 |
|
|
|
|
|
|
|
|
Multiplication and repeated addition |
2016-11-23 |
|
Anandmay pose la question :
Hello
I was looking closely at early arithmetic where I found how we discovered properties of Arithmetic.
Like:2 x 3 = 3 x 2.
This can be proved by considering a 2-D figure(actually,quadrilateral) having length consisting of 2 boxes of
1-by-1 dimensions and breadth of 3 boxes of the same dimensions.
Now,consider it again,but,this time,length of 3,and breadth of 2 of such 1 by 1 boxes.
We now notice that we can fit the 2 types of rectangles formed on each other precisely.
So the multiplicative property of commutativity is true for all natural numbers as we can generalize the result(in our mind,for self satisfaction).
Now,can you find me a nice satisfactory reason of why a fraction times a natural number equals the number times the fraction?
I mean, for example,i can understand the meaning of 3 x 2/3 to be three times 2-3rd,that is, 2/3+2/3+2/3.Fair enough.
But here is the problem:By definition and actual meaning of multiplication, a x b means the repeated sum of b,done 'a' times.
So what is the meaning of doing 2/3 x 3?The repeated addition of 3 how many times??2/3 times??Not making sense,right?And even
we have not proved yet the commutative property of numbers INCLUDING fractions.So how can we resolve this problem and make these things meaningful?
Thanks
Penny Nom lui répond. |
|
|
|
|
|
|
Why are equivalent fractions equal? Part 2. |
2016-11-22 |
|
Anandmay pose la question :
Hi!
I saw one of your answered questions:Why are equivalent fractions equal?
The same question I had for why i searched and ended up entering this wonderful site.
The answer was so much experimental based.I mean,for example,it was explained how
3/4 was equal to 6/8 by dividing a unit into 4 equal parts and taking four of the parts,and then dividing the
same unit into 8 equal parts and then taking 6 of them.The result was that both the taken parts were equal.
(That is,3 out of 4 equal parts were equal to 6 of the 8 equal parts.)
But,this was very much non-generalized and experimental-based result(proof).
And we all know that in mathematics,we confirm some particular thing for all the numbers iff we generalize
it.
So,can you explain more clearly 'HOW' the 3 parts of the 4 equal parts and the 6 of the 8 equal parts of the unit
equal(that is the same)?I don't want experimental proof.I want clear proof,and thus please give a generalized
proof for all fractions and their equivalents.
Thanks!
Penny Nom lui répond. |
|
|
|
|
|
|
A square inside a circle inside a square |
2016-11-13 |
|
Jeff pose la question :
Greetings,
I came across a question from a textbook from years ago. I've been trying to solve it, but am not sure if my approach is correct.
There are 2 squares (1 inner, 1 outer) & 1 circle.
The inner square is the largest square that will fit inside the circle. It has an area of 1 unit.
The circle is the biggest that will fit in the outer square.
What is the area of the outer square?
Penny Nom lui répond. |
|
|
|
|
|
|
The amount of material remaining on a roll |
2016-11-11 |
|
Yoh pose la question :
Question from Yoh:
Hello,
I am trying to find impressions on a roll (either full roll or partial).
Let's say I have the following information.
- Outer Diameter of roll
- Inner Diameter of roll (cardboard core)
- thickness per layer
- Each cut off length (impression length)
Now let's say a roll has a 40in outer diameter, the cardboard core has a 3.75in diameter and a thickness of .002. Each impression has a cut off of 14inches.
With this the roll will have approximately 2,700 impressions. How would I find the remaining impressions if the outer diameter of the roll is only 6.5inches?
Thank you.
Penny Nom lui répond. |
|
|
|
|
|
|
A fish and eight parakeets |
2016-11-11 |
|
Cindy pose la question :
Cindys fish weighs 8 times as much as her parakeet. Together the pets weigh 63 ounces. How much does the fish weigh?
Penny Nom lui répond. |
|
|
|
|
|
|
4444 base five |
2016-11-11 |
|
John pose la question :
If 4444 is a number in Base5, is 624 its value?
Penny Nom lui répond. |
|
|
|
|
|
|
An equation with fractions |
2016-11-09 |
|
Tina pose la question :
How do you solve x+1/3=x+2/5. X+1 divided by 3= x+2 divided by 5. What's x=
Penny Nom lui répond. |
|
|
|
|
|
|
Volume of liquid remaining in a tilted cylinder |
2016-11-08 |
|
Brian pose la question :
I am trying to determine the amount of a liquid remaining in a 55 gallon drum when it is tilted at 45 degrees and the liquid level is low enough so that the liquid does not completely cover the bottom of the drum.
Your help is greatly appreciated.
Harley Weston lui répond. |
|
|
|
|
|
|
The area of a rectangle |
2016-11-05 |
|
Ivan pose la question :
If the vertices of a rectangle are a(1,3),b(3,-4),and c(1,-4),find it area.
Penny Nom lui répond. |
|
|
|
|
|
|
A key for a lock with five tumblers |
2016-11-02 |
|
Aeriel pose la question :
A lock works by having a key turn a sequence of tumblers. Consecutive tumblers have different heights, and in order to unlock the lock, the sequence of heights on the key must exactly match those of the lock. The picture below shows a lock with four tumblers.
How many different keys can be made for a lock that has 7 tumblers with 5 possible heights each?
Penny Nom lui répond. |
|
|
|
|
|
|
A problem with a recipe |
2016-10-31 |
|
Ted pose la question :
Recipe calls for 3 1/2 c of sugar & 4 c of water. I only have 3c of sugar how much water do I use
Penny Nom lui répond. |
|
|
|
|
|
|
Three circles |
2016-10-30 |
|
yolani pose la question :
two equal circles with centre A (1;1)and B (4;5)touch a third circle with centre P as shown in the diagram. If P ,A and B Lie on a straight line find the coordinates of P
Penny Nom lui répond. |
|
|
|
|
|
|
A pattern rule for a sequence |
2016-10-28 |
|
Grace pose la question :
Here's a Grade 7 question, we need to find the pattern rule:
1 - 1
2 - 3
3 - 6
4 - 10
......
It may involve exponents, but we can't seem to figure it out.
thank you.
Grace.
Penny Nom lui répond. |
|
|
|
|
|
|
The derivative of the inverse of a function |
2016-10-28 |
|
Kate pose la question :
Hi, I'm in a College level Calculus course and I can't seem to figure out the answer to this question.
Find the derivative of f^-1(4) if f(3)=4 and f'(3)=1/7
Penny Nom lui répond. |
|
|
|
|
|
|
Parallel lines |
2016-10-26 |
|
Jordan pose la question :
(7,-5) 3x -4y=5
Penny Nom lui répond. |
|
|
