Thursday, October 1, 2015
POTW #5 - Puzzling Products
Way to go on another great POTW question. The total surface area for last week's question was 74m squared. If you obtained a different result, please go back and look at some of your peers' work to see where you may be incorrect. POTW#5 is below. Please try to complete these sooner, rather than later (each are due every Thursday).
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Here's how I answered the question:
ReplyDeleteF8 x 3L = 2730
First to get the ones digit you would have to find a number that when multiplyed by eight will have a 0 as a ones digit, the only multiply that isn’t ten is 5 so L must be five because when multiplying 2 digit numbers the second number skips a place.
L=5
F8 x 35 = 2730
Next I multiply 3 and 8 to find one of the tens digits I have to add to equal 3 with or without carrying over, 3 x 8 equals 24 so 4 + x = some number with 3 as the ones digit. so since 4 is already bigger than three you go to the tens digit and 13 and 13 - 3 equals 9 so the number 5 has to be multiplied by to equal a number with 9 as the ones digit when you add 4 because of the carry over. This means 5 needs to multiply by a number that has a 5 as its ones digit, 3,5,7,and 9 are all possible answers but we need to remember that the hundreds column in the final answer must be 7, this means 3 would be too small because 5x3=15 which would need to be added with a number that has 5 as it’s hundred’s digit which wouldn’t be possible with the current numbers, 9 would also be to high as 5x9=45+4=49 which would mean that the hundred's digit in the number that we add to get the final answer has to be a 2 which isn’t possible because you have to multiply 3 by something which is wouldn't work when multiplying whole numbers.Also 5 is also to little to multiply for the hundreds column to become 7. That leaves 7 as the only possible number to be F.
F=7
78x35=2730
Double check:
First row:
5x8=40-----------------xx0
5x7=35+4=39--------390
Second row:
--------------------------xxx0
3x8=24----------------xx40
3x7=21+2=23-------2340
Adding it all together:
390
+2340
--------------
2730
The value of F is 7 while the value of L is five.
my answer is:
ReplyDeleteF=7
L=5
I stared at the question for a while and realized that the last ones digit in the number 2730(aka the answer) is 0. This is the only digit that is unchanged by addition.
What i mean by this is:
11
x11
____
11
11
____
121- this number is unchanged.
This means that L*8= something with a 0 in the ones digit.
The only number is 5, 5*8=40 ends with a zero.
So since L is determined to be 5 and 3L is 35, I put 35 back in the equation by doing 2730/35=78.
With that i figured out that F= 7, because 78 works for my equation.
So therefore, F=7 AND L=5
To start I identified the only digit that when multiplied by 8 would equal 0:
ReplyDelete8 x 5 = 40
This means that L=5
Now there is only there is only one unknown: F
So it`s a digit from 1-9 8 x 35 = 2730
I know that 35 x around or less than 80 = over 2700 as 8 x 3 = 28 so 80 x 30 = 2800
Since F = something 8, I guessed it was F =78 since 78 is very slightly less than 80
Then I tried plugging the number into the equation :
78 x 35 = 2730
The equation proved to be true meaning my values are correct as well.
All in all, F = 7 & L=5
In the equation of F8 X 3L = 2730, F = 7 and L = 5. I found this by using something similar to "Guess & Check".
ReplyDeleteBecause 3 was in the tens column (that we knew for sure), I divided 2730 by 30 because the answer would give me a hint about what F equaled.
2730÷30=91, so F would be something around 9. So I replaced 91 with 88 and divided 2730÷88=21, but if 8=F, then the result of the division should have been 3L (something starting with 3 and ending with a number between 0 and 9).
So I replaced 8 with 7 and did 2730÷78=35, which (obviously) has a 3 in the tens column and ends in a number between 0-9, which tells me that F8 = 78 (F=7) and 3L = 35 (L=5).
So 78 X 35 = 2730.
I think that F = 7 and L = 5
ReplyDeleteI used guess and check
I kept trying different equations and the closer I was, the less numbers I didn't try
I ended up getting 78x35 which is equal to 2730, the answer in the problem F8x3L
In order to solve the problem I began by solving for what L's value is based on logic. 8 x L must make L 5, as that's the only number that will make 0 as 8 times 5 is 40. 8 times 0= 0 would not work as the answer 2730 will most not likely work with that. (L8 x 30=2730 is not possible)
ReplyDeleteThe equation right now F8 x 35= 2730
I can solve the problem by dividing 2730 by 35 to find the first digit of the first number.
2730 divide by 35=78
So the value of F is 7, and L is 5.
I decided to use a strategy similar to guess and check. I started with 3L since it seems like it has a lesser range or difference than F8 since 3 is in the tens column. The answer for this has to be thirty something since there is only 2 digits and there is only 1 unknown. I decided to make L=0 for now just to put it into the equation. 2730/30=91. This means that the answer to F8 is close to 91. I decided to use 88. However 2730/88=21.022 which did have a 3 in the tens column. I decided to try with 78. So 2730/78=35. This time not only was there an 8 in the ones column, but also a 3 in the tens column and it also has 2730. To double check I did 2730/35=78 and 78*35=2730. Therefore F=7 (F8=78) and L=5 (3L=35).
ReplyDeleteFirst, I multiplied 30 by 8, as it is uncertain what is L and F, but calculating this the long way would work with no issues from the variables. Doing this and then subtracting from the product will get us the total product created by these variables, to make calculation of the tens digit easier.
ReplyDelete30 x 8 = 240
2730 - 240 = 2490
Now that we have a accurate number of the total product carried using our variables, we shall calculate variable L through logic.
