Last week we had a great question posed by Fiona. Thanks Fi! If you have any questions about it and want to see the solution please look to my comment to POTW #10 (in the thread for it).
We have another question posed by a student. As you all know, or should know, we have a wondrous new addition to the Intermediate group. Rory Shan comes to us from Hertbert H. Carnegie and he has had a really great start here. His classmate Seayrohn has acted as a great support for Rory, so much so that Seayrohn created a POTW about him!
POTW #11 Grade 7/8 Question:
Welcome Rory!
It’s Rory’s first day of Michael Cranny and he decides to bring an apple for Mr. Milette (very kind). However, on the way to school, Rory got a little hungry… Rory ate ½ of the apple after the first quarterway there. From there, Rory split the apple in half and gave one half to Edwyn. For the next 8 kilometers, Rory ate twice the amount of apple as Edwyn. By then, Rory and Edwyn already arrived at Cranny. If Rory finished his apple and took the remainder of Edwyn’s apple, then how much apple did Rory kindly give to Mr. Milette? Represent answers in fractions and percents. How long was the bus-ride? Represent answers in fractions, decimals, and percents.
Rory gave Mr.Milette 1/8 of his apple. So, 12.5% of the apple.
ReplyDeleteWhat about the second part?
DeleteGrade 7/8 POTW
ReplyDeleteI kind of did the math as I made this POTW so I'll probably answer at the end replying to this comment as in I already know the answer.
It is Thursday and I think I waited enough.
DeleteApples given to Mr. Milette: 1/8, 12.5%
Bus Ride Distance: 10 2/3 km, 10.666...km, 1066.666...% of km
Work done on the page I made this POTW.
Grade 7/8 POTW (Not sure if I did this one correctly)
ReplyDeleteInformation:
- Rory ate ½ of the apple after the first quarterway there
- Split the apple in half and gave to Edwyn
- Next 8 kilometers Rory ate twice the amount Edwyn ate.
- Finished the apple and took the remainder of Edwyn's.
Need to find: How much did Rory give to Mr. Milette
- How long was the bus ride
NEED TO REPRESENT IN DECIMALS, FRACTION AND PERCENT.
Work:
I can use 100% to represent the whole apple. Since Rory ate half of the apple on the way to Cranny, he ate 50% of the apple.
Then, he spilt the remainging 50% into 2 parts for himself and Edwyn. So, he ate another 25% and gave Edwyn the other 25%.
If Rory ate twice as much as Edwyn did, I need to find the amount of apple Rory ate and divde that percentage by 2 to get how much Edwyn ate. In total, Rory ate 75%, but assuming that the question means the 25% he ate after the first 50%, Edwyn ate 12.5% of his apple. He has 12.5% remaining.
Since Rory finished his apple and Edwyn's remainder to Mr. Milette, I can conclude that Rory gave 12.5% of the apple to Mr. Milette. or 125/1000 (a fraction cannot have decimals because the fraction itself is a decimal) Simplified 1/8
Decimal: 0.125 (I found this out by using the percent and divided it by 100)
Percent: 12.5% (I found this out by looking above and seeing that
Fraction: 1/8 (I found this out by looking at my fraction above and simplifying it, also because of decimal expansions (Thank you SMS).
Second Question:
Now I need to find the duration of the bus ride. Assuming that the total bus ride was quarterway plus 8 kilometers, I can figure out how long the bus ride was. If 8 was 3/4 of the trip, I can divide 8 by 3 (to find 1/4) and mutiply by 1 (1/4).
The answer is 0.375. To find this in kilometers, I can mutiply this 10 so the equation makes more sense and is in kilometers. I can also use logic as 1/4 has to be smaller than 3/4 (8 kilometers)
The answer is 3.75. Now, I need to add up the 2 decimals and figure out how long the bus ride was is total.
8+3.75=11.75 kilometers. The ride was 11.75 kilometers.
Percent: 1175% (To find this out, I mutiplied the decimal by 100)
Decimal: 11.75 (To find this out, I looked above to see the decimal).
