Conjectures
A “conjecture” is an educated guess. I noticed something when I divided a whole number and a fraction so I’m making a “conjecture”. Your job is to see if my conjecture is always true, sometimes true, or never true. You will do this by checking my work and then positing your own 3 examples. If you cannot find an example that disproves my conjecture you should assume it is always true. If you can find even one example that disproves my conjecture you would conclude that my conjecture is sometimes true. In this example, we know that “never true” isn’t an option because my examples are true! Here we go:
I took 60 and divided it by 1/2 (not 2) and my calculator said the answer was 120.
60 ÷ (0.5) = 120
I took 10 and divided it by 1/4 (not 4) and my calculator said the answer was 40.
10 ÷ (0.25) = 40
I took 75 and divided it by 1/10 (not 10) and my calculator said the answer was 750.
75 ÷ (0.1) = 750
My conjecture: When you divide a whole number by a fraction the answer is more than you started with. Is this always true or sometimes true? In order to pick “sometimes true” you have to come up with an example that disproves my conjecture.
I think its always true because all your answers are corrext and my calculator says the same thing.
Correct
3×1=3
4×2=8
5×3=15
This a correction for the other problems. I changed them because the whole numbers weren’t mutiplied by decimals.
3×(0.2)=0.6
5×(0.5)=2.5
6×(0.1)=0.6
Good start Jasmin. Make sure you pay super close attention to the operations being used. My original conjecture was about dividing whole numbers by fractions.
Always true . Ms.Ellison divided correctly and I did some questions to prove my answer was right . 82/(0.05)=1640 and 56/0.08=700 and they equal more than what I started with . With other fractions or improper fractions it doesn’t always work but is you use numbers in the hundredths place it always works.
Always true because each time you divide a whole number
By a decimal your answer is always bigger
Examples:
1. 10/(0.1)=100 the answer is always bigger
2.100/(0.2)=500 the answer is always bigger
3.1/0.1=10 the answer is always bigger
Great start Laila! What happens if you divide by an improper fraction?
The conjuncture is always true. When a whole number is divided by a fraction it is always bigger than the whole number you started with.
Ben…Where are your examples that prove your conjecture?
Always True:
Because all answers were greater.
#1 75 ÷ (0.2) = 375
#2 50 ÷ (0.125) = 400
#3 413 ÷ (0.375) = 1101.33333
Great start Ally! What happens if you divide by an improper fraction?
Always true.
Cristian, Where are your examples that prove your conjecture?
The conjecture is sometimes true.
16 divided by (0.25) (my moms tablet doesn’t have a lot of symbols (iPad mini))
If you make 16 into 16/1 and 0.25 into 1/4 then you cancel out the 16 and the 4 , it makes the problem into 4/1 divided by 1/1 which equals 4. 4 is less than 16 so the conjecture is “sometimes true”
Great job Sydney! I like how you extended your thinking to include other types of fractions!
always true.
I checked Ms. Ellisons answers and she divided correctly and I did some question to check like 45/(0.01)=4500 or 96/(0.75)=128
and they all answered more than I started with. But if you use fractions like 1.5 or 1.2 then its sometimes true but Ms.Ellison wasn’t clear on the type of fraction we should use.
Great job Skylar! I like how you extended your thinking to include improper fractions!
I think your conjecture is always true because all the problems gave the same answer as what the problem above have. The three examples I am giving is 19 divided by 0.3 and got 63.3… Which is bigger than 19. The second example is 20 divided by 0.4 and got 50 which is bigger than 20. The last example is 98 divided by 0.2 and got 490 which is bigger than 98. I think the conjecture is true for these reasons.
Great start Cierra! What happens if you divide by an improper fraction?
what I did was I took several whole numbers and divided them by fractions and found that I always ended up with more than I started with so I find this statement to be always true.
Rachel, Where are your examples that support your conjecture?
