Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 Help Me ! » translate math words into » 2022-03-17 03:10:36

Hannibal lecter
Replies: 1

hi, I saw this in a book can someone translate these highlighted words into numbers because I get confused in English some times







#2 Re: Help Me ! » dividing small number over a larger number concept » 2022-03-17 03:05:56

Bob wrote:

Let's say you want to do 1 / 3 as a decimal.

Let's try 100 / 3 first.

100 - 3 = 97         97 - 3 = 94         Oh dear! This will take ages.  Let's speed it up by taking 30 at a time.

100 - 30 = 70      70 - 30 = 40         40 - 30 = 10

Now I haven't got enough left to take another 30 so I'll switch to taking 3s.

10 - 3 = 7       7 - 3 = 4      4 - 3 = 1 

Now I haven't got enough to take any more 3s so I'll switch to taking away 0.3 each time.

1 - 0.3 = 0.7        0.7 - 0.3 = 0.4        0.4 - 0.3 = 0.1   

This is going to go on forever because I always get a bit left over. 
If I was setting this out as a division the answer space would have this:


If I want to do 1 / 3, it's exactly the same except the decimal point shifts two places left.

1 / 3 = 0.33333333


I understand everything now completely but that last segment of your post it's a little not clear to me
because you take 100 - 3 until you reached 40 - 30 = 10 then stopped (first time)
then you take 10 - 3 = 7       until you reached      4 - 3 = 1  then stopped (second time)
finally you take 1 - 0.3 = 0.7        until you reached        0.4 - 0.3 = 0.1  then stopped (third time)
so the number would be 0.3? right? it's 3 times right?? how it's 33.333333 or 0.33333333 it should be 0.3 right

#3 Re: Help Me ! » dividing small number over a larger number concept » 2022-03-16 13:20:48

So we record that in the answer space as not 4 subtracts but 0.4 subtracts because we shifted the carriage one place.

I mean we made 15 become 1.5 the number is changed who gives the right to do such a thing is that legal in math and clearly understandable? is there explaintion for that ..
I mean we chose a different number it's 1.5
I can't imagine that is there interactive example like 6 apples iver 16 people

#4 Re: Help Me ! » dividing small number over a larger number concept » 2022-03-16 07:47:23

First you try 6 - 15.  Cannot do that as you're trying to take away too much.  So 'shift the carriage' and try to take away 1.5s.  You can do that exactly 4 times; 6 - 1.5 - 1.5 - 1.5 - 1.5 = 0.  So we record that in the answer space as not 4 subtracts but 0.4 subtracts because we shifted the carriage one place.

bob why we can't do repeated subtraction
like 8 ÷ 4
8 - 4 = 4 (1 time)
4 - 4 = 0 (1 time)
then the result is 2

why in 5 ÷ 16 you said (Cannot do that as you're trying to take away too much)
what you mean by that can you please explain further to me

and after that you said :-

, so 'shift the carriage' and do 1 - 0.6 = 0.4.  You can do that once but then there's not enough left to do it again.

what you mean by "there is not enough left"

can you please explain that further for a beginner

#5 Re: Help Me ! » dividing small number over a larger number concept » 2022-03-13 10:09:43

Hannibal lecter wrote:
Bob wrote:

I'm old enough to have used mechanical calculators to do arithmetic.

can you please tell me or send me a photo of that mechanical calculators and where to do you have a similar links to buy it from amazon or ebay

And to do division you had to do repeated subtraction.

I couldn't understand how division is a repeated subtraction

example.  If the calculation was 48 divided by 6 you would set up 48 in the register, then set up 6 as the amount to subtract, and then wind the handle backwards so the display showed 42, then 36 then 30 and so on until zero was showing.  A side register would show how many times you had turned the handle and it would be showing 8 in the case.

but 48 divided by 6 is 8 directly how could it displayed 42 at first from where did we get this number even in papers couldn't find it

If the calculation was 1 divided by 8 the procedure was as follows:
Now you are subtracting 0.08 each time. 

the number is 0.08?? is very ambiguous to me, from where we get that number even in papers I tried a lot I couldn't figure it
you said " subtracting 0.08 each time "

and thanks you so much you understand what I want it's really my problem I can't understand division process

#6 Help Me ! » dividing small number over a larger number concept » 2022-03-09 09:02:35

Hannibal lecter
Replies: 10

What is the concept of dividing small number over a larger one (ex: 1/6)
is 1 divided into 6 pieces and become 0.16666666666
and these pieces called units of 1 or something like that?
so 0.16666666666 * 6 = 1
what is the concept of this division and why number one cut into pieces and become exactly 0.16666666666
how to measure that or represent it on Number line!
also when calculation 0.16666666666 * 6 it's 0.99999999996 not 1 !!!
and is there a resources and math books to illustrate this but not YouTube channel please it's only give the ways to calculate it not explantion.