Fraction: 11 3/4 (To find this out, I looked at the number before the decimal and placed it as the whole number and to find the fraction, I looked at the 75 and realized that it was 3/4 of 100, so I put 3/4 as the fraction part of this mixed fraction.
TADA!!
Ummmm. 8/3 isn't 3.75.
Delete8/3? I thought that 8 was 3/4...
DeleteIt is, but to find out 1/4, 8/3. You said 3.75, it isn't that.
DeletePOTW:
ReplyDeleteOk, so let's see here, the wording kind of confused me, but I think that I understood the question.
First of all, Rory ate half an apple already, so he has 1/2 of the apple left. Then, he gave half of that to Edwyn, so Rory has 1/4 of the apple and so does Edwyn. Rory finished his apple, which means that he finished the 1/4 of the apple, and since it says that he finished twice the amount of Edwyn, Edwyn only finished 1/8. Using this, since Edwyn started off with 1/4 and he ate 1/8, I subtract 1/4 by 1/8, and I get 2/8-1/8 = 1/8 of the apple left. Rory ate 3/4 of the apple and Edwyn ate 1/8 of the apple, so there is 1/8 of the apple left to give to Mr. Milette.
Percent would be 12.5%, and the decimal would be 0.125.
Second part: It says that the next 8 kilometers Rory finished his apple, blah blah blah. However, it says that they arrived at school already. So, this would mean that 8 = 3/4 of the ride since it says Rory ate some of the apple on the first quarterway there. So, 1/4 = 8/3 = 2.6666666, basically 2 and 2/3. 2 and 2/3 is 1/4 of the ride, so I can multiply it by 4 to get the total distance for the bus ride. That is 2 2/3*4 = 8/3*4 = 32/3 = 10 2/3. The ride was 10 and 2/3 kilometers I'm guessing? Decimal would be 10.66666666 and the 6 goes on forever, and percent would be 10066.66%, with the 6 repeating as well.
I'm not sure if I understood the wording correctly, but I sure hope I did!
-Alan
P.S. Congrats to Kevin and Tin for doing well on the Caribou!(Seems appropriate to write it on the Math POTW website.)
Awesome shout-out to the Caribou peeps Alan (how did you see their scores?) Ella did amazing in Ms. Osborne's class too!
DeleteAs for the POTW Q, it is worded that way on purpose. That way you have to critically think!
Kevin's score was seen in the top 50 on the caribou page. I did tell Alan about Tin, but he already knew so not sure about Tin.
DeleteOh that's cool. I wasn't sure how many scores the Caribou website shows up until.
DeleteAlso, Alan. Decimal wasn't necessary. RWA, a decimal of an apple isn't used. Either way, the question didn't state anything about NOT representing in decimals so I guess it's fine.
DeleteOh yeah. Alan, there was actually more question of this. There were 4 parts I think??? Either way, that was worded bad on my part so Mr. Milette left that part out. Imagine if that was included. The funny part is that I somehow understand the question very clearly. Then again, I did make it.....
DeleteAlan, look at 10066.666...%. You made a small mistake. It's fine though! (I wanted you to find the mistake, I still do. There is a minor error. Find it.)
DeleteRory ate 1/2 of the apple then Edwyn half of what is left. That means that they both have 1/4 of the apple. Rory eats two times faster than Edwyn and he finished his 1/4 apple by the time he gets to school. If he ate 1/4 and eats 2 times faster than Edwyn, Edwyn only ate half of 1/4 or 1/8. That mean 1/8 is still left for Mr. Milette.
ReplyDelete1/8 = 0.125 = 12.5%
Rory gave Mr. Milette 1/8 of the apple.
Avi, what about the second part?
DeleteAnd once again (said in other comments), the decimal for the apple wasn't necessary. RWA.
DeletePOTW #11: WELCOME RORYYYYYYYYYYYYYYYYYYYY woot woot toot toot
ReplyDeleteAs stated in the question, Rory was kind enough to bring Mr. Milette an apple. But sadly, he ate most of it by the time him and Edwyn arrived at school.