Hey Ellison :0 it’s Turie in 5′ and I’d like to explain that if you devise any number by the fraction 1/10 you just add an extra zero like 80 and decide it by the fraction 1/10 you get 800 and the same exact thing with sixty you get 600 even with the number five you get fifty
With love
From
BEYONCÉ (Turie)
Great start Turie! What happens if you divide by an improper fraction?
always true
Dylan..Where are your examples that prove your conjecture?
My conjecture is that when you divide a whole by a fraction its only sometimes true. Sure when you divide a whole number by a proper fraction you get a bigger number than what you stared with, but when you divide a whole number by a improper fraction you get a smaller number.
If you divide 4 by 1/2 you get 8
4 divided by 0.5=8
But when you divide 2by 8/5 you get 1.25
2 divided by 1.6=1.2
So that’s why when you divide a whole number by a fraction you only get a bigger number sometimes.
Great job Gracie! I like how you extended your thinking to include improper fractions!
the answer for this is going to de always true
Lisbeth…Where are your examples that support your conjecture?
i think it is true becuse i did these examples and i got more these are the examples :19divided by 0.5 and got 38 the next one was 13 divied by 0.75 and got 17.333333 tha explanes why i got it is true .<3 ;p
Great start Alexa! What happens when you divide by an improper fraction?
As i found out is the all you or your calculator are really just multiplying the whole number with the denominator. So your answer is going to end up being bigger then what you started with.
Oh no! Whose post is this?
As I found out that it is true because all you or your calculator are just doing is multiplying the whole number with the denominator of the fraction. so the answer is going to end up being bigger then what you started with.
Oh no! Whose post is this?
ok well im new to this so sorry if i get it wrong! 🙁
Alright,so in a calculater you cant put 1/4 so i learnd that you just have to put THE QUESTION in like the same way you did so just do that and you will find your answer! #hope its right!!!!!
This should be the answer to the blog question Wendy. You are checking to see if my conjecture is true or not.
I did 70 divided by .5 and got 14O IT WORKED
I did 1 divided by .5 and got 2 THAT ALO WORKED
I did 246 divide by .5 and got 492 THIS WILL ALWAYS BE TRUE
I did 5 divided by .25 and go 20 IT WORKED
I did 90 divided by .25 and got 360 THIS WORKS TOO
I did 500 divided by .25 AND THIS WILL ALSO ALWAYS BE TRUE
I did 55 divided .1 and got 550 IT WORKED
I did 25 divided by .1 and got 250 THIS ALSO WORKED
I did 35 dividedby .1 and got 350 THIS IS ALSO TRUE
this statement will be sometimes true
Good start Landon! It seems that all of your examples proved my conjecture true. Why did you make the conjecture that it is “sometimes true”?
When you divide a whole number by a fraction the answer is more than what you started with. This conjecture is always true.
I took 175 and divided it by 1/4 (not 4) and got 700 as an answer. Then I checked on my calculator to make sure.
Great start Citlally! You need to do more than one experiment to prove your conjecture!
the answer for this is always true because when you are devideing by a decimal it is like multiplying and no matter what number or decimal you divide by you always end up with more than you started with examples 13 divided by 0.5 = 26
27 divided by 0.5 = 54.
Great start Audra! What happens if you divide by an improper fraction?
This conjecture is always true when you divide a whole number by a fraction the answer is always more than what you started with. It is always true because if you are dividing a smaller number than your first number, your answer will turn out being bigger than your first number and your second number you had started with.
Ex. ; 60 divided by (0.5) would be 120.
Your first number is bigger than your second number but your answer is bigger than both of your numbers.
Bernice…Where are your examples that support your conjecture?
The answers to the problems are always true.
1) 55 / (0.4) = 137.5
2) 124 / (0.5) = 248
3) 64 / (0.8) = 80
Great start Tristin! What happens if you divide by an improper fraction?
The answer is always true. Because both of your starting numbers are going to be smaller than your answer. It says in the question when you divide a whole number by a fraction, the answer is more than you started with. Both of your starting numbers are going to be smaller than your final answer.
Katie…Where are your examples that support your conjecture?
here are my examples that support my conjecture.
42 divided by 0.4 equals 105
74 divided by 0.3 equals 246 with a repeating 6
12 divided by 0.2 equals 60.
