Jeff took 8 hours to travel from Town A to Town B.
Nick took 12 hours to travel from Town B to Town A
Both Jeff and Nick started at 0930.
At what time would they pass each other on the way?
Actually, this is a relatively simple question... If you know how to do it, it is very easy.
The solution is below.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
METHOD 1:
Let the distance between Town A and Town B be 24km.
Speed of Jeff : Dist/Time = 24km/8h = 3km/h
Speed of Nick : Dist/Time = 24km/12h = 2km/h
Time taken to meet = Dist/Total speed
= 24/ 3+2
= 24/5
= 4.8h = 4h 48 min
0930 --4h 48 min ------ 1418--> ANSWER!
Simple???
METHOD 2 :
Jeff : 8h --> 1 journey
1h --> 1/8 journey
Nick : 12h --> 1 journey
1h --> 1/12 journey
1/8 + 1/12 = 3/24 + 2/24 = 5/24
5/24 journey = 1h
24/24 journey = 24/5 h = 4.8h = 4h 48min
Friday, April 3, 2009
Wednesday, April 1, 2009
Applying the concept of simple and compound interest on practical situations
You may ask, Why do I even need to learn simple/compound interest? All I have to do is not borrow and not lend money! Well, that thinking is very childish! GROW UP! In our life, I bet that we will borrow or lend money, and simple interest is for, well, simple amounts. For example, in primary school you may come across people saying"You lend me $1 I return you $2 tomorrow" This is a perfect and simple example of simple interest. You borrow money at a 100% interest.(Which is very stupid)
Now, compound interest. Its pretty much the same as simple interest, and you can think of compound interest as a series of back-to-back simple interest contracts. The interest earned in each period is added to the principal of the previous period to become the principal for the next period. For example, you borrow $10,000 for three years at 5% annual interest compounded annually:
p = principal (original amount borrowed or loaned)
i = interest rate for one period
n = number of periods
interest year 1 = p x i x n = 10,000 x .05 x 1 = 500(i1)
interest year 2 = (p2 = p1 + i1) x i x n = (10,000 + 500) x .05 x 1 = 525(i2)
interest year 3 = (p3 = p2 + i2) x i x n = (10,500 + 525) x.05 x 1 = 551.25
Total interest earned over the three years = 500 + 525 + 551.25 = 1,576.25. Compare this to 1,500 earned over the same number of years using simple interest. You will find that you earned A LOT of money as compared to charging simple interest.
So there you have it for those aspiring entrepreneurs, charge compound interest for any amount you lend, and you will be rolling in the green stuff if the lender is a procrastinator and takes ages to pay back. Ditto loan sharks
=)
Source: http://www.getobjects.com/Components/Finance/TVM/iy.html
Now, compound interest. Its pretty much the same as simple interest, and you can think of compound interest as a series of back-to-back simple interest contracts. The interest earned in each period is added to the principal of the previous period to become the principal for the next period. For example, you borrow $10,000 for three years at 5% annual interest compounded annually:
p = principal (original amount borrowed or loaned)
i = interest rate for one period
n = number of periods
interest year 1 = p x i x n = 10,000 x .05 x 1 = 500(i1)
interest year 2 = (p2 = p1 + i1) x i x n = (10,000 + 500) x .05 x 1 = 525(i2)
interest year 3 = (p3 = p2 + i2) x i x n = (10,500 + 525) x.05 x 1 = 551.25
Total interest earned over the three years = 500 + 525 + 551.25 = 1,576.25. Compare this to 1,500 earned over the same number of years using simple interest. You will find that you earned A LOT of money as compared to charging simple interest.
So there you have it for those aspiring entrepreneurs, charge compound interest for any amount you lend, and you will be rolling in the green stuff if the lender is a procrastinator and takes ages to pay back. Ditto loan sharks
=)
Source: http://www.getobjects.com/Components/Finance/TVM/iy.html
Non-routine Mathematics Questions
Here are some non-routine maths questions for you to have some fun with.
Q1. 3 men go on a business trip and pay $30 altogether at a hotel. The manager of the hotel discovers that he has overcharged them and refunds them $5. The 3 men decide to accept $1 each and give the $2 to a bellboy. So, each man has spent $9 so they have an expenditure of $27. Including the tip, that's $29. So where is the missing $1?( Remember, they paid $30)
Answer: Actually, there is no missing $1. The men do pay a total of $9.00 each (total of $27.00) for the room, but only after you add in the amount they tipped the bellboy($2). They paid $25 for the room and they gave the bellboy $2 as a tip. ($25 + 2 = $27.00). Including the $3 the men received as a refund, you will get the full $30( $27+$3=$30).
Q2. A road is 300km long. Car A is at the very start of the road and Car B is at the very end of the road. They start driving at exactly the same time towards each other. A bird is on the roof of Car A. As soon as both cars start moving, the bird travels at a speed of 150km/h towards Car B. When it reaches Car B, it turns around and returns to Car A, then Car B, so on and so forth, until both cars reach the mid-point of the road. How far has the bird flown if Car A and Car B travel at 60km/h and 90km/h respectively?
<-------------------------------------------300km------------------------------------------->
Car A>------------------------------------>ROAD<--------------------------------------Car B
Answer: This question is really quite simple. It can be solved in just 2 steps. However, you must know the formula for calculating Distance, Time and Speed first. For your info, it is Distance= Time * Speed. Thus, before we find out the distance the bird has flown(" How far has the bird flown") , we must find out its speed and time. We already know its speed( 150km/h). So, how do we know its time?
We know the road is 300km long and Car A and Car B travel at a total speed of 150km/h( 60km/h + 90km/h). Hence, we can work out easily that they will take 2 hours to meet. That is the time given to the bird to travel.