In order find out how much of the apple, Rory gave Mr. Milette, I used percents. Rory first started off with a full apple (100%, 1.00, 1/1), but by the time they covered a quarter-way to the school, he ate half of it (50%, 0.5, 1/2). He then gave Edwyn half of what was left of the apple (50% / 2 = 25% or 0.25, 1/4).
The question then states that for the next 8 kilometers, Rory ate twice the amount of apple as Edwyn. There wasn't a specific amount of apple specified, so I just went with dividing 25% of the apple by 2, which gave me 12.5%.
Now, they have arrived at Michael Cranny and Rory takes Edwyn's 1/8 (12.5%, 0.125) of an apple to give to Mr. Milette.
The question then asks how long the bus ride was. It never stated that they walked the first quarter-way to the school, so I just assumed that they were on the bus for the entire time. After the section in the question: "For the next 8 kilometers, Rory ate twice the amount of apple as Edwyn", it was said that they had arrived at school by that time. Previously, I knew that Rory at half the apple during the first quarter-way to the school. This way, I can assume (once again) that 8 kilometers was 3/4 of the way to school. So, I divided 8 by 3, to get the last 1/4. This gave me 2.6 (repeating), or 2 and 2/3. Then, I added 2 2/3 and 8 to get a total of 10 and 2/3 kilometers.
Therefore, Rory gave Mr. Milette 1/8 (12.5%, 0.125) of an apple, and the bus ride was 10 and 2/3 kilometers.
P.S. Thank you Seayrohn for this great question. I'm excited to find out the answer. Also, I think Rory miiiiight need to bring an extra apple next time. :P
It IS a GREAT question. Good luck to the vball team tomorrow!
DeleteThanks Ella and Mr. Milette!!! It is weird that I made it before he came though... Good Luck at volleyball for those on the team!
DeleteAlso, I'm sorry to point out that the question states to answer the apple part in fractions and percents (you did that along with decimals which is fine because it didn't state not to), and for the kilometers, decimals, percents, and fractions. You just gave a fraction. You still need to represent the kilometers in decimals and percents (take your time).
Once again, THANKS!
We can give Rory 40+ from the snack bin (Faribarn and Milette)!!! But in that case, none of us can give Mr. Milette that JUICY apple:(
DeleteRory ate 1/2 of his apple meaning there is 1/2 left. Then he gave half of that to Edwyn leaving 1/4 of the apple left. Then it states that at that point Rory has ate twice the amount as Edwyn. If Rory ate 1/4, it means that Edwyn must have eaten 1/8 of the apple since 1/4 is twice of 1/8. That leaves us the remaining of the apple to give to Mr.Milette. The rest is just 1/8. Therefore Rory gave 1/8 of his apple to Mr.Milette.( in percent it's 12.5)
ReplyDeletethe second part asks for how long the bus ride was. In the question, it said that Rory ate 1/2 of his apple in the first 1/4, and the rest was 8km to the school. This means that 8km should be 3/4 of the distance since the first part he traveled was 1/4. So to find out what was 1/4, I did 8 / 3 which gave me 2 and 2/3. Take that and add it to 8 gives me the total of 10 and 2/3, or 10.6666....
Firstly, you forgot percents for km, and secondly, you forgot units.