and I have example of a second problem it's 6/15 as following in the picture ..
my question is who gives as the rights or standards to put zero down? (u will see what I mean from the picture)
and my second question is who gives as the right and standards to place a decimal point (you will see that also from the picture)


#7 Help Me ! » if condition and math » 2022-03-06 14:35:14

Hannibal lecter
Replies: 1

The university bookstore has a Kilobyte Day sale every October 24, giving an 8 percent
discount on all computer accessory purchases if the price is less than $128, and a 16 percent
discount if the price is at least $128. Write a program that asks the cashier for the original price
and then prints the discounted price

solution :
If original price < 128
discount rate = 0.92
Else                              // i't mean if the other condition true which is (if original price ≥ 128) but the problem not here!
discount rate = 0.84

discounted price = discount rate x original price

my problem is what is the meaning of 0.92?
and what is the meaning of 0.84?
in the exercise it said discount only 8% mentioned and 16%, from where did we get 0.92 and 0.84???

because I solve it like that :
discount price = original price - DiscountedValue
example : 110
discount price = 110-8.8  // because discountPrice will be (8/100 * 110 = 8.8)...
this way of mine is gives the same answer! why the book used something like that and how the book find that rate?

#8 Puzzles and Games » logic gate » 2022-02-10 10:44:03

Hannibal lecter
Replies: 2

which logic gate gives :

x y result
0 0   1
0 1   0
1 0   1
1 1   0

this is the question :

if (A = '1') and (B = '1') then tempY <= '0';
elsif (A = '0') and (B = '0') then tempY <= '0';
else tempY < = '1';
end if;
if (A = '0' and B = '0') then tempZ <= '1';
elsif(A = '0' and B = '1') then tempZ <= '0';
elsif(A = '1' and B = '1') then tempZ <= '0';
elsif(A = '1' and B = '0') then tempZ <= '1';
end if;
end process;
Y <= tempY;
Z <= tempZ;

Y is an xor gate
but what is z

#9 Re: Help Me ! » Complete the table » 2022-02-08 10:51:36

I am now completely understand how we get f and g
my problem was I tried to start to solve it row by row not the column f first then column g so sorry
now I remamber and completely understand

#10 Help Me ! » even and composed functions » 2022-02-08 10:40:42

Hannibal lecter
Replies: 2

If g(x) is an even function then f(g(x)) is even for every
function f(x).

solution :

True. We have g(−x) = g(x) since g is even, and therefore f(g(−x)) = f(g(x))

is that mean wherever I compose f(even function input) the output will be even?

#11 Help Me ! » Complete the table » 2022-02-07 11:24:15

Hannibal lecter
Replies: 2

Hi please see this question in the following pic :
I tried a lot to solve it and to complete the table values but it didn't work for me
I know composed function and studied it and know how to calculate functions like f(g(x)) or f(f(x)) .. etc but I stopped in this exercise
I don't know what is my weak point that made me stop from solving and understanding it, the silly thing that I got the solution and still don't understand it!


solution from solution book :


#12 Re: Help Me ! » composed function » 2022-02-01 23:04:18

thanks, and how to think in reverse? for example :


the answer of 36. is f(x) = x^3   , g(x) = x + 1
and Answer of 39. is f(x) = e^x  , g(x) = 2x

can you tell me what is the step of thinking to extract the inside function and outside function?
why not g(x) = x^3 , and f(x) = x+1 is that possibles. it's very difficult to determine them in just looking at them please tell me how to think to find them in any question

#13 Help Me ! » composed function » 2022-02-01 10:21:38

Hannibal lecter
Replies: 3



the book solution :-

why is that? it should be

  which is 


  is wherver I find x I should double it so when I found
I should replace the x by x^2
hence will be

am I right? If I'm not right why how should I look to the problem.

#14 Re: Help Me ! » Shifting a function » 2022-01-31 23:07:59

oh sorry you are right I got a mistake
I saw it goes up a little so I thought it didn't moved to the left sorry now everything is clear I use a grapher not by hand
do you advice me to plot things on paper or keep using grapher computer?

#15 Help Me ! » Shifting a function » 2022-01-31 09:38:10

Hannibal lecter
Replies: 3

In math whatever we plug number to x it shift it horizontally but if plug it like that f(x) +1 it shifted it vertically
But my problem in e^x it shifted on y-axis when I plug 1 for example. what is the secret behind that
Like e^(x+1)
It should shift the e^(x+1) to the left! But it’s didn’t happen why
Like x^2 when plug +1 which became (x+1)^2 it shifted it to left! Correct

#16 Coder's Corner » how can we find the first digit of a number using log10 » 2022-01-25 04:17:42