So, since Distance= Speed * Time, Distance flown= Bird's Speed* Bird's time to travel=150km/h * 2h= 300km.( Answer)
Q1. 3 men go on a business trip and pay $30 altogether at a hotel. The manager of the hotel discovers that he has overcharged them and refunds them $5. The 3 men decide to accept $1 each and give the $2 to a bellboy. So, each man has spent $9 so they have an expenditure of $27. Including the tip, that's $29. So where is the missing $1?( Remember, they paid $30)
Answer: Actually, there is no missing $1. The men do pay a total of $9.00 each (total of $27.00) for the room, but only after you add in the amount they tipped the bellboy($2). They paid $25 for the room and they gave the bellboy $2 as a tip. ($25 + 2 = $27.00). Including the $3 the men received as a refund, you will get the full $30( $27+$3=$30).
Q2. A road is 300km long. Car A is at the very start of the road and Car B is at the very end of the road. They start driving at exactly the same time towards each other. A bird is on the roof of Car A. As soon as both cars start moving, the bird travels at a speed of 150km/h towards Car B. When it reaches Car B, it turns around and returns to Car A, then Car B, so on and so forth, until both cars reach the mid-point of the road. How far has the bird flown if Car A and Car B travel at 60km/h and 90km/h respectively?
<-------------------------------------------300km------------------------------------------->
Car A>------------------------------------>ROAD<--------------------------------------
Answer: This question is really quite simple. It can be solved in just 2 steps. However, you must know the formula for calculating Distance, Time and Speed first. For your info, it is Distance= Time * Speed. Thus, before we find out the distance the bird has flown("
We know the road is 300km long and Car A and Car B travel at a total speed of 150km/h( 60km/h + 90km/h). Hence, we can work out easily that they will take 2 hours to meet. That is the time given to the bird to travel.
So, since Distance= Speed * Time, Distance flown= Bird's Speed* Bird's time to travel=150km/h * 2h= 300km.( Answer)
Sunday, March 29, 2009
Compound Interest
Compound Interest is the act of adding accumulated interest back to the principal sum, so that interest is earned on the earlier gained interest from that moment onwards. It is different from Simple Interest in the way that Simple Interest does not involve any compounding.
Which means to say, Compound Interest includes the interest paid on the initial investment AND on the interest accrued while Simple Interest does not include the additional interest.
Let me demonstrate; say, a house mortgage has a 1% interest and compounds once every month.
(In 1 month)
Compound Interest: Number of times of Compounding= 1, Principal=$100,000, Interest= 1%.
Simple Interest: Number of times of Compounding=0, Principal= $100,000, Interest=1%.
Thus, in 1 month, the amount owned is $100,000 X 101%= $101,000 for both Simple and Compound Interest.
In 2 months, the amount owned will be 101% X (principal plus interest)( $101,000), which will equal $102,010 for Compound Interest. However, for Simple Interest, the outstanding mortgage loan will instead be 102%( 100%+ 1% X Number of Months) X principal, which will equal $102,000. In a 6 months, the amount owned will be approximately $106,152.02 and $106,000 for Compound and Simple Interest respectively.
Thus, we can tell that Simple Interest is mostly used for short term loans, usually within the span of half a year. Compound Interest is used for long durations or periods, such as a year or more as it catches up with Simple Interest in 6 months. So, if we need a loan for 5 months or less, we know that we should take a Compound Interest loan and if we need a loan for 6 months or more, we know that we should take a Simple Interest loan instead.
On the other hand, if we are investing in bonds, Simple Interest is the way to go for up to 5 months and Compound Interest from then on.
Math Joke:
Q: What do you get if you divide the circumference of a jack-o-lantern by its diameter?
A: Pumpkin Pi!
Singapore (Channel News Asia). At Changi International Airport today, a Chinese male who claimed to be a math teacher was arrested by airport officials on duty while attempting to board a flight while in possession of a compass, a protractor and a calculator.
According to the officials, he is believed to have ties with several terrorist networks, including the infamous Al-Coolda network. He will be charged in court on Monday for carrying weapons of math instruction.
Which means to say, Compound Interest includes the interest paid on the initial investment AND on the interest accrued while Simple Interest does not include the additional interest.
Let me demonstrate; say, a house mortgage has a 1% interest and compounds once every month.
(In 1 month)
Compound Interest: Number of times of Compounding= 1, Principal=$100,000, Interest= 1%.
Simple Interest: Number of times of Compounding=0, Principal= $100,000, Interest=1%.
Thus, in 1 month, the amount owned is $100,000 X 101%= $101,000 for both Simple and Compound Interest.
In 2 months, the amount owned will be 101% X (principal plus interest)( $101,000), which will equal $102,010 for Compound Interest. However, for Simple Interest, the outstanding mortgage loan will instead be 102%( 100%+ 1% X Number of Months) X principal, which will equal $102,000. In a 6 months, the amount owned will be approximately $106,152.02 and $106,000 for Compound and Simple Interest respectively.
Thus, we can tell that Simple Interest is mostly used for short term loans, usually within the span of half a year. Compound Interest is used for long durations or periods, such as a year or more as it catches up with Simple Interest in 6 months. So, if we need a loan for 5 months or less, we know that we should take a Compound Interest loan and if we need a loan for 6 months or more, we know that we should take a Simple Interest loan instead.
On the other hand, if we are investing in bonds, Simple Interest is the way to go for up to 5 months and Compound Interest from then on.
Math Joke:
Q: What do you get if you divide the circumference of a jack-o-lantern by its diameter?