So it’s always true that both your starting numbers will be smaller than your final answer. Sorry I didn’t put that in my first comment.
Here are my examples that support my conjecture.
———
42 divided by 0.3 equals 140
———
12 divided by 0.2 equals 60
———
70 divided by 0.4 equals 175.
———
So this proves that both your starting numbers are going to Be smaller than your final answer when you divide a whole number by a fraction. Sore I didnt include this in my last answer.
(Also Im fixing the other one that I posted)
The First problem is always true because 60 divided by 0.5 does equal 120 and some examples to prove it aré 40 divided by 0.2 equals 250, 30 divided by 0.3 equals 100, and 70 divided by 0.2 equals 350.
The second problem is sometimes true because even IF you divide a whole nombre and a fraction the problem 10 divided by 0.27 disproves 10 divided by 0.25.
Lastly the third problem is always true because i tried three other problem like 66 divided by 0.2 =330, 50 divided by 0.2=250, and 70 divided by 0.7=100. None of Them disprove the example
Great start Susana! What happens if you divide by an improper fraction?
1. 8/0.4= 20
2. 9/0.75=12
3. 36/0.4=90
If you look at my three examples they demonstrate that it is always true because 20 is my answer and it is bigger than 8 which is what i started with .Also 12 is bigger than 9 and that’s what i started with.Same with the last one 90 is bigger than 36, so this would prove that it i always true.
Great start Jeanette! What happens if you divide by an improper fraction?
I tested the conjecture that when divide a whole number by a fraction the answer is more that you started with, and I found out that it is always true. Examples:
2 / 0.5 =4
3 / 0.3 = 33.333333333
78 / 0.8 = 97.5
1,000,000 / 0.5 = 2,000,0000
Great start Daniel! What happens when you divide by an improper fraction?
i took 60 and divided it by 1/2 (not 2) and the calculator said the answer was 120.
60divided(0.5)=120
i took 10 and divided it by 1/4 (not 4) and the calculator said the answer was 40
10divided(0.25)=40
i took 75 and divided it by 1/10 (not 10) and the calculator said the answer was 750
75divided(0.1)=750
These are MY examples Jessica! Where is your conjecture and YOUR examples that support your conjecture?
i think it is sometimes true because when u multiply 9 tenths by 24 you get about 27, and that is bigger than 24. but when you multiply an improper you would get a smaller than what you started with.
Good start Dayne. Make sure that you pay very close attention to the operations being used in the original post. My conjecture was based on DIVIDING whole numbers by fractions.
when you dvide a improper fraction and some times true and somtimes not. 24 divided nine tensth and got 27.
85 divided 1/8 and got 680
420 divide 6/5 and got 350.
Great job Eric! I like how you extended your thinking to include improper fractions!
Sometimes true, but if i divide it by a impropper fraction it’ll be lover than the answer than i got:
FOR EXAMPLE:
10 divided by 1 over 7 (fraction)=(answer,higher)
22 divided by 20 over 21 (fraction)=(answer,higher)
39 divided by 20 over 13 (impropper fraction)=(answer,lower than above)
Great job Ashleigh! I like how you extended your thinking to include improper fractions!
the first problem is true
the second problem is true
finally the third problem is true
my first problem is 24/9/10=27
my second problem is 85/1/8=650
my third and final problem is 420/6/5=350
the conjecture is sometimes true because not all came out with a bigger number so that makes the conjecture sometime true
Great job Savannah! I like how you extended your thinking to include improper fractions!
If you divide a improper fractoins the number can be smaller. so yhe anwser is somtimes true!
Nick…Where are your examples that prove your conjecture?
My Conjecture: Sometimes true but if i divide by an improper fraction my answer is not always true.
Ex1: I got 24 and divided it by 9/10 and got 27.
Ex2: I got 85 and divided it by 1/8 and got 680.
Ex3: I got 420 and divided it by 6/5 and got 350.
NOT ALWAYS TRUE!!!
