Chapter 1 : Proportion
Discuss and give examples to show how you can tell if two quantites are in direct proportion or inverse proportion.
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54 comments:
Yes, you are at the right place. Do your assignment here!
how to write the journal
write where i mean?
Ms Chum i am sorry that i post here as i am in a hurry
For direct proportion,the definition is when two quantities are related to each other ,their changes may follow a certain pattern.For instance,if a plate of chicken rice costs $2 a plate,so if the number of plates increase the price will also increase so we can infer that the two quantities are in direct proportion.The formula is hereby y/x=k where by k is a constant
For inverse proportion, the definition is where an increase in one quantity results in a corresponding decrease in another related quantity.for instance,the number of men affects the time taken to build a building So if one men take 30days to build a building,5men will take 6days to build a building.
Here we can see that the time taken is decreased by number on men increasing.So we can infer that the two quantities are in inverse proportion,whereby the formula is y=kx
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Direct Proportion
It means that when 2 different quantities, take for example, a and b, varies in the way when b is divided by a always remains a same constant, k. Simply, it is like when one of the constant increase, the other constant will also increase.
For example, a car travels for 50km and the time taken to travel 50km is 2hrs. If the distance increase, the time taken to travel will also increase at the same pattern.
FORMULA: b = ka
Inverse Proportion
It means that when 2 different quantities, take for example, a and r, varies in the way when t is times by b and remains a same constant, k. Simply, it is like when one of the constant increase, the other constant will decrease.
For example, when the rate of water flow affects time taken to collect water. The faster the rate of water flows, water will b collected at a quicker timing.
FORMULA: rt = k
Done by: Chen Liyun (02)
For Inverse proportions,The graph if planned will be called a hyperbola which is a curve on the graph.An inverse proportion happens when 1 quantity's increase causes a corresponding decrease in another related quanity.For example,the time taken for a car to travel to its destination depends on the speed of the car. The equation for inverse proporions is xy=k.In this example,we will let time be x.We have said that the time taken depends on the speed hence we need to ake the time multiply by the speed of the car in which it is travelling.So, xy=k.If the speed is 60km/hr ,time taken is 30minutes and we need to find out the constant which is k,we must take 30(60/60)=k.Hence,k is 30.If the time is unknown and the speed is 90km/hr,we would need to do this. x(90/60)=30.to find out the time, we must take 30 / 1.5 to find out the time.
For direct proportions,The graph if planned will be a straight line due to the directly proportional quantities.A direct proportion is used when the 1st quantity is directly proportional to the 2nd quantity.For example ,if the cost of a plate of chicken rice is $2,the number of plates i can buy s directly proportional to the amount of money i have .For direct proportions,the equation for it is y=kx. For the example above, let the paltes of chicken rice i can buy be y.We have said that the plates of chicken rice i can buy is directly proportional to the amount of money i have so let x be the amount of money i have hence, y=kx.
If i hv $10 and the plates of rice i can buy is 5,we have to divide them to find k,which is the constant.Therefore, 5=k10. 10/5=2 so k =2. If i have $50 and the plates of chicken rice i can buy is unknown,we can apply the method hence we take $50 / 2=25 so i can uy 25 plates of chicken rice.
Direct proportion
In direct proportion,a change in 1 quantity corresponds to a change in another quantity and the 2 quantities are always in the same ratio.If y is directly proportional to x,then y=kx where k is a constant where k is not equal to 0 .The graph of y=kx is a straight line passing through the origin.Some examples which are in direct proportion are:
A worker earns $10 for every hr he works.If the number of hours a worker works is 4 hr, the amount of wages he earned increases correspondingly.
A bowl of fishball noodle costs $3.The cost of a fishball noodles will increase as the number of bowls increase.
Inverse proportion
In inverse proportion, when 1 quantity increases ,the other quantity decreases or vice versa.If y is inversely proportional to x, then xy=k, where k is a constant and not equal to 0.The graph of y against x is part of a curve calledhyperbola.The graph of y against 1/x is part of a straight line which passes through the origin.Some examples which are in inverse proportion are:
The time taken by a driver to travel a certain distance decreases when the speed increases or vice versa.Example:the speed is originally 60km/h,when the driver increases the speed to 90km/h ,the time taken to travel will decrease.