A: Pumpkin Pi!
Singapore (Channel News Asia). At Changi International Airport today, a Chinese male who claimed to be a math teacher was arrested by airport officials on duty while attempting to board a flight while in possession of a compass, a protractor and a calculator.
According to the officials, he is believed to have ties with several terrorist networks, including the infamous Al-Coolda network. He will be charged in court on Monday for carrying weapons of math instruction.
Saturday, March 21, 2009
Finding Perfect Numbers
Okay, I found this very interesting way to find perfect numbers.By the way, this question came from Ms Wun's enrichment worksheets(how many of you actually DO them?)
Finding Perfect Numbers
1) 1+2=3(3 is prime)
3x2=6=perfect number =)
2)1+2+4=7 (7 is prime)
4x7=28=perfect no. =)
3)1+2+4+8=15 (15 is not prime)
8x15=120≠perfect no. =(
4)1+2+4+8+16=31 (31 is prime)
16x31=496=perfect no. =)
.
.
.
.
.
.
and so on...
In "1)" we get 1+2 because 1x2=2. In "2)" we get 1+2+4 because 2x2=4.
And so on
In "1)" we get 3x2 because the two numbers are between the equal sign. Ditto others.
HOWEVER this method will not work for "3)" because 15 is not prime.
Ta-Da! =)
GET IT?
Finding Perfect Numbers
1) 1+2=3(3 is prime)
3x2=6=perfect number =)
2)1+2+4=7 (7 is prime)
4x7=28=perfect no. =)
3)1+2+4+8=15 (15 is not prime)
8x15=120≠perfect no. =(
4)1+2+4+8+16=31 (31 is prime)
16x31=496=perfect no. =)
.
.
.
.
.
.
and so on...
In "1)" we get 1+2 because 1x2=2. In "2)" we get 1+2+4 because 2x2=4.
And so on
In "1)" we get 3x2 because the two numbers are between the equal sign. Ditto others.
HOWEVER this method will not work for "3)" because 15 is not prime.
Ta-Da! =)
GET IT?
Monday, March 16, 2009
Speed, Uniform Speed and Average Speed
Speed, uniform speed and average speed. Three topics which might confuse people. Actually, they are quite simple and are easy to understand. I will now explain them in simple terms.
What is speed? To put it in a typical Singaporean's terms, "speed is how fast something travels lor." However the real meaning according to Wikipedia is "the rate of motion, or equivalently the rate of change of distance"
Uniform speed is actually just constant speed if you are confused by the word. Just remember that your school uniform never changes so it is always the same. An example of uniform speed would be if a motorcycle was travelling at the same speed (50km/h) for 1 hour, the distance that he covered would be the speed he was travelling (50km). Of course this distance the motorcycle travelled starts only when it has reached 50km/h as it needs to accelerate.
The average speed of an object tells you the average rate at which it covers a certain distance. For example, if a bus is travelling at an average speed of 50km/h for two hours, it would have travelled 100km in that two hours.
To sum this up, speed is simply distance divided by time, distance is speed times time and time taken is distance divided by speed. Speed= Distance/Time, Distance=Speed X Time, Time= Distance/Speed.
Maths Joke:
Q: Why was 6 afraid of 7?
A: Because 7 8 9!
Explanation if you have no imagination: seven ate (Eight and ate? Geddit?) 9
sources:http://en.wikipedia.org/wiki/Speed,http://www.batesville.k12.in.us/Physics/PhyNet/Mechanics/Kinematics/AveSpeed.html
What is speed? To put it in a typical Singaporean's terms, "speed is how fast something travels lor." However the real meaning according to Wikipedia is "the rate of motion, or equivalently the rate of change of distance"
Uniform speed is actually just constant speed if you are confused by the word. Just remember that your school uniform never changes so it is always the same. An example of uniform speed would be if a motorcycle was travelling at the same speed (50km/h) for 1 hour, the distance that he covered would be the speed he was travelling (50km). Of course this distance the motorcycle travelled starts only when it has reached 50km/h as it needs to accelerate.
The average speed of an object tells you the average rate at which it covers a certain distance. For example, if a bus is travelling at an average speed of 50km/h for two hours, it would have travelled 100km in that two hours.
To sum this up, speed is simply distance divided by time, distance is speed times time and time taken is distance divided by speed. Speed= Distance/Time, Distance=Speed X Time, Time= Distance/Speed.
Maths Joke:
Q: Why was 6 afraid of 7?
A: Because 7 8 9!
Explanation if you have no imagination: seven ate (Eight and ate? Geddit?) 9
sources:http://en.wikipedia.org/wiki/Speed,http://www.batesville.k12.in.us/Physics/PhyNet/Mechanics/Kinematics/AveSpeed.html
Knowing the concept of simple interest and its formula
Knowing the concept of simple interest and its formula
Well, simple interest is indeed simple !
When money is borrowed, interest is charged for the use of that borrowed money for a certain period of time. When the money is paid back, the person would then have to pay the original amount of money he had borrowed together with the interest.
You may wonder -- Then what is interest?
Interest -- The amount of interest mainly depends on 3 main factors.
1) The amount of money borrowed
2) The length of time that the money is borrowed for
3) The interest rate
Therefore, the formula for finding simple interest is :
Interest = Principal* Rate * Time
Example : If $50 was borrowed for 2 years at a 10% interest rate, the interest would be
$50x10/ 50x2 = $10
OR
$50x 10% x2 = $5x2 = $10
Therefore, as a conclusion, simple interest is generally charged for borrowing money for short periods of time only. It is used for uncompounded stocks, shares and bonds as it is the amount of interest paid only on the original principal, not on the interest accrued or accumulated.