Hannibal lecter
Replies: 1

int number 123456;
int firstDigit;
int totalDigits = (int) Math.log10(number);
firstDigit = (int) (number/ (int) Math.pow(10,totalDigits));
System.out.println("First Digit is: " + firstDigit);

how could log10 of a number like 123456 is 5?
I type that in google and it's 5.09151220163 not 5, I know we used casting so it discard the fractional parts to get 5, but my question is not about the Java it's about log10 why log10 always get the total digits with fractional parts always!
like log10 of 532 is 2.7259116323 which is 2 digits that is working! but how mathematically is that

how can Math.log10(12345) calculate the number of digits which is 5 correct!?
only that first part of the code is really ambiguous

#17 Re: Coder's Corner » algorithm for tiles a floor , very important to move on » 2022-01-13 22:03:09

so you mean for example :

for (1,1)

(1 % 2) + (1 % 2) = 1 + 1 = 1 white, is this the way I apply by numbers? am I correct
and please why the book in the end used additional mod :

color = ( (row % 2) + (column % 2) ) % 2

look he used again %2!! he found sum of reminders than take mod 2 again? why? and where locations should I apply this formula only in the last row? because he said "fourth entries" is he mean the last row, isn't enough to use only (row%2) + (col%2)

#18 Coder's Corner » algorithm for tiles a floor , very important to move on » 2022-01-13 19:20:22

Hannibal lecter
Replies: 3

Hi, I have this problem the solution it needs is not advanced not using "if and else statement" the book needs to see the answer with simple algebra.
I have the question and the solution but it's not understandable completely expect I know that we need mod 2 (ODD and even) in my solution.

A robot needs to tile a floor with alternating black and white tiles. Develop
an algorithm that yields the color (0 for black, 1 for white), given the row and
column number. Start with specific values for the row and column, and then


////// solution of the book start
Solution of the book :

Clearly, the answer depends only on whether
the row and column numbers are even or odd,
so let’s first take the remainder after dividing by 2. Then we can enumerate all expected


In the first three entries of the table, the color
is simply the sum of the remainders. In the
fourth entry, the sum would be 2, but we want
a zero. We can achieve that by taking another
remainder operation:
color = ( (row % 2) + (column % 2) ) % 2

////// solution of the book Ended

pls explain the book solution only I want to understand it step by step I didn't understand what he mean by dividing
note that the dividing here is integer division ex : 3/2 = 1 not 1.5 because it discard the fractional part

I didn't understand the solution from beginning like " first take the remainder after dividding by 2"
which reminder? and what number we are dividing it by 2 ?
the solution is confusing be and ambiguous

#19 Re: Help Me ! » write a function of this graph : » 2021-12-26 04:46:19

Mathegocart wrote:


thank you a lot

#20 Re: Help Me ! » write a function of this graph : » 2021-12-25 09:54:20

can you plot D area in the graph please I want to see it and to feel it, you give me excellent explantion but still the image not completed in my mind

#21 Help Me ! » write a function of this graph : » 2021-12-19 09:35:41

Hannibal lecter
Replies: 4

Hi pls see this graph :


the answer is :


what he mean by "D, difference between the horizontal asymptote and the graph appears"
and how could we made this function in this form? what is the meaning of number 1
and how cold be  D = 4 − y?

#22 Help Me ! » what is the step by step to convert a negative reciprocal » 2021-12-19 08:55:58

Hannibal lecter
Replies: 1

how cold write

to become

is there simple another example by numbers only without variable to illustrate this because I'm so beginner in these algebra

#23 Science HQ » microfabrication » 2021-12-18 18:57:31

Hannibal lecter
Replies: 1

what is microfabrication related to mathematics?
if anyone have ideas, comments, opinion, on that topic please talk here

#24 Re: Help Me ! » rate of growth/decay in exponential function » 2021-12-16 04:38:26

Mathegocart wrote:

How so? As zetafunc mentions above, the function

is equivalent to the function you mentioned, and the equation is continuous.

can you please see this YouTube link it talked about it and it said there is differences :-

also see this sheet pls :


#25 Re: Help Me ! » rate of growth/decay in exponential function » 2021-12-15 14:53:28

Mathegocart wrote:

Yes, the equation does represent continuous growth. As noted, you can convert that equation into the form of the continuous standard equation

with the substitution mentioned above.

I think it's not right, because I found the answer today
the form model without e and k like this :

is called non-continuous exponential models functions
because in case of increasing (a>1) while in case of model contain e, and k, if k is positive it's increasing continuously rate (because any positive number is acceptable and in case of base a there is numbers less then 1 are positive but not included)
and in case of decreasing (0<a<1) while in case of e, and k, here k is has to be negative <0 so it's continuously decreasing rate

so  now

its growth rate is not continuous,

am I right?

by the way I learned this today from a YouTube channel but I still don't understand why we can't called the base a a continuous if it's >1
I knew because it doesn't included the numbers that less than 1 and bigger than 0
but why? why this is a reasons that we can't call it continuously, what is meaning continuously in this case anyway? because every graph I draw in form of non-continuous exponential models I see them clearly in my naked eyes that they are continuous, I draw these random examples as in example I see them all goes beyond without end


Board footer

Powered by FluxBB