The time required to complete a certain job is inversely proportional to the number of workeres available,example:the time required to complete the job decreases as the number of workers increases or vice versa,provided that each worker works at the same rate.
When y divided by x is a constant, we can say that y is directly proportional to x. But when y multiplied by x is a constant, we can say that y is inversely proportional to x. It is certainly obvious to see which things that happen in life are actually using direct proportion or inverse proportion. For example, a plate of chicken rice is sold @ $2 per plate. When the plates of chicken rice increases, the amount of money also increases by $2 for every plate. Which is obviously, in direct proportion. Therefore, the formula is in y=kx. Well as for inverse proportion, when there are two students making a lantern, it takes a day or so. But when three or more students make the same lantern, it takes less than a day. Since the number of days increases but lesser time is used, it is obvious that this example is in inverse proportion. Thus, the formula is concluded as xy=k. If you want to tell exactly which quantity is in direct proportion or inverse proportion, you can actually draw a graph, although it takes up some time, when it is in direct proportion in the x vs y form, the graph drawn will normally be a diagonally straight line going up touching the origin. As for inverse proportion in the x vs y form, it will form a hyperbola.
Jeannie Siong (24) I AM 2A OF COURSE
if pkg can be carried a km for $x, find the cost of carrying q kg a distance of b km.
p kg-> $x,1 kg->$x/p
q kg->$xq/p
a km->$xq/p
1km ->$xqp/pq
b km->$xqb/pq
if 20 men can do a piece of work in 9 days, how long will it take 15 men do half as much work again?
let men be m,
days be d,
m is directly porportional to 1/d,
m+k/d.
when m =20, d = 9,
20/1 = k /9,
k =180,
m=180/d,
when m = 15,
15/1=180/d,
d= 180/15
d= 12
12/2= 6 days.
math journal:
In direct proportion, when one quantity increases, the other quantity will also increase. When one quantity decreases, the other quantity will also decrease. Hence, the two quantities are always in the same ratio and the change always follow a certain pattern.
For example, if a pen costs $2 in the school bookshop. It will cost me $4 for buying 2 and $6 for 3 of them. Let the amount of money be x and the number of pens be y. Thus, the amount of money that I have to pay is directly proportional to the number pens that I have bought. Therefore, x is directly proportional to y and the formula is y= kx or y/x=k where k is a constant.
Whereas in inverse proportion, when one quantity increases, the other quantity decreases. When one quantity decreases, the other quantity increases. However, the product of the two quantity is a constant(k).
For example, a motorist travels from town A to town B uniformly. When he increases his speed, time taken will decrease correspondingly and he will reach town B earlier. When he traveled in a slower speed, time taken would increase and thus take a longer time to reach town B. Therefore, the speed is inversely proportional to the time taken, hence, the formula is yx=k, where k is a constant.
Irene Tan Mei Chin (26)
When two quantities, x and y, vary in such a way that y/x is a constant, they are said to be in direct proportion. In direct proportion, y/x=k. The graph of y=kx is a straight line passing through the origin. When y increases, x will also increase. For example, when a worker worked for 10 hours, he will get $150. Let the number of hours be h and the amount of money be m. The equation will be m=15h (m/h) and h will increase when m increases.
When two quantities x and y, vary in such a way that xy is a constant, they are said to be in inverse proportion. In inverse proportion, xy=k, where k is a constant. The graph of xy=k is a hyperbola which is a curved line. The graph of y against 1/x is part of a straight line, which passes through the origin. Therefore the equation connecting x and y in inverse proportion is xy=k or y=k (1/x). An increase in one quantity results in a corresponding decrease in another related quantity or vice-versa. For example, when a car travels at a faster speed, the time taken to cover a certain distance is reduced.
To identify if two quantities are in direct proportion, the two quantities are related to each other and their changes may follow a certain pattern. For example, a pen cost $1.80 in a particular stationeries shop, we will then have to pay $3.60 for 2, $5.40 for 3... $18 for 10 and $19.80 for 11. The formula is y/x=k, whereby k is a constant and both x and y must increase at the same rate.