Maths Joke:
A group of mathematicians and a group of engineers are traveling together by train to attend a conference on mathematical methods in engineering. Each mathematician has a ticket whereas only one of the engineers has one. The mathematicians laugh at the unworldly engineers and look forward to the moment the conductor shows up.
Suddenly, one of the engineers shouts: "Conductor coming!"
All the engineers disappear into one washroom.
The conductor checks the ticket of each mathematician and then knocks at the washroom door: "Your ticket, please."
The engineers stick the one ticket they have under the door, the conductor checks it and leaves. A few minutes later, when it is safe, the engineers come out of the washroom. The mathematicians are impressed.
When the conference has come to an end, the mathematicians decide that they are at least as smart as the engineers and also buy just one ticket for the whole group. This time the engineers do not buy a ticket at all.
Again, one of the engineers shouts: "Conductor coming!".
All the mathematicians rush off to one washroom. One of the engineers goes to that washroom, knocks at the door, and says: "Your ticket, please..."
sources: http://www.aaamath.com/g84-simple-interest.html
Well, simple interest is indeed simple !
When money is borrowed, interest is charged for the use of that borrowed money for a certain period of time. When the money is paid back, the person would then have to pay the original amount of money he had borrowed together with the interest.
You may wonder -- Then what is interest?
Interest -- The amount of interest mainly depends on 3 main factors.
1) The amount of money borrowed
2) The length of time that the money is borrowed for
3) The interest rate
Therefore, the formula for finding simple interest is :
Interest = Principal* Rate * Time
Example : If $50 was borrowed for 2 years at a 10% interest rate, the interest would be
$50x10/ 50x2 = $10
OR
$50x 10% x2 = $5x2 = $10
Therefore, as a conclusion, simple interest is generally charged for borrowing money for short periods of time only. It is used for uncompounded stocks, shares and bonds as it is the amount of interest paid only on the original principal, not on the interest accrued or accumulated.
Maths Joke:
A group of mathematicians and a group of engineers are traveling together by train to attend a conference on mathematical methods in engineering. Each mathematician has a ticket whereas only one of the engineers has one. The mathematicians laugh at the unworldly engineers and look forward to the moment the conductor shows up.
Suddenly, one of the engineers shouts: "Conductor coming!"
All the engineers disappear into one washroom.
The conductor checks the ticket of each mathematician and then knocks at the washroom door: "Your ticket, please."
The engineers stick the one ticket they have under the door, the conductor checks it and leaves. A few minutes later, when it is safe, the engineers come out of the washroom. The mathematicians are impressed.
When the conference has come to an end, the mathematicians decide that they are at least as smart as the engineers and also buy just one ticket for the whole group. This time the engineers do not buy a ticket at all.
Again, one of the engineers shouts: "Conductor coming!".
All the mathematicians rush off to one washroom. One of the engineers goes to that washroom, knocks at the door, and says: "Your ticket, please..."
sources: http://www.aaamath.com/g84-simple-interest.html
Knowing how to convert units
You may be wondering, why should I learn how to convert units? Isn't it a waste of time since there aren't any road signs in Singapore stating "50 miles/hour"? However, what if you go on an overseas attachment or holidaying to countries like America? There, they only use miles; there is no such thing as kilometres or metres.
Furthermore, there is a huge difference between 1 cm and 1 m and its not the extra letter "c". What if your teacher asks you to bring a 15cm ruler and you bring a 15m one? Or, if your mother asks you to buy 1 kilogram of vegetables and you buy 1 gram?
So, are you eager, bursting with anticipation about learning how to convert units?
Read this to find out!
First of all, we must know some basic facts and unit convertions.
Weight
1)1 gram= 0.001 kilogram
2) 1 centimetre= 0.01metre
3) 1metre= 0.001 kilometres
4) 1 mile = 1609.344 meters
5) 1 knot = 1.852km/h( For boats, ships, other vehicles that travel on large bodies of water.)
3) 24 hours= 1 day
4) 7 days = 1 week
Weight is pretty straightforward. For example, if something weighs 1045grams, to get its weight in kilograms, we simply take 1045grams X 1/1000(0.001), which will give us 1.045 kilograms. Similarly, to convert any object's weight from kilograms to grams, we multiply it by 1000. For example, if a metal block weighs 0.567 kilograms, we take 0.567 X 1000, which would give us an answer of 567 grams.
Now you try: 1) 3469 grams= ? (Scroll to the last line for the answer.)
2) 0.892 kilograms=?
Time and length/distance are also quite easy, since we use it all the time and should be familiar with it. For example, if you need to calculate how long 5 minutes is in an hour, take 5 X 1/60 since 1 minute is one-sixtieth of 1 hour. Do the same for the rest; eg. convert 5 minutes into 300s as 1 min= 60s= 5 min= 5 X 60s= 300s. As for length/distance, still do the same thing. Such as 5 mm= 0.005 metre as 1 mm= 0.1cm=0.01mX 1/10(0.1)= 1mm= 0.001 metre. Thus, 5 X 1mm= 0.001 m X 5= 0.005m.
Speed is the trickest of all so read carefully.
First -- How do we convert km/h to m/s ?
When we are converting km/h to m/s, we are converting from a higher quantity to a lower one, thus we must multiply.
For example : 85km/h= ____ m/s?
To get this answer, we would first do (85x1000)m / (1hrx60min x60seconds)s = 23.61 m/s
Second, lets go on to convert mph to meters/sec
Lets do an example... What us 55 mph in terms of meters/sec then?
As we know, 55 mph is 55 miles/hour. To convert this to meters/sec, we need to convert the miles on top to meters and the hour on the bottom to seconds.