DeleteRory gave 1/8 (or 12.5%) of the apple to Mr.Milette. This was gotten because the apple starts off at 1. It then got split in half when he ate half. Then he split the remaining half with Edwyn so they each have 1/4 of the apple. He then finished his apple and since Edwyn only ate half of what Rory ate there is 1/8 of the apple left which he gave to Mr. Milette. For the trip there it said that nothing happened for the first quarter way and then the rest of what happened so that means 3/4 of the trip was 8km so then 8/3 would be 2 2/3 and if you add that to 8km so then the trip was 10 2/3 km
ReplyDelete¼ - ⅛
ReplyDelete=1/8
He gave ⅛ or 0.125 or 12.5% of the apple to Mr. Milette. The bus ride is 10.666… or 1066.66% or 10 and 66/100 km long. I got the amount of apple by first knowing that Rory ate ½ of the apple before giving Edwyn half. That means he gave Edwyn ¼ of the apple, and kept ¼ for himself. After he eats twice the amount of apple Edwyn ate, that means that Rory ate ¼ of his apple and Edwyn ate ⅛ of his apple. That leaves ⅛ of the apple to give to Mr. Milette. 8 is ¾ of the entire bus ride as the first quarter is told before the next 8 km. 8/3 is 2.6666666…. Multiplying by 4 will give the whole distance. 2.66666… is 10.666666….
Grade 8 POTW:
ReplyDeleteHe gave 1/8, 0.125 or 12.5% of the apple to Mr. Milette. This bus ride was 66/100, 10.666 or 1066.66%. I did my work in my math notebook.
The bus ride fractions, and decimals and percents aren't equivalent.
DeletePOTW:
ReplyDeleteRory gave Mr. Milette an 1/8 of his apple. This could also translate into 0.125 or 12.5% of his apple. The bus ride in which he ate parts of his apple (along with Edwyn) was 66/100 km. This could also translate into 10.66666... or 1066.6%. of the drive.
Rory gave Mr. Milette 1/8/0.125/12.5% of his apple,and the bus ride was 10.6... kilometres. (10 2/3 kilometres or 1066.66...%
ReplyDeletePOTW #12
ReplyDeleteInfo:
-Rory ate half the apple one quarter of the way to school
- He split it in half and gave on half to Edwyn
- He ate twice as much than Edwyn in the next 8 km
- Rory finished his and took the remainder of Edwyn's apple
Question(s):
- How much of the apple was left (for Mr.Milette)? Answer in fractions and percents.
- How long was the bus ride? (Fractions, decimals, percents)
Solving:
Half of an apple is 1/2
1/2 divided into 2 is 1/4
1/4 in two is 1/8
1/8 of the apple was given to Mr.Milette.
1 divided by 8 = 0.125 => 12.5%
1/8, or 12.5% of the apple was given to Mr.Milette.
Since it states that Rory ate half of the apple one quarter of the way there, then I would know that 8km is 3/4 of the route.
8 divided by 3 = 2.66...
2.66 + 8 = 10.66...
10.66... x 100 = 1066.66...which is 10 2/3
The bus ride was 10 2/3 km or 1066.66..%.
First Part:
ReplyDeleteRory ended up giving Mr. Milette an 1/8 of his apple (Decimal: 0.125, Percent: 12.5%). This is because Rory ate 1/2 of the apple then Edwyn ate half of what was left. That means that they both have 1/4 of the apple. For the rest of the ride, Rory ate the apple twice as fast as Edwyn. This means you do 1/4 * 1/2 to get 1/8. Therefore, Rory could only give Mr. Milette 1/8 of the apple.
Second part:
The bus ride would have to be 10.666... kilometres long because 8 is equivalent to 3 quarters since they used up a quarter of their time in the apple question. That is why we do "8/3 * 4". This expression equals 10.666... or 10 2/3 or 1066.666...%
POTW: (I did mine on paper so I'll just write whats important)
ReplyDeleteSo... 1 half is 1/2. And since he split it that is 1/4. And you'll end up with 1/8 if you just multiply 1/4 by 1/2.
1/8=0.125=12.5%
So Mr. Milette gets 1/8 of a bitten apple.
Bus Ride:
This is pretty simple. 8 kilometers is 3/4 of the bus ride. So:
8/3*4
=10.6... or 10 2/3 or 1066.6...%
POTW
ReplyDeleteRory first ate 1/2 of the apple, and gave 1/2 of the 1/2 apple to Edwyn, so he has 1/4 of the apple. Then, since he ate 2x the amount of Edwyn, and finished his apple, that means that Edwyn ate 1/8 of the apple, and assuming that Mr.Milette got the rest of the apple, Rory gave Mr.Milette 1/8th, 0.125, or 12.5% of a (very unsanitary) apple.