However, to identify if two quantities are in inverse proportion, the increase in one quantity results in a corresponding decrease in the other quantity or vice-versa. For instance, a tap that is turned on to the maximum, a big tub will fill up in 30minutes. When one more identical tap is also turned on to the maximum, it will only take 15minutes. The formula is thus y=kx instead where k is also a constant.
In our daily lives, we will counter many situations related to direct proportions and inverse proportions. These formulae that we have learnt would help us in many ways such as being able to calculate faster when buying things when we are in a rush. And to use this shorter method perhaps when we become a carpenter in future to calculate the number of workers needed to build a particular building before the deadline. All this would help to prevent us from getting into unnecessary troubles like being late for meetings or getting reprimanded when the project cannot be handed up on time.
Direct proportion is when two quantities x and y, vary in such a way that y/x is a constant. They are then in direct proportion, or y is said to be directly proportional to x.
For example, you are buying cans of soup at the supermarket. Let each can of soup be $0.50
Suppose that you buy 4 cans. You would pay $2.00.
Suppose that you buy 8 cans. You would pay $4.00.
So, changing the number of cans that you buy will change the amount of money that you pay.
the number of cans changed by a factor of 2, since 4 cans times 2 is 8 cans.
Also, the amount of money that you must pay also changed by a factor of 2, since $2.00 times 2 is $4.00.
Both the number of cans and the cost changed by the same factor, 2. Therefore, 2 is a constant
When quantities are related this way, they are in direct proportion.
In the above example the number of soup cans is in direct proportion to the cost of the soup cans.
Inverse proportion is when two quantities, x and y, vary is such a way that xy is a constant. They are then in inverse proportion or y is said to be inversely proportional to x.
For example, you are driving a car and you are going to travel 60 km. This is a constant distance throughout .
Suppose that you spent 1 hour driving. Your average speed would be 60km/h
Suppose that you spent 2 hours driving. Your average speed would be 30km/h
So, changing the number of hours that you drive will change the average speed that you will travel.
The number of hours, the time, that is, changed by a factor of 2, since 1 hour times 2 is 2 hours.
Also, the speed at which you were traveling changed by a factor of 1/2, since 60 km/h times 1/2 is 30 km/h.
The two quantities, time and speed, changed by factors. Time changed by a factor of 2; speed changed by a factor of 1/2.
When quantities are related this way, they are in inverse proportion. That is, when two quantities change by factors, they are inversely proportional.
In the above example the time is in inverse proportion to the average speed.
Chapter 1:Proportion
To find out if two quantities are in direct proportion,the two quantities should be related to each other and changes may follow a certain increasing of decreasing pattern.For example,if a necklace costs $5,2 necklaces will cost $10,3 necklaces will cost $15 and so on.Thus in direct proportion,y=kx,where k is a constant.
To find out if two quantities are in inverse proportion,the two quantities will change whereby one quantity results in a corresponding decrease/increase in the other related quantity or vice-versa.For example,it will take 5 days for 5 men to finish painting a building but it will take 25 days for 1 man to finish painting it.Thus in inverse proportion,xy=k,where k is a constant.
Miss Chum, i am here to do the maths journal.... sorry.... in a hurry...
For the direct proportion,we can see from the part where both amount increses. For example, when we have a fixed number of something, taking it as a plate of rice, when we increases the amount of plates to be ordered, the total price of the rice will increase too and not decrease. This will show the direct proportion, y/x=k.
For indirect proportion, it means that when one amount increases, the other side of the amount will decrease. For example, we have 3 workers at first to complete the work, they will finish in lets say 2 days, but when we increase the amount of workers to 6, the period where they need to complete the whole work will decrease. They will no longer be y/x=k but is y=kx.
To conclude, in direct proportion, both amount increases, while in an indirect proportion, an increse in one number will result in the other number to decrease.
aiya, ms chum i dun care le. i post the stuffs here
When x and y are in direct proportion, it is in such a way that y/x=k or y=kx where k is a constant and not zero.
Example:
A pack of chocolates cost $3, two packs of such chocolates costs $6 and so on. Thus, in direct proportion, a quantity increasing will lead to a corresponding increase of the other related quantity.
When x and y are in inverse proportion, it is in such a way that xy=k where k is a constant and not zero.