As we already know what 1 mile= 1609.344 meters and 1 hour =3600 seconds, this isn't at all difficult !
Answer : 55miles 1609.344 meters 1 hour 24.5872 meters
------- ( --------------- ) ( ------------ ) = ----------------
hour 1 mile 3600 seconds second
Just follow this simple and easy step and the answer is OUT!!!
Third, we shall go on to yet another fun practice!
Convert meter/sec to miles/hour
Example - Convert 10 meter/sec to miles/hour
DO NOT FRET -- After so many practices, this should not be a problem at all !
Answer : 10 meters 1 mile 3600 seconds 22.369 miles
--------- ( ---------------- ) ( -------------- ) = ------------
second 1609.344 meters 1 hour hour
Keep practicing and one day you will get it all RIGHT!!!
Maths Jokes:
George W. Bush visits Algeria. As part of his program, he delivers a speech to the Algerian people: "You know, I regret that I have to give this speech in English. I would very much prefer to talk to you in your native tongue. But unfortunately, I was never good at algebra..."
Answers:
1) 3469 grams= (3469 X 0.001) kilograms= 3.469 kilograms
2) 0.892 kilograms=( 0.892 X 1000) grams= 8920 grams
sources: http://physics.webplasma.com/physics03.html
Furthermore, there is a huge difference between 1 cm and 1 m and its not the extra letter "c". What if your teacher asks you to bring a 15cm ruler and you bring a 15m one? Or, if your mother asks you to buy 1 kilogram of vegetables and you buy 1 gram?
So, are you eager, bursting with anticipation about learning how to convert units?
Read this to find out!
First of all, we must know some basic facts and unit convertions.
Weight
Length/Distance
1) 1minimetre= 0.1centimetre2) 1 centimetre= 0.01metre
3) 1metre= 0.001 kilometres
4) 1 mile = 1609.344 meters
5) 1 knot = 1.852km/h( For boats, ships, other vehicles that travel on large bodies of water.)
Time
2) 1 minute = 1/60 hour1) 1 second= 1/60 minute
3) 24 hours= 1 day
4) 7 days = 1 week
Speed
1) 1 metre/s = 3.6km/h
2) 150 kilometres/ hour= 150 000metres/ 3600s
2) 150 kilometres/ hour= 150 000metres/ 3600s
Weight is pretty straightforward. For example, if something weighs 1045grams, to get its weight in kilograms, we simply take 1045grams X 1/1000(0.001), which will give us 1.045 kilograms. Similarly, to convert any object's weight from kilograms to grams, we multiply it by 1000. For example, if a metal block weighs 0.567 kilograms, we take 0.567 X 1000, which would give us an answer of 567 grams.
Now you try: 1) 3469 grams= ? (Scroll to the last line for the answer.)
2) 0.892 kilograms=?
Time and length/distance are also quite easy, since we use it all the time and should be familiar with it. For example, if you need to calculate how long 5 minutes is in an hour, take 5 X 1/60 since 1 minute is one-sixtieth of 1 hour. Do the same for the rest; eg. convert 5 minutes into 300s as 1 min= 60s= 5 min= 5 X 60s= 300s. As for length/distance, still do the same thing. Such as 5 mm= 0.005 metre as 1 mm= 0.1cm=0.01mX 1/10(0.1)= 1mm= 0.001 metre. Thus, 5 X 1mm= 0.001 m X 5= 0.005m.
Speed is the trickest of all so read carefully.
First -- How do we convert km/h to m/s ?
When we are converting km/h to m/s, we are converting from a higher quantity to a lower one, thus we must multiply.
For example : 85km/h= ____ m/s?
To get this answer, we would first do (85x1000)m / (1hrx60min x60seconds)s = 23.61 m/s
Second, lets go on to convert mph to meters/sec
Lets do an example... What us 55 mph in terms of meters/sec then?
As we know, 55 mph is 55 miles/hour. To convert this to meters/sec, we need to convert the miles on top to meters and the hour on the bottom to seconds.
As we already know what 1 mile= 1609.344 meters and 1 hour =3600 seconds, this isn't at all difficult !
Answer : 55miles 1609.344 meters 1 hour 24.5872 meters
------- ( --------------- ) ( ------------ ) = ----------------
hour 1 mile 3600 seconds second
Just follow this simple and easy step and the answer is OUT!!!
Third, we shall go on to yet another fun practice!
Convert meter/sec to miles/hour
Example - Convert 10 meter/sec to miles/hour
DO NOT FRET -- After so many practices, this should not be a problem at all !
Answer : 10 meters 1 mile 3600 seconds 22.369 miles
--------- ( ---------------- ) ( -------------- ) = ------------
second 1609.344 meters 1 hour hour
Keep practicing and one day you will get it all RIGHT!!!
Maths Jokes:
George W. Bush visits Algeria. As part of his program, he delivers a speech to the Algerian people: "You know, I regret that I have to give this speech in English. I would very much prefer to talk to you in your native tongue. But unfortunately, I was never good at algebra..."
Answers:
1) 3469 grams= (3469 X 0.001) kilograms= 3.469 kilograms
2) 0.892 kilograms=( 0.892 X 1000) grams= 8920 grams
sources: http://physics.webplasma.com/physics03.html
Percentage
(Click here to read the glossary first)
Now, since we all have a deeper insight into Percentage,allow me to explain it in greater detail.
To change a fraction to a percentage, simply multiply the denominator and numerator by 100 divided by the denominator, such that it becomes 100. Then, just take the numerator and add a percentage sign behind it for good measure.