Great job Jimena! I like how you extended your thinking to include improper fractions!
my conjectures it is not alwase true .If it is a inproper it gets smller .If it is proper it gets biggre.NOT ALWAYS TRUE!!!
ex1: i got 24 and dived it by 9/10 and got 27
ex2: i got 85 and dived it by 1/8 and got 680
ex3: i got 420 and dived it by 6/5 and got 350
Great job Alexa! I like how you extended your thinking to include improper fractions!
the first problem is true
the second problem is also true
the third problem is as well true
my first problem of my own is 24\9\10=27
my second problem is 85\1\8=680
my third problem is 420\6\5=350
sometimes the conjecture is true because the problems dont have to always come out with a bigger number so thats why the conjecture is sometimes true it is not always true though.
Great job Ana! I like how you extended your thinking to include improper fractions!
yes it is rigth because i fond out that you can divided a frachion by any whole number and get a whole number but u have to change the frachion in to a desimle and then divided the number to get your answer for example 1/4 divided by 2=0.125 was what i got and hears another way u can do this problum 2 divided by 0.25=0.125 and tats why my answer is yes.
Great start Alesha! What happens if you divide by an improper fraction?
Always true because you start with a big or small and you will get all the same answer even when you turn them around.
Kelton, Where are your examples that prove your conjecture?
This always true because when you multiply whole numbers and fractions the answer is always lower than the number you started with. For example: 14×0.5= 7 but 14/.5= 28
Example 2: 84x.2=16.8 but 84/.2=420
Example 3: 2485x.8=1988 but 2485/.8=3106.25 Your conjecture is always true.
Great start Trey! What happens if you divide by an improper fraction?
This conjecture is always true. I know this because every time i multiplied a whole number by a fraction i got a bigger number. For example 15 divided by 1/2 is 30. Another example would be 9 divided by 1/4 is 36. My final example is 25 divided by 1/5 is 125.
Great start Kateena! What happens if you divide by an improper fraction?
Your conjecture is sometimes true. If you divide 0 by a fraction then your quotient won’t be more than you started with, it would be the same. For example, 0 ÷ 0.25 = 0, 0 ÷ 0.5 = 0, 0 ÷ 0.47 = 0. In any other circumstance, your conjecture is true, though.
Very clever Jianna! I like how you disproved the conjecture with zeros. What if you divide by an improper fraction.
We can tell that your answers are never true because even I did them on a calculator. So we can tell that these problems are always true
Your answer is a bit confusing Chase. Make sure you reread your comment before you post. Also, where are your examples that prove your conjecture?
You’re conjecture is always true because I tried doing everything but it always becomes a higher number. Anyway I made a cconjection by saying if you multiply an even number by an even number you will always get a even number.
26×10=260
12×14=168
8×42=336 it is always going to be an even number
Make sure you pay close attention to the operations and instructions in the blog post. My conjecture was based on DIVIDING a whole number by a FRACTION.
The conjecture is always true if you are dividing by a fraction that is less than1 for example 100 divided by 1/100 equals 10,000 and 2 divided by 1/2 equals 4, but if you divide by a fraction that is greater than one it makes the conjecture sometimes true, for example 10 divided by 8/4 equals 5
The conjecture is always true only if the fraction you are dividing by is less than 1 for example 100 divided by 1/100 equals 10,000 and 2 divided by 1/2 equals 4, but if you are dividing by a fraction that is greater than 1 then the conjecture is sometimes true. For example 10 divided by 8/4 equals 5.
Oh no! Who does this belong to?
Conjectures: When you divide a whole number by a fraction you get a higher number. In my opinion i think this is true because when i tried dividing a whole number by a fraction i kept getting higher numbers. Also,when i tried dividing i got close to the whole number but not below it. So ”i think” that Mrs.Ellison’s conjecture is correct.
Great start Rheon! What happens when you divide by an improper fraction?
This conjecture is sometimes true. Here are my 3 examples:
10 divided by 1 1/4 = 8
10/1.25= 8
7 divided by 1/ 1/2=6.66667
7/ 1. 05=6.66667
8 divided by 1/4=32
8/0.25=32
The number has to be over 1 to be under your original number. If its not 1 and something your answer will be over.