L is the only ones digit variable existing, and thus means that it is the only variable which can influence the ones digit.
As we know what the other ones digit is (8), we would look at our final ones digit, which is 0, which only occurs (to 8) when being multiplied by 5. This leaves 5 as the only possible digit for L to be.
8 x 5 = 40
Now, we can calculate the rest of the long multiplication for single digits section, whilst the remainder leads to variable F.
2490 - 5 x 8 = 2450
The remainder is completely produced using variable F and 35.
To calculate variable F, divide 35 by 2490, getting the number originally used to get the product 2490.
2450 ÷ 35 = 70
Variable F is 70, and Variable L is 35
78
x_35__
2730
o solve this question, I had to find the values of F and L. The simplest way to solve this would be through a form of “logical guess and check”. First, I though through the steps of a multiplication in this form. I’d have to multiply 8 by L, and get a number which ends in 0. L would have to be 5 (8*5=40), seeing as though the product 8 times any other digit from 0-9 doesn’t end in a 0. Therefore, L = 5. I’d also need to know the value of F, which can be found by using the newfound value of L. Knowing the value of L allows me to rewrite the multiplication;
ReplyDeleteF8
35
*_____
2730
This can also be written as F8*35 = 2730, and also 2730/35 = F8.
2730/35 = 78
So, 78 = F8, telling me that F is equal to 7.
Therefore, L = 5 and F = 7.
To find the numbers that represented F and L, I thought of what single digit number when multiplied by 8 would be something in the 10s. That was 5; 8 x 5 = 40.
ReplyDeleteNow I was at:
4
F8
x 35
2730
To find F, I used guess and check.
I started off with 6 since it’s a fair number, meaning that it would be easy to experiment with since it was an “middle” digit.
4
68
x 35
2380 < too little
I found that 4 was way little, but was close which is why I increased the number by changing it to 7.
4
78
x 35
2780 < was the given answer
The answer is F= 7, and L = 5
I solved this project using logic. Since the last digit in the product was zero, I knew that 8 had to multiply with the digit below it (L) to equal 0, because if it was larger, the last number would be different. I know from my background knowledge that 5 is the only number from 1-9 that you can multiply with 8 to get a number with zero at the end. That meant L=5. Now I knew that the bottom digit was 35, so all I had to do was divide 2730 by 35 to get the top number. I did that and 2730/5 =78. That meant F=8. I also knew this was correct because the second digit was 8, like in the the picture.
ReplyDeleteF=7 and L=5
ReplyDeleteIn the equation F8*3L=2730, to find these variables I needed to find a number that when multiplied by 8 had 0 in the ones column. Two numbers I found were 0 and 5 (0*8=0 and 5*8=40). Tested out 0 first but since any number multiplied by 0 is just 0 I skipped it and went to 3, and wrote the number 0 in the ones column. Now I did 3*8 giving me 24 which means the 4 is in the tens column meaning 0 can't be L as the product of the 2 numbers is 2730. This left with 5, meaning L=5 and the second number is 35. So I tested if 5 was L by dividing 2730 by 35. It gave me 78 which could work because the second number in F8 is 8. This also means F=7. How can I prove that F=7 and 3=L? By multiplying 78 and 35 which gave me 2730, the product of the 2 numbers.
ReplyDeleteAnswer
one of the numbers has to be a 5 because the number ends in 0 so i can try numbers till i get the answer
58
X 31
1798
the ending number started in 8 so i should switch f from being 5 to l
18
X 35
630
i am trying too low so i will skip a few numbers
48
X 35
1680
still too low
68
X 35
2380
still too low
78
X 35
2730
there is the answer l is 5 and f is 7
To solve this problem, I used a form of "logic" and "guess and check."
ReplyDeleteFirst, I found the value of L. I review the equation and saw that the last digit of the answer is a zero. From previous knowledge, I know that 5 is the only one-digit number that - when multiplied - gets an answer that ends in zero. So, L is equal to 5.
This make the equation:
F8
x 35
2730
Then, To find the value of F, I divided 2730 by 35, and got 78. This meant that F is equal to 7.
Therefore, the values of L and F are 5 and 7, respectively.
The answer that I got was L = 5 and F = 7
ReplyDeleteSince the product ends in a 0, 8 needs to be multiplied by 5 (L) to get 40 which ends in a 0, obviously. I used the number 5 because it was the only number thats from 1-9 that gives a product to end in 0. If L equals to 5 then that number was 35.
4
F8
x35
2730
Now that I found one of the numbers I can just divide 2730 by 35 to find the top number. When I divided it I got 78 making F equal to 7.
Then I double checked by multiplying 35 by 78 to get 2730. Thats how I knew that I was correct.
L is 5 because using logic, since the number ends with 0, 5 is the only number that if you multiply by 8 you get that ends with 0. Then by dividing 2730 by 35 it would tell me the unknown which is F
ReplyDelete2730/35=78, so the unknown is 8.
L=5
F=8
78x35= 2730
To solve this problem, I started by looking at the product and seeing what was done to get this product. Since the product is 2730 I decided to start by figuring out L. I then did the multiplication. 8 x ? = a number with a 0 at the end. Since I know 5 x 8 =0 I decided to try 5 as L. Then I simply devided 2730 by 35 to get 78. I then doubled checked 35 x 78 = 2730 witch means I got the correct answer. The answer for this question is l=5 f=7
ReplyDeletePlease see the correct answers below. Make sure you see why you may have obtained a different response.
ReplyDeleteF = 7
L =5