For example, take a typical fraction, like 3/4. 100 divided by 4 is 25, thus, we must multiply 3 and 4 by 25, which would give us 75/100. Take the numerator and throw a percentage sign and bingo! 75%.
For the reverse, simply swap the percentage sign for a /100 and simply the fraction.
One example is: 80%. We switch the percentage sign for a /100--->80/100. Finally, we simplify it--->80/100=4/5.
Otherwise, if you wish to change a percentage to a decimal, just take away the percentage sign and place the decimal point two places forward.
Like such, 63%, we take away the "%" sign, get 63, move the decimal point 2 places forward, and achieve our answer---> 0.63.
Again, if you wish to do the opposite, just move the decimal point 2 places backwards and give it a percentage sign in return.
As such: 0.57, move the "." two places back, get 57, present it with a "%", and get your answer--->57%.
Percentage is usually used to express the quantity of something compared to another. For example, a typical percentage question would be: "Jim has 15 apples. Tom has 20 apples. What is the percentage of Jim's apples over Tim's apples?How about Tim's over Jim's?
A)We convert 15/20 to a percentage, as we have learned earlier, and get 75%, which is our answer.
B)Again, we convert 20/15 to a percentage, and get 120%, which is our answer.
However, if the question is phrased like this: "Jim has 20 apples.Tom has 25 apples. How much more percent is Tim's apples than John's apples?
(Notice I have bold-ed and italic-ed "than". )
In any percentage question, this is probably the most crucial word to look out for, something that could change the entire meaning of the question. WHY? Very simple.
In any percentage question, the person who's name is after "than", is the 100% guy, which means that he/she is the one whose quantity or number of something should be converted to 100%, that is, be the denominator. I cannot stress too much how important this is.
For example, in the question above, John is the 100% guy. Thus, we must convert 25 /20 to 125/100= 125%/100% Lastly, we deduct 100% from 125% to get 25%, which is our answer.
Here is the same question phrased differently again:
"Jim has 20 apples.Tom has 25 apples. How much less is the percentage pf John's apples than Tim's?"
Here, Tim is the 100% guy. Thus, we must convert 20/25 to 80/100=80%/100%. Finally, we take away 80% from 100% and get 20%, which is our answer. If we didn't know about the "than", we might have gotten 25%, like our previous answer.
This is a very common mistake that is very costly.
Now, since we all have a deeper insight into Percentage,allow me to explain it in greater detail.
To change a fraction to a percentage, simply multiply the denominator and numerator by 100 divided by the denominator, such that it becomes 100. Then, just take the numerator and add a percentage sign behind it for good measure.
For example, take a typical fraction, like 3/4. 100 divided by 4 is 25, thus, we must multiply 3 and 4 by 25, which would give us 75/100. Take the numerator and throw a percentage sign and bingo! 75%.
For the reverse, simply swap the percentage sign for a /100 and simply the fraction.
One example is: 80%. We switch the percentage sign for a /100--->80/100. Finally, we simplify it--->80/100=4/5.
Otherwise, if you wish to change a percentage to a decimal, just take away the percentage sign and place the decimal point two places forward.
Like such, 63%, we take away the "%" sign, get 63, move the decimal point 2 places forward, and achieve our answer---> 0.63.
Again, if you wish to do the opposite, just move the decimal point 2 places backwards and give it a percentage sign in return.
As such: 0.57, move the "." two places back, get 57, present it with a "%", and get your answer--->57%.
Percentage is usually used to express the quantity of something compared to another. For example, a typical percentage question would be: "Jim has 15 apples. Tom has 20 apples. What is the percentage of Jim's apples over Tim's apples?How about Tim's over Jim's?
A)We convert 15/20 to a percentage, as we have learned earlier, and get 75%, which is our answer.
B)Again, we convert 20/15 to a percentage, and get 120%, which is our answer.
However, if the question is phrased like this: "Jim has 20 apples.Tom has 25 apples. How much more percent is Tim's apples than John's apples?
(Notice I have bold-ed and italic-ed "than". )
In any percentage question, this is probably the most crucial word to look out for, something that could change the entire meaning of the question. WHY? Very simple.
In any percentage question, the person who's name is after "than", is the 100% guy, which means that he/she is the one whose quantity or number of something should be converted to 100%, that is, be the denominator. I cannot stress too much how important this is.
For example, in the question above, John is the 100% guy. Thus, we must convert 25 /20 to 125/100= 125%/100% Lastly, we deduct 100% from 125% to get 25%, which is our answer.
Here is the same question phrased differently again:
"Jim has 20 apples.Tom has 25 apples. How much less is the percentage pf John's apples than Tim's?"
Here, Tim is the 100% guy. Thus, we must convert 20/25 to 80/100=80%/100%. Finally, we take away 80% from 100% and get 20%, which is our answer. If we didn't know about the "than", we might have gotten 25%, like our previous answer.
This is a very common mistake that is very costly.
Uses of Percentage
Percentage is often used by merchants, businessman, shop owners and companies that involve services and products to find out the amount of tax or duty they must pay. In Singapore, there is the Goods and Services Tax, also known as the GST. This is the tax that must be paid to the government. It comprises of 7.5% of the product or service.
For example, if a television set costs $800, its GST would be 7.5%X$800, which is $(7.5X8), equals $60. Thus, $60 must be paid to the government. This is essential knowledge as many shops and companies pass on the GST to their consumers, thus, whenver we buy something, its price is actually 107.5% of the original cost. However, there are duty-free shops which absorb this GST and thus you will only pay for only the original cost of the product or service.