Great job Hailey! I like how you extended your thinking to include improper fractions!
It is sometimes true.
Where are your examples that prove that your conjecture is true Alyssa???
I think your conjecture is always true because i tried it with 3 different examples and all of my answers were more than what i started with:
50/(0.10)= 500
25/(0.5)= 50
80/(0.10)=800
Great start Kevin! What happens if you divide by an improper fraction?
It is always true. Because dividing by a fraction is like multiplying by the whole number of that fraction.
Good start Madison. Where are your examples that support your conjecture?
Whenever you divide a whole number by a fraction, the answer will always be more than you started with. That’s because whenever you are multiplying a number by a fraction, you have to change the second number into its reciprocal and multiply the two numbers and multiply them instead of dividing them. For example, when you take 20 and divide it by 2/8, you get 80. since I switched 2/8 into 8/2, I multiplied 20 by 8 and 1 by 2. I got 160 over 2 which is equal to 80.That’s why whenever you multiply a number by a fraction, you get more than you started with.
———————————————————————————
work:
20/1 / 8/2 = 20/1 * 2/8
20/1 * 2/8 = 160/2
160/2= 80
80 is more than 20.
Great start Juliana! What happens if your dividing by an improper fraction? Also, make sure that you complete at least 3 experiments to prove your conjecture!
I took 60 and divided it by 3/5 and my calculator got 50.
60÷0.2=50
I took thirty and divided it by 3/5 and my calculator got 160.
30÷0.6=50
I took 80 and divided it by 1/2 and my calculator got 160.
80÷0.5=160
When you divide a whole number by a fraction the answer IS ALWAYS more than what you started with!!!
I took 60 and divided it by 3/5 and my calculator got 50.
60÷0.2= 50
I took thirty and divided it by 3/5 and my calculator got 160.
30÷0.6=50
I took 80 and divided it by 1/2 and my calculator got 160.
80÷0.5=160
When you divide a whole number by a fraction the answer IS ALWAYS more than what you started with!!!
Great start Angel! What happens if you divide by an improper fraction?
This is always true i know this because i did as an example
50 divided by (0.5)=250 which is more than what i started with.
Good start Shyann! You need two more examples to support your conjecture!
His conjecture was true because when he divided a fraction by a hole number he got a larger number as a answer.
30/.5=60
90/.75=120
70/.25=280
as you can see by my examples I got a larger number.
Great start Brandon! What happens when your fractions are improper?
Always true because it just multiplying by how much it is trying to take out of. Example: 40÷1/2=80 half of 80 is 40; 20÷1/4=80 1/4 of 80 is 20;15÷3/4=20 3/4 of20 is 15
Great start Walter! What happens if your fractions are improper?
Sometimes true
Make sure you justify your thinking Sydney! Where are your examples that support your conjecture?
for the first problem i got always true because after i divided 60 by 1/2 i got 120 and the i double checked it by converting 1/2 into a decimal (0.50) and still got 120. Then i did 120 divided by 1/2 and got 60 so i knew my anwser was right. For the second equation i got always true because after i divided 10 by 1/4 (0.25) i got 40 and to check i did 40 times 1/4 (0.25) and got 10. For the last equation i got always true too because when i divided 75 by 1/10 or (0.10) (0.1) i got 750 either way and to check i multiplied750 by 1/10 and it equaled 75 so i knew that my anwser was right.
Those are my examples Mason. Where are your examples that you used to test the conjecture?
I believe its all ways true because when you multiply a fraction i has to be larger than the number. If not you are doing something wrong such as dividing or subtracting.
Make sure that you pay very close attention to the operation being presented in the blog post Christian. We were dividing not multiplying. 🙁
Your answer is always true because when I did those problems I divided like you did and got the exact same answers you got so your conjecture is always true.
Good start Jaqueline! Where are your experiments that support your conjecture?
2×3=6
3×4=12
4×5=20
5×6=30
6×7=42
Conjectures are true most of the time
Rogelio, How does this apply to the problem in the blog?
