each time and the top is adding 3 to the numerator each time while the denominator stays at 4 if you're doing it as an improper fraction.
If you're doing it was a mixed fraction It's like youre adding 0.75 each time. For example
1peep 3/4= 0.75
2peeps 1 and 1/2= 1.50
3peeps 2 and 1/4= 2.25
See what I mean It's like you're adding 0.75 each time. For the 11th sub you'll need 33/4. I got that since the pattern is multiply the number of people by 3 and thats the numerator while the denominator is 4 every time this is only if you're using the improper version way.
If you're using the mixed fraction way the answer for the 11th one would be 8 and 1/4. I got that by multiplying 0.75 by 11 and getting 8.25 which is 8 and 1/4 as a fraction.
Slide 6
4 goes into 9 is the same as
9 divided by 4 and 9/4 when your dividing your trying to see how much a number goes into a number, in this case how many times 4 goes into 9. It's also the same as 9/4 because that's what it looks like as a fraction. It's also the same as 9 in da house and 4 comes a knockin'
Slide 7
4 goes into 9 is not
4 divided by 9 and 4/9. Or 4 in da house and 9 comes a knockin'. This is basically the opposite of slide 6.
Slide 8
1/2 of 24 = 12 (Chop 24 in half and you get 12)
1/4 of 24 = 6 (Chop 24 in half then cut it into half again)
1/8 of 24 = 3 (Chop 24 in half then in half again then in half again)
1/3 of 24 = 8 (Just chop 24 into 3 equal pieces)
The pattern here is you're basically chopping them in half every time.
Slide 11
Since you probably have filled out your charts all the way to the 3rd row this should be easy.
120 people
For 120 people you would need 90 subs. I got that just by looking at how many subs go into 12 and that's 9. It's easy because 120 is just 12 multiplied by 10. So all you had to do was multiply 9 by 10 and you get 90. Easy as that.
60 people
For 60 people you would need 45 subs. I got that just by looking at how many subs goes into 6 and that's 4 and 1/2. It's easy because 60 is just 6 multiplied by 10. So all you do is multiply 4 and 1/2 by 10 and you get 45.
48 people
For 48 people you would need 36 subs. I got that just by looking at how many subs goes into 24 and that's 18. It's easy because 48 is just 24 multiplied by 2. Soo just multiply 18 by 2 and you get 36.
Formula
The second way is a formula I made up. It's number of people divided by 4 times three. It works. I'll show you.
120 divided by 4= 30
40 times 3 = 90
60 divided by 4 = 15
15 times 3 = 45
48 divided by 4 = 12
12 times 3 = 36
See it works on all of them.
Wow it took me like forever to finish. I was even drinking coffee since it took so long and I needed to stay awake of boredom. Wow again because I can't beleive I did all the slides, but some were easy because I did a few yesterday and I just had to copy and paste some.
1/4+2/4 is greater than 1/6+3/6
because...
1/4 on the clock would equal 15 mins. and 2/4 on the clock would equal 30 mins.
when you add that together 15mins+30mins you get 45 mins.
and for the 1/6 on a clock would equal 10 mins and 3/6 out of and hour would equal 30 mins... added together 10mins.+30mins you get 40 mins.
.....
so for the first anwser 45/60.. 60 because thats what it is out of on the clock (60 mins)
and the second one 40/60.
SO... 1/4+2/4 is greater than 1/6+3/6.
p.s it really helped when i got to understand the clock thing.
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