Additionally, percentage is utilized to show the discount on a certain product or service. For example, in shopping malls, we often spot large signs saying "All shirts 50% off!" or "Up to 70% discount on jeans!" This signs signifies that the products the shops sell are half its original price and 30% its original price respectively. The price of the shirts is the percentage infront of the word "discount" is subtracted from 100%, then mulitplied by the original cost of the shirt.
Like so: A shirt costs $50. The shop advertises that "All shirts 50% off!".
Thus, Price of Shirt= (100%-50%)X$50= 50%X$50= $25.
Percentage is also used in the stock market and Forex( Foreign Exchange) to determine profit and loss, or increase and decrease. To determine profit or increase in value, take the percentage of the later value minus 100%, then mulitply it by the amount invested. For example, I buy a share in Microsoft for 1 million dollars. Fortunately, Microsoft's shares' value all increase by 12%. Thus, the new value of my share is 112% of my original 1 million.
Hence, my profit is 112% of $1,000,000-100% of $1,000,000=12% of $1,000,000= $120,000.
So, I have earned $120,000. :)
To determine loss or decrease in value, take the 100% minus the later percentage, then mulitply it by the amount invested. Another example is as such: I invest $50,000 of my profit, $120,000, in American Insurance Group(AIG). However, this time my luck runs out; AIG files for bankruptcy days after I complete my investment. Luckily, I had a tip-off that it would flop, thus I quickly sold my share before it collapsed. At that point of time, it was 70% of its original value.
Thus, my loss/decrease in value is 100% of $50,000-70% of $50,000= 30% of $50,000= $7500
Hence, I have lost $7500. :(
To determine loss or decrease in value, take the 100% minus the later percentage, then mulitply it by the amount invested.
Maths Joke:
Q^A Joke:
Q: Why do you rarely find mathematicians spending time at the beach?
A: Because they have sine and cosine to get a tan and don't need the sun!
For example, if a television set costs $800, its GST would be 7.5%X$800, which is $(7.5X8), equals $60. Thus, $60 must be paid to the government. This is essential knowledge as many shops and companies pass on the GST to their consumers, thus, whenver we buy something, its price is actually 107.5% of the original cost. However, there are duty-free shops which absorb this GST and thus you will only pay for only the original cost of the product or service.
Additionally, percentage is utilized to show the discount on a certain product or service. For example, in shopping malls, we often spot large signs saying "All shirts 50% off!" or "Up to 70% discount on jeans!" This signs signifies that the products the shops sell are half its original price and 30% its original price respectively. The price of the shirts is the percentage infront of the word "discount" is subtracted from 100%, then mulitplied by the original cost of the shirt.
Like so: A shirt costs $50. The shop advertises that "All shirts 50% off!".
Thus, Price of Shirt= (100%-50%)X$50= 50%X$50= $25.
Percentage is also used in the stock market and Forex( Foreign Exchange) to determine profit and loss, or increase and decrease. To determine profit or increase in value, take the percentage of the later value minus 100%, then mulitply it by the amount invested. For example, I buy a share in Microsoft for 1 million dollars. Fortunately, Microsoft's shares' value all increase by 12%. Thus, the new value of my share is 112% of my original 1 million.
Hence, my profit is 112% of $1,000,000-100% of $1,000,000=12% of $1,000,000= $120,000.
So, I have earned $120,000. :)
To determine loss or decrease in value, take the 100% minus the later percentage, then mulitply it by the amount invested. Another example is as such: I invest $50,000 of my profit, $120,000, in American Insurance Group(AIG). However, this time my luck runs out; AIG files for bankruptcy days after I complete my investment. Luckily, I had a tip-off that it would flop, thus I quickly sold my share before it collapsed. At that point of time, it was 70% of its original value.
Thus, my loss/decrease in value is 100% of $50,000-70% of $50,000= 30% of $50,000= $7500
Hence, I have lost $7500. :(
To determine loss or decrease in value, take the 100% minus the later percentage, then mulitply it by the amount invested.
Maths Joke:
Q^A Joke:
Q: Why do you rarely find mathematicians spending time at the beach?
A: Because they have sine and cosine to get a tan and don't need the sun!
Sunday, March 15, 2009
Ratio,Rate, Direct and Inverse Proportion
(Click here to read the glossary first)
Now that we have a through understanding of the 4 terms: Ratio,Rate, Direct and Inverse Proportion, I shall further elaborate on them.
Ratio and proportion are commonly used by us.We use it to solve mathematics problem sums. We use it to calculate whether the 230 grams of potato chips in NTUC Fairprice costing $2.30 is worth more than the 300 grams one in Cold Storage costing $2.70. In this case, the one in Cold Storage would be cheaper. This is illustrated in the explanation below:
NTUC Fairprice: 230g: $2.30 (Direct Proportion and Ratio)
Thus, 10g : $0.10
Hence, we know that for NTUC Fairprice, 10grams of chips cost $0.10.
Cold Storage: 300g: $2.70
Hence, 10g : S0.09
Thus, we know that for Cold Storage, 10grams of chips cost $0.09.
Finally, after calculating, we deduce that Cold Storage's potato chips are cheaper and buy theirs.
Furthermore, they are also utilized in industries like the automobile, traveling, medicine, shopping, stock trading and everyday activities, such as driving, babysitting, etc.
For example, when we are contemplating on buying either Car A or Car B, which are identical in all aspects except that they consume 100 litres of petrol per 100 kilometres traveled and 999 litres of petrol per 1000 kilometres traveled respectively.
By using ratio, rate and proportion in the diagram below:
Car A: 100l: 100km
Thus, 1l : 1km
Hence, we know Car A consumes 1 litre of petrol per kilometre or 1l/km
Car B: 999l: 1000km
Hence, 1l : 1 and 1/999km or approxiametely 1.001001001001001........