I think what you mean by this, Mrs.Ellison, is:
47 divided by 1/8 (.125)= 356
So I put 1/8 and got .125. Then I did 47/.125=356.
The answer is BIGGER than the original problem, so Mrs. Ellison is right.
83 divided by 4/8 (.5)=166
First I did 4/8 and got .5, so I used that as my decimal. I entered 83/.5 (4/8) and got 166.
The answer is still BIGGER then the problem, and Mrs. Ellison is still right.
22 divided by 3/12 (.25)= 88
I took 3/12 and got .25, so then I inserted that in to 22/.25 (3/12) and came out with 88.
Answer…..Still…….BIGGER……Then…….Original…….Problem……..
Mrs.Ellison………Still……..Right………!
So in conclusion, I think I’ve proven that Mrs.Ellison is right with her conjecture.
Great start Sammie! What would happen if your fraction was improper?
I check the teacher work and got the same answer. The first thing I did was that I took 65 and I divided it by ¾ and my calculator said the answer was 86.66. The second thing I did was that I took 83 and divided it by ¼ and my calculator said the answer was 332. The third thing I did was that I took 56 divided by 0.2 and my answer was 280.
Based on what I found by checking the teacher work and making my own examples I believe that her conjecture is always true because when I did my problems I always came up with a bigger answer.
Great start Kaeden! What would happen if the fraction were improper?
always true
Where is the justification for your conjecture Rain?
Sometimes true: the reason it’s sometimes true is because you never said the fraction had to be proper so 5 divided by 10/5 would be 2.5. Also if you were to do 10 divided by 5/5 it would be 10 therefore not more nor less than what you started with
Great job Mateo! I like how you extended your thinking to improper fractions as well!
true
This does not provide any evidence that the conjecture is true. Please make sure you justify your thinking or I can not tell what you were thinking. 🙁
My conjecture is when you divide a whole number by a fraction the answer is always more than what you started with.
Ex. 8 / 0.21= 38.095 proving that is it always bigger than when it started.
Great start Allyson. Make sure you have at least 3 experiments to prove your conjecture!
always true because when you divide a whole number by a fraction it is always bigger. Examples: I took 30 and divided it by 5 my calculator got 60. i divided 50 by 0.5 and my calculator got 250. i took 8 and divided it by 0.21 and my calculator got 38.095. which proves the answer is always bigger.
Always true because when dividing whole numbers by decimals you have to move the decimals over which will make your answer larger than when you started, or less. Ex: 15 / (0.3)= 50 Ex2: 45 / (0.4)=112.5 Ex3: 56 / (0.33)=169.69697
always true
How can you make a conjecture without any examples Cole????
The conjecture would be true if the fractions you are dividing by are less than one for example 100 divided by 1/100 (.01) equals 10,000 and 2 divided by 1/2 (.5) equals 4. The conjecture is sometimes true if you divide by an improper fraction, for example 10 divided by 8/4 (2) equals 5, which is smaller than what you started with.
i think the answer is alway going to be true because we have to get numbers and connect the numbers to the answer try to make to true?
first i divude 60 by 5 and i got 20
and with my other question i divided 1 by 75 and got 75 and with my last quetsion my answer was 4
and thats how i got my answers
Sometimes true: The reason it’s sometimes true is because you never said the fraction had to bve proper so 5 divided by 10/5 would be 2.5.
all of them are true because I have used all of my msth and the couculater to see if all the answer are true.
i think all of your questions are correct so your conjecture is true
1.) 55 / (0.4) = 137.5
2.) 124 / (0.5) = 248
3.) 64 / (0.8) = 80
(The answer to the problem is always true.)
All ways true because when you conjecture is made the answer is usually correct
I am sorry miss Ellison but I can not come up with any examples of my own so I am going to just assume that it is always true because you said that if we can not come up with an answer we should just assume that you are always right because you are always right because you are a math teacher. P.S, I think you are the greatest math teacher ever, also miss Taylor, but you to (: =-)