Tuesday, July 22, 2008
Have questions about math problems
Have questions about math problems, get help on this website. You will learn the toughest questions with the easiest way to solve it!!
Monday, July 21, 2008
Using math to solve daily problem!
Math Problems Solving: A peasant wants to sell his stuff and get some salt and other supply back home. However, he has to cross a river with a small boat. How can you help him carry a sheep, wolf as well as cabbage across the river? You can only carry one item across at one time.
Math problem solving: Hint, Remember, sheep eat cabbage, wolf eat sheep.
That us solve and analysis it together.
1) Carry the sheep first across and leave wolf and cabbage behind, because we know wolf does not eat cabbage.
2) Go back and get the wolf and leave only cabbage behind. Then come back with the sheep in the boat, so it is not eaten by the wolf. I know it takes a lot of effort.
3) Put sheep back and get the cabbage. Leave the cabbage with the wolf, and it won’t touch it!
4) Get the sheep across!!
We are successful!!
Math Problems Solving: A peasant wants to sell his stuff and get some salt and other supply back home. However, he has to cross a river with a small boat. How can you help him carry a sheep, wolf as well as cabbage across the river? You can only carry one item across at one time.
Math problem solving: Hint, Remember, sheep eat cabbage, wolf eat sheep.
That us solve and analysis it together.
1) Carry the sheep first across and leave wolf and cabbage behind, because we know wolf does not eat cabbage.
2) Go back and get the wolf and leave only cabbage behind. Then come back with the sheep in the boat, so it is not eaten by the wolf. I know it takes a lot of effort.
3) Put sheep back and get the cabbage. Leave the cabbage with the wolf, and it won’t touch it!
4) Get the sheep across!!
We are successful!!
Sunday, July 20, 2008
Algebra: quick ways to solve
Solving math problems quickly: algebra
Do you know what is 5*5? 15*15? Or 25*25?
It gets harder and harder as you increase the numbers before 5. However, I have an easy way to help you get the answer without using a pen or calculator!!
Here is the way:
Please pay a close attention to the pattern:
5*5=25
15*15=225
25*25=625
35*35=1225
45*45=2025
:
What is the pattern? Correct! The results we get all have 25 as the last two digits. So how about the other digits?
Then you should find 1*2=2; 2*3=6; 3*4=12; and so on...
Then the other number should be the number before 5 multiple the same number plus 1.
Using this method, what is 65*65=?
Ans: 4225
What is 11*11=? 121
111*111=? 12321
1111*1111=? 1234321
What is 111111^2=?
Similar method!
Do you know what is 5*5? 15*15? Or 25*25?
It gets harder and harder as you increase the numbers before 5. However, I have an easy way to help you get the answer without using a pen or calculator!!
Here is the way:
Please pay a close attention to the pattern:
5*5=25
15*15=225
25*25=625
35*35=1225
45*45=2025
:
What is the pattern? Correct! The results we get all have 25 as the last two digits. So how about the other digits?
Then you should find 1*2=2; 2*3=6; 3*4=12; and so on...
Then the other number should be the number before 5 multiple the same number plus 1.
Using this method, what is 65*65=?
Ans: 4225
What is 11*11=? 121
111*111=? 12321
1111*1111=? 1234321
What is 111111^2=?
Similar method!
Friday, July 18, 2008
Math problems: 2 to the power of x, exponential equations
Hey, do you hate the high rate of interest at banks? Do you want to borrow money from me? I have a whole different system of rate! Start from 2 cents a day!
Here is my system:
If you borrow $100.00 from me, the first day the interest is 2^1 cents, that is 2 cents. The second day is 2^2 cents, that is 4 cents. The third day is2^3, 8 cents....do you know how many interest you have to pay after 5 days? 10 days?
Let’s calculate together!
Ans: 2^1+2^2+...+2^5=2+4+8+16+32=62 cents
For ten days:
62+2^6+2^7+...+2^10=62+64+128+256+512+1028=2050 cents that are $20.50
What a treat!!
Check out how much you have to pay me in a month that is going to be a nightmare for you!! So, remember nothing will come for free and remember the beauty of mathematics!!
Here is my system:
If you borrow $100.00 from me, the first day the interest is 2^1 cents, that is 2 cents. The second day is 2^2 cents, that is 4 cents. The third day is2^3, 8 cents....do you know how many interest you have to pay after 5 days? 10 days?
Let’s calculate together!
Ans: 2^1+2^2+...+2^5=2+4+8+16+32=62 cents
For ten days:
62+2^6+2^7+...+2^10=62+64+128+256+512+1028=2050 cents that are $20.50
What a treat!!
Check out how much you have to pay me in a month that is going to be a nightmare for you!! So, remember nothing will come for free and remember the beauty of mathematics!!