Example:
When a car travels at 120km/h, it will take only half an hour to cover 60 km while travelling at 60km/h will take an hour to cover the same distance. Thus, in inverse proportion, a quantity increasing will lead to the corresponding decrease of the other related quantity.
ps sorry for any typo. I'm rushin for time... pai seh...
the variable y is said to be directly proportional to the variable x, if there exists a non-zero constant k such that
y=kx.
if an object travels at a constant speed, then the distance traveled is proportional to the time spent traveling, with the speed being the constant of proportionality.
inverse proportion means that as the value of one variable gets bigger, the value of another gets smaller, such that their product (the constant) is always the same.
the variable y is inversely proportional to the variable x if there exists a non-zero constant k such that
y=k/x
For example, the time taken for a journey is inversely proportional to the speed of travel; the time needed to dig a hole is (approximately) inversely proportional to the number of people digging.
In chapter 1, there are two proportions we have learned. They are direct and inverse proportion. In direct proportion, the formula is y=kx. An example is the copies of books in a bookshop. If there are 10 copies of books and each book costs $15, the more copies of books, the more money the books will be worth. If the money the books are worth is y, the copies of books is x, the profit will always be the same when y/x=k where k is a constant.
In inverse proportion the formula is different. It is xy=k whereby k is a constant. An example is the number of trees required to be planted on a hillside when the distance between two adjacent trees is x m. For example when the number of trees required is y, the distance is x, if the distance is longer, lesser amount of trees will be planted. This results in xy=k whereby k will be a constant.
Index number(41)Zeng Fan Jun
First of all, when two quantities are in proportion, a change in one quantity corresponds to a change in the other. A proportion is an equation showing two ratios are equivalent. In direct proportion, when one quantity decreases, the other quantity also decreases. Hence, the two quantities are always in the same proportion. If y is directly proportional to x, then (a) y=kx or y/x=k, where k is a constant and k is not equal to 0. (b) the graph of y=kx is a straight line which passes through the origin. (c) y1/y2=x1/x2 or y1/x1=y2/x2 where (x1,y1) and (x2,y2) are any two pairs of values of x and y. Example 1: 3y=5x
Solution: since y/x=5/3 is a constant, then y is directly proportional to x. Example 2:Given that y is directly proportional to the cube root of x and y=6 when x=27, find (a) an equation connecting x and y (b) the value of y when x=125 (c) the value of x when y=18 Solution: (a) y=k(cube root of x) when x=27, y=6, 6=k(cube root of 27) 6=3k, k=2, hence, y=2(cube root of x) (b) when x=125, y=2(cube root of 125), y=2(5), y=10 (c) when y =18, 18=2(cube root of x), cube root of x= 18/2, cube root of x=9, x=9x9x9, x=729
In inverse proportion, when one quantity increases, the other quantity decreases and vice versa. However the product of the two quantities is a constant. If y is inversely proportional to x, then (a) xy=k or y=k/x where k is a constant and k is not equal to 0. (b)the graph of y against x is part of curve called a hyperbola. (c) the graph of y against 1/x is a straight line passing through the origin. y is directly proportional to 1/x. (d) x1,y1=x2,y2 where (x1,y1) and (x2,y2) are any two pairs of values of x and y. Example 1: y=4x Solutions: since y/x=4 or y(1/x)=4 is a constant, then y is inversely proportional to 1/x. Example 2: Given that y is inversely proportional to x and y=6 when x=3, find (a) an equation connecting x and y (b) the value of y when x=9 (c)the value of x when y=4.5 Solutions: y=k/x when x=3, y=6, 6=k/3, k=6x3, k=18, hence y=18/x (b) when x=9, y=18/9, y=2 (c) when y=4.5, 4.5=18/x, x=18/4.5, x=4
Gan She Hwa(6) 2A
When two quantities are related to each other ,their changes may follow a certain pattern.For example,if a plate of rice costs $1 at the school canteen,you will have to pay $2 for two plates of rice and $3 for three plates of rice and so on.Thus the amount you pay is related to the number of plates of rice ordered.This is direct proportion.So,when two quantities,x and y,vary in such a way that y/x is a constant,they are said to be in direct proportion.