Thus, we know that Car B consumes 1 litre of petrol per 1.001001001001001...km or 1l/1.001001001001001...km.
Lastly, we find out that Car B travels 0.001001001001001...km per litre more than Car A and purchase it.
Another example of how Inverse proportion is used in our daily lives is when traveling from one place to another, be it to the supermarket, hotel, restaurant or bank. If we decide to arrive at our destination at a certain time, we will have to use Inverse proportion to find out how fast we should travel.
For example, Jim is going to the airport. His flight is at 7 p.m. He plans to set off for his journey at 4 p.m. at 40km/hr and the distance between the airport and his home is 120km. He falls asleep and wakes up at 6 p.m. Hurriedly, he rushes to the airport. However, he is unsure of whether to take a bus or a taxi which travel at 60km/hr and 120km/hr respectively.Help Jim find out which is the correct choice so he does not miss his flight.
At first:
We know that Jim has 3 hours to get to the airport---->4 p.m.---7 p.m.--->3 hours
We know that the distance he needs to travel in the 3 hours---->120km
Average speed per hour---> 120km/3hr---->40km/hr
Afterward:
We know that Jim has 1 hour to get to the airport---->6 p.m.---7 p.m.--->1 hour
Since 1 is 1/3 of 3, the time has been multiplied by a third, we must multiply the average speed by 3, which is the reciprocal of 1/3.
Average speed multiplied by 3---> 40km/hr X 3= 120km/hr.
Thus, Jim must take the taxi as he needs to travel 120km in 1 hour.
Common Misconceptions:
Often, people confuse Direct and Inverse proportion. Just remember that with direct proportion, both quantitative terms are changed by the same factor while with inverse proportion, they are changed by different factors.
Math Joke:
An infinite crowd of mathematicians enters a bar.
The first one orders a pint, the second one a half pint, the third one a quarter pint...
"I understand", says the bartender - and pours two pints.
(get it? Because n+ n/2+ n/4+ n/6+....where n stands for any positive number will never reach 2n.)
Thanks for reading my post!
Now that we have a through understanding of the 4 terms: Ratio,Rate, Direct and Inverse Proportion, I shall further elaborate on them.
Ratio and proportion are commonly used by us.We use it to solve mathematics problem sums. We use it to calculate whether the 230 grams of potato chips in NTUC Fairprice costing $2.30 is worth more than the 300 grams one in Cold Storage costing $2.70. In this case, the one in Cold Storage would be cheaper. This is illustrated in the explanation below:
NTUC Fairprice: 230g: $2.30 (Direct Proportion and Ratio)
Thus, 10g : $0.10
Hence, we know that for NTUC Fairprice, 10grams of chips cost $0.10.
Cold Storage: 300g: $2.70
Hence, 10g : S0.09
Thus, we know that for Cold Storage, 10grams of chips cost $0.09.
Finally, after calculating, we deduce that Cold Storage's potato chips are cheaper and buy theirs.
Furthermore, they are also utilized in industries like the automobile, traveling, medicine, shopping, stock trading and everyday activities, such as driving, babysitting, etc.
For example, when we are contemplating on buying either Car A or Car B, which are identical in all aspects except that they consume 100 litres of petrol per 100 kilometres traveled and 999 litres of petrol per 1000 kilometres traveled respectively.
By using ratio, rate and proportion in the diagram below:
Car A: 100l: 100km
Thus, 1l : 1km
Hence, we know Car A consumes 1 litre of petrol per kilometre or 1l/km
Car B: 999l: 1000km
Hence, 1l : 1 and 1/999km or approxiametely 1.001001001001001........
Thus, we know that Car B consumes 1 litre of petrol per 1.001001001001001...km or 1l/1.001001001001001...km.
Lastly, we find out that Car B travels 0.001001001001001...km per litre more than Car A and purchase it.
Another example of how Inverse proportion is used in our daily lives is when traveling from one place to another, be it to the supermarket, hotel, restaurant or bank. If we decide to arrive at our destination at a certain time, we will have to use Inverse proportion to find out how fast we should travel.
For example, Jim is going to the airport. His flight is at 7 p.m. He plans to set off for his journey at 4 p.m. at 40km/hr and the distance between the airport and his home is 120km. He falls asleep and wakes up at 6 p.m. Hurriedly, he rushes to the airport. However, he is unsure of whether to take a bus or a taxi which travel at 60km/hr and 120km/hr respectively.Help Jim find out which is the correct choice so he does not miss his flight.
At first:
We know that Jim has 3 hours to get to the airport---->4 p.m.---7 p.m.--->3 hours
We know that the distance he needs to travel in the 3 hours---->120km
Average speed per hour---> 120km/3hr---->40km/hr
Afterward:
We know that Jim has 1 hour to get to the airport---->6 p.m.---7 p.m.--->1 hour
Since 1 is 1/3 of 3, the time has been multiplied by a third, we must multiply the average speed by 3, which is the reciprocal of 1/3.
Average speed multiplied by 3---> 40km/hr X 3= 120km/hr.
Thus, Jim must take the taxi as he needs to travel 120km in 1 hour.
Common Misconceptions:
Often, people confuse Direct and Inverse proportion. Just remember that with direct proportion, both quantitative terms are changed by the same factor while with inverse proportion, they are changed by different factors.
Math Joke:
An infinite crowd of mathematicians enters a bar.
The first one orders a pint, the second one a half pint, the third one a quarter pint...
"I understand", says the bartender - and pours two pints.
(get it? Because n+ n/2+ n/4+ n/6+....where n stands for any positive number will never reach 2n.)
Thanks for reading my post!
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