Thursday, July 17, 2008
dimensional questions
Math problems
: dimensional questions 2
There is an ant at the corner of a cube, and their destination is the opposite corner where there is a dead fly. The cube’s edges are 5 centimetres. What is the shortest way and how many centimetres?
Do you know the answer?
Ans:
2*5=10
10^2+5^2=ab^2=125
(125)^-2=ab
Do you know why? It is the shortest distance between two points method!! Just go straight without any turns will be the fastest way!! Try it yourself!
: dimensional questions 2
There is an ant at the corner of a cube, and their destination is the opposite corner where there is a dead fly. The cube’s edges are 5 centimetres. What is the shortest way and how many centimetres?
Do you know the answer?
Ans:
2*5=10
10^2+5^2=ab^2=125
(125)^-2=ab
Do you know why? It is the shortest distance between two points method!! Just go straight without any turns will be the fastest way!! Try it yourself!
Wednesday, July 16, 2008
Math Problems:
Math Problems:Solving quadratic equation
For some questions, you have some conditions that you don’t know. So you can use a symbol such as “n” to set up several equations according to the questions. Then solve the equations that you set up in order to get the value for “n”.
Here is an example:
If you spend five dollars on shoes, two dollars on gloves and after that you still have four dollars left. How many dollars do you have originally?
Ans: Make the amount of money you have originally “n”, so:
n-5-2=4
n=4+5+2=11
Thus, you have 11 dollars originally!!
Solving math problem-quadratics equation, and quadratics formula derivation:
Example 2:
ax^2+bx+c=0
1x^2+4x+4=0=
(x+2)^2
0=x+2
x=-2
quadratics formula derivation:
ax^2+bx+c=0 divide both side by a
x^2+b/ax+c/a=0, then put c/a to the other side
x^2+b/ax=-c/a,
x^2+b/ax+(b/2a)^2=(b/2a)^2-c/a
(x+b/2a)^2=b^2/4a^2-c/a
x+b/2a=(+/- (b^2-4ac)/4a^2)^(-2)
x= (b+_(b^2-4ac))^(-2)/2a
For some questions, you have some conditions that you don’t know. So you can use a symbol such as “n” to set up several equations according to the questions. Then solve the equations that you set up in order to get the value for “n”.
Here is an example:
If you spend five dollars on shoes, two dollars on gloves and after that you still have four dollars left. How many dollars do you have originally?
Ans: Make the amount of money you have originally “n”, so:
n-5-2=4
n=4+5+2=11
Thus, you have 11 dollars originally!!
Solving math problem-quadratics equation, and quadratics formula derivation:
Example 2:
ax^2+bx+c=0
1x^2+4x+4=0=
(x+2)^2
0=x+2
x=-2
quadratics formula derivation:
ax^2+bx+c=0 divide both side by a
x^2+b/ax+c/a=0, then put c/a to the other side
x^2+b/ax=-c/a,
x^2+b/ax+(b/2a)^2=(b/2a)^2-c/a
(x+b/2a)^2=b^2/4a^2-c/a
x+b/2a=(+/- (b^2-4ac)/4a^2)^(-2)
x= (b+_(b^2-4ac))^(-2)/2a
Tuesday, July 15, 2008
Simple probability math problems
I would say probability is largely encountered in our daily life. Probability is very interesting. Let’s explore it together.
Start from the easy part. If you roll a die, what is the chance that you get a 5? Or an 1? Or a 2?
Ans: 1/6. You have six probabilities. 1, 2...6, and the chance of getting each number is the same. So the probability of getting each number is 1/6,
If you have a bag where there are 3 white balls and 3 red balls. If you pick out one ball, what is the chance of getting a red ball?
Ans: 3/6 (1/2). Same as the first example, you have six choices. However, you have 3 red balls that mean you have three cases in which you will get a red ball.
If you pick out two balls, what is the chance of getting a white and a red ball?
Ans: 3/6*3/5=9/30=3/10
3/10*2=3/5
Now you know for the first one you can get a red ball and the probability is 3/6. After that, there are only 5 balls in the bag. So the probability of getting a white ball is 3/5. Multiply them together. Remember there are two ways of getting a white and a red ball. You can get a red ball first, or a white ball first. So the answer is 3/5!
Your math problem:
What is the probability of getting two red balls?
Ans: 3/6*2/5=1/5 and...
Start from the easy part. If you roll a die, what is the chance that you get a 5? Or an 1? Or a 2?
Ans: 1/6. You have six probabilities. 1, 2...6, and the chance of getting each number is the same. So the probability of getting each number is 1/6,
If you have a bag where there are 3 white balls and 3 red balls. If you pick out one ball, what is the chance of getting a red ball?
Ans: 3/6 (1/2). Same as the first example, you have six choices. However, you have 3 red balls that mean you have three cases in which you will get a red ball.
If you pick out two balls, what is the chance of getting a white and a red ball?