Sometimes,we do come across situations where an increase in one quantity results in one quantity results in a corresponding decrease in another related quantity or vice-versa.For example,when a motorist travels at a faster speed,the time taken to cover a certain distance is reduced.This is inverse proportion.So,when two quantities,x and y,vary in such a way that xy is a constant , they are said to be in inverse proportion.
In direct proportion, when one quantity increases,the other will increase. Similarly,when one quantity decreases,the other will also decrease. Therefore, an equation of kx=y is formed,where k is a constant. For example:
A car(k) is traveling steadily along a highway. Its consumption of petrol(l) is directly proportional to the distance(d) traveled by the car.
From here,we can form the equation kl=d(kx=y). As the distance the car travels increases,the petrol consumption also increases;it is in the form of kx=y, therefore it is in direct proportion.
In inverse proportion,when one quantity increases,the other decreases. But when one quantity decreases, the other will decrease. However,in inverse proportion,the product of 2 quantities is a constant,forming an equation of xy=k. For example:
8 men(m) take 21 days(d) to build a garage(k). How many days would it take for 14 men to build the same garage?
From here, we can form an equation md=k(xy=k), where the number of days would increase when the number of men decrease. Therefore, it is in inverse proportion.
Direct proportion refers to two quantities that are related to each other. Their changes may follow a certain pattern. Example, a pen cost $1, two pens cost $2, three pens cost $3. The amount you pay, is related to the amount you get in return.
Inverse proportion refers to increasing in one quantity leads the other quantity to decrease. For example, the faster speed a motorist travels, the time taken to reach the destination would be faster. It would not make sense if the faster i drive, the slower i reach my destination.
For direct proportion.
When two quantities,for example A and B,are in direct proportion,it should be A=kB, where k is a constant and is not equal to zero.There is a connection between the quantities.
For example,the number of books bought(A) is 1 and the cost of one book (B) is $15. As the number of books bought increases,the cost of the books also increases.It will result in 1/15, 2/30, 3/45 and so on.When the fraction is brought down to the simplest form,it will be 1/15(k),where k is a constant and is not equal to zero.So the formula will be A=(1/15)B.
We can also tell whether two quantities are in direct proportion by drawing a graph.If the there is a straight line that passes through the origin,it is in direct proportion.
For inverse proportion.
When two quantities,for example C and D,are in inverse proportion, the formula should be CD=k,where k is a constant and is not equal to zero.Similar to direct proportion,there is also a link between the two quantities.
For example,the corresponding volume of air inside a syringe(C) is 120 and the pressure(D) is 1.As the pressure increases, the volume decreases.It will result in 1x120, 2x60, 3x40 and so on.The solution to all the equations will be 120.So the formula is CD=120.
We can also see if two quantities are in inverse proportion by drawing a graph with the equation 1/C.If the graph shows a curve line which is also called a hyperbola,it is in inverse proportion.
Proportion is about scales, inverse, and direct proportion. To know the exact distance of the land, we wiill need to take the scale of the map. For instance if the scale is 1:200, we will need to times 200 the distance on the map. Direct proportion, we will need to take the formula x=ky. Example is five plates chicken rice which cost $2 each sum up to $10. For inverse proportion, formula is k=xy. 60 people (x) take ten days (y)to construct a house. But 20 people will take 30 days. the k is constant
hi ms chum sorry that i posted late... The definition of DIRECT PROPORTION is that when two quantities a and b vary in a way that b/a is constant b is said to be directly proportional to a. The properties of DIRECT PROPORTION is: when two quantities a and b is in direct proportion, b=ka, where k is constant and for the graph of b=ka is a straight line passing through the origin.
The definition for INVERSELY PROPORTION, when two quantities a and b vary in a way that ab is constant a and b are said to be in inverse proportion. The proprties for INVERSELY PROPORTION: when two quantities a and b are in inverse proportion, ab=k, where k is constant and for the graph of b against a is part of a curve called hyperbola and the graph of y against 1/x is part of a straight line which passes through the origin.