For the second part of the question, since 8 kilometers is 3/4 of the bus ride, I need to find 1/3 of 8, and add that to 8km to get the length of the bus ride. Because that is approximately 3.75 km, and 8+3.75 is 11.75km, the bus ride was 11.75km long
POTW #11:
ReplyDeleteIn the question, Rory wants to give Mr. Milette an apple. However, on the bus ride there, he ate 1/2 of the apple. So now we have 0.50 of the apple left. Then, he gave Edwyn half of what was left.
0.50 / 2 = 0.25
The question mentions that Rory ate twice as much as Edwyn. To find out how much of the apple is left, we first have to divide the amount of the apple Edwyn had.
0.25 / 2 = 0.125
Since Rory ate twice as much as Edwyn, we can say that Rory ate 1/4 of the apple and Edwyn ate 1/8.
Mr. Milette was given 1/8 or 0.125 or 12.5% of the apple.
SECOND PART OF THE QUESTION.
Since the question states that he ate half of the apple one quarter on the way there. Then, it mentions "For the next 8 kilometers..." This means that 3/4 of the ride was 8 km
8 / 0.75 = 2.6666...
8 + 2.6666... = 10.6666...
Now, we convert the decimal into a fraction.
The bus ride was 10 2/3 km or 10.666... or 1066.66..%
First Part:
ReplyDeleteIn the question, the apple starts off as 1. But then, Rory ate ½ of the apple. So half of 1 is 0.5.
Then, it says that Rory split the apple in half and gave a half to Edwyn.
So, one half of a half is 0.25, which is a fourth.
Then, it says that Rory ate twice the amount of apple as Edwyn.
So to figure out the amount of the apple left, we have to find out how much Edwyn ate. Since Rory ate twice as much of the apple as Edwyn, we have to divide how much Rory ate by 2 to get how much Edwyn ate.
0.25/2 = 0.125
0.125 is equal to 1/8 and 12.5%.
So, Rory gave 1/8, 0.125 or 12.5% of the apple to Mr. Milette.
Second Part:
For this you cannot really find how LONG the ride was wince it doesn't really give how long a certain part of it was, but you can find how FAR it was.
So, it would be 1/4 of the ride plus 8. So if I can find a third of 8 and add it to 8, I would get the answer.
8/3 is 2.66666....
8+2.6666...=10.6666666..
As a percent this is 1066.666666...% and as a fraction it is 10 2/3.
So the bus ride was 10 2/3, 1066.6666..% or 10.6666.... kilometers.
An POTW # 11
ReplyDelete- Rory ate ½ of the apple the first quarter of the bus ride
Half of the apple is left
- Rory split the apple in half and gave one half to Edwyn
2 Quarters between Edwyn and Rory
- For the next 8 kilometers, Rory ate twice the amount of apple as Edwyn, and finished his part
if they both had a quarter, Rory ate a quarter, which is x2 more than and eighth, Edwyn had an eighth of the apple.
- Took the remainder of Edwyn’s apple and kindly gave to Mr. Milette
Mr. Milette got 1/8 of the apple.
Or, 1 ÷ 8 = 0.125
Mr. Milette got 0.125 of the apple.
0.125 x 100 = 12.5
Mr. Milette got 12.5% of the apple.
How long was the bus-ride?
- In the first quarter, he ate 1/4 of the apple
- In the next 8km, they arrive at Michael Cranny
That means that 8km was 3/4 of the ride. If 8km was 3/4 of the ride,
8 ÷ 3 = 2.7
8 + 2.7 = 10.7
The bus ride was 10.7km long.
10 wholes and 0.7 km
The bus ride was 10 and 7/10 km long.
The decimal was 10.7
10.7 x 100 = 1070
The bus ride was 1070% of a kilometer long.