Ans: 3/6*3/5=9/30=3/10
3/10*2=3/5
Now you know for the first one you can get a red ball and the probability is 3/6. After that, there are only 5 balls in the bag. So the probability of getting a white ball is 3/5. Multiply them together. Remember there are two ways of getting a white and a red ball. You can get a red ball first, or a white ball first. So the answer is 3/5!
Your math problem:
What is the probability of getting two red balls?
Ans: 3/6*2/5=1/5 and...
Monday, July 14, 2008
Math Problems on geometry
The best part I like about math is geometry. Math problems about geometry train your observation skills and allow you to have a different view of buildings and other stuff in life.
First I want to talk about the sum of angles in a polygon with respect to the number of sides or corners.
Triangle is the simplest polygon, and it has three sides, with a total degree of 180.
Square has four sides, with a total degree of 360.
Pentagon has five sides, with a total degree of 540.
:
Then we find if the number of sides is “n”, the size of the sum of the angle would be:
(n - 2)*180
Try out yourself if it is right?!
Have you noticed that the degree of the angle is always the same respect to a line which is connected of two points on the circle? This is very simple to prove. Can you do that?
Also, for a 3-d product, such as a cube, there are length, width, and height. How many sides does it have? How many faces? How many corners?
Think more about math problems in your life, and you will find far more interesting things than you would find in the math classes! Make math your friend!
First I want to talk about the sum of angles in a polygon with respect to the number of sides or corners.
Triangle is the simplest polygon, and it has three sides, with a total degree of 180.
Square has four sides, with a total degree of 360.
Pentagon has five sides, with a total degree of 540.
:
Then we find if the number of sides is “n”, the size of the sum of the angle would be:
(n - 2)*180
Try out yourself if it is right?!
Have you noticed that the degree of the angle is always the same respect to a line which is connected of two points on the circle? This is very simple to prove. Can you do that?
Also, for a 3-d product, such as a cube, there are length, width, and height. How many sides does it have? How many faces? How many corners?
Think more about math problems in your life, and you will find far more interesting things than you would find in the math classes! Make math your friend!
Sunday, July 13, 2008
Some interesting math problems
Today we will disscuss some interesting math problems together. First of all,
1) Do you know how many corners a triangle will have if you cut down one of its corner?
Ans: Actually, this is a multi-answer question. It really depends on how you will cut it. However, according to the literal meaning of the problem, the answer should be two. In fact, this is not a correct answer.
Some possible anwers are: 3 and 4
Picture 1 shows the reasons.
2) Have you ever thought about how many it is to add 1 to 100?
You may think it should be a really big number, and it may take you an hour to do it. However, the fact is not so.
Ans: 1+2+3+4+5+...+97+98+99+100=
if you are quick at finding out things, you may figure out that there is actually a pattern:
1+100=101
2+99=101
:
How many 101 are there in the sum?
50
so 50*101=5050
Thus, 5050 is the right answer!!
Have you gotten it?
Comments:
Math problems are not hard once you know the shortcuts. It is important for you to find out the patterns and regularities. So please don't jump into math problems directly and try to calculate it until you make a mistake, rather you should look at the question and think about it for a few minutes first.
Saturday, July 12, 2008
Math Problems: Where the cleverest gets smarter!
Math problems are very attractive. Although a lot of people are confused about mathmatics, once you understand the concept, you will figure out the ways to solve that type of math problems quickly. Math problems can train your brain. Starting from simple algebra to deeper calculus, math problems enhance your IQ gradually. Math is about numbers, and that is a kind of another language which is commonly used throughout the world. 0, 1, 2, 3...9 the primary ten numbers make up all the math problems we encouter today.
It is important that you are a hard worker. Everything takes time, the same for improving your math. You have to start from the very basic math problems and practise that type of questions over and over again until you are confident that you have completely understood and been able to use that knowledge. Another way to improve your math skills quickly is to challenge some harder math problems. Although it may takes a longer time for you to solve, the harder math problems will open your eyes and allow you to think in multi-ways. Plus the satisfied feelings you get after solving the math problems is hard to describe and forget.
Be confident and diligent, and you will be successful! Math problems make the cleverest gets smarter!
It is important that you are a hard worker. Everything takes time, the same for improving your math. You have to start from the very basic math problems and practise that type of questions over and over again until you are confident that you have completely understood and been able to use that knowledge. Another way to improve your math skills quickly is to challenge some harder math problems. Although it may takes a longer time for you to solve, the harder math problems will open your eyes and allow you to think in multi-ways. Plus the satisfied feelings you get after solving the math problems is hard to describe and forget.
Be confident and diligent, and you will be successful! Math problems make the cleverest gets smarter!
Friday, July 11, 2008
Math Problems Blog is Born!!
Hi everyone and welcome to my blog about math problems. I will be discussing many different types of problems here on this blog.
Subscribe to:
Posts (Atom)