When two quantities, x and y, vary in such a way that y/x is a constant, they are said to be in direct proportion, or y is said to be direcly proportional to x. When two quantities, x and y, are in direct proportion, y = kx, where k is a constant, and the graph of y = kx is a straight line passing through the origin. For example, a book cost $5, two books will definitely cost $10, which shows that [y = kx] = [5 = (5)1].
When two quantities, x and y, vary in such a way that xy is a constant, they are said to be in inverse proportion, or y is said to be inversely proportional to x. When two quantities, x and y, are in inverse proportion, xy = k, where k is a constant, and the graph of y against 1/x is part of a straight line which passes through the origin. The graph of y against xx is part of a curve called a hyperbola. For example, the speed of a car is 80km/hr, it takes 3hrs to cover the distance of 240km. But, when it increases its speed to 90km/hr, it only takes 2hrs 40min to cover the distance of 240km. So, in inverse proportion, an increase in a quantity will lead to the decrease of the other quantity.
SORRY MISS CHUM. I DID NOT KNOW THE DEADLINE WAS YESTERDAY. SORRY.
Anyway,
Direct proportion refers to when for example, y is divided by x and is a constant. Which also means that when one side increases, the other side increases as well.
Indirect proption refers to when for example, y is multiplied by x and is a constant. Which also means when one side increases, the other side decreases.
Direct and indirect proportion are often used in real life. Although sometimes we may not notice it happening.
For example when you buy things. If you buy a handphone which costs $100, the money will increase if you buy 2 handphones instead of one and that wil be $200. That is for direct proportion.
As for indirect propertion, construction workers can be examples. If a construction worker takes 12 days to construct a house, 2 workers will take 6 days to construct a house if the amount of work done is the same.
Sorry Miss Chum. I'm here to continue my journal. I haven't finish and suddenly my computer hang. Sorry!
Therefore in direct proportion, y=kx and in indirect proportion, xy=k.
Graphs can be also used to diffrentiate from direct to indirect proportion. However, it is very time consuming.
In direct proportion, the graph is a straight line passing through the origin. In indirect proportion, the graph will form a curve which is called hyperbola.
LOL i found out tt i did it later than wanling LOL hahas anywaes i found out tt many ppl left the definition of the proportion thingy... COOL!! hahas btw pls do not laugh at my blog nick... i noe it sounds stupid...
OH YAR!!! did anyone experienced the same situation of almost dying due to readin only 2 comments at most??
Sorry Miss Chum. i didn't have a chance to use the computer until now.Really sorry!
Direct proportion refers to y equals to kx whereby k is a constant which also means that when y increase, x increases too. The graph of y=kx passes through its origin. For example, the pay for worker who works 1 hour is $5 and the worker works for 8 hours, which show that [y=kx]=[y=5x8] whereby 5 is k and k is a constant.
Inverse proportion refers to k equals to xy whereby k is a constant which also means that when x increases, y will decreases. In the graph of y against 1/x, passes through the origin but it will form a curve line when k=xy and the curve line is called a hyperbola. For example, 3 workers need 6 days to complete painting a roof. But when the number of workers is increase by three more, it will only take 3 days.
*Miss Chum, sorry for the late work,i didn't know when as the deadline.
DIRECT PROPORTION
When two quantities,x and y,vary in such a way that y/x is a constant, they are said to be in direct proportion, or y is said to be directly proportiobal to x.
When two quantities, x and y, are in direct proportion,
- y = kx, where k is a constant and k is not = to 0,
- the graph of y = kx is a straight line passing through the origin.
When two quantities are related to each other, their changes may follow a certain pattern. For example, if a bowl of noodles cost $2, i will have to pay $2 for a bowl of noodles, $4 for 2 bowls of noodles, $6 for 3 bowls of noodles and so on. Thus the amount i pay is related to the number of bowls of noodles ordered.
INVERSE PROPORTION
When two quantities, x and y, vary in such a way that xy is a constant, they are said to be in inverse proportion, or y is said to be inversely proportional to x.
When two quantities, x and y, are in inversely proportion,
- xy = k, where k is a constant anf k is not = to 0.
- the graph of y against x is part of a curve called hyperbola.
- the graph of y against 1/x is part of a straight line which passes through the origin.
In our daily life, we do come across situations where an increase in one quantity results in a corresponding decrease in another related quantity or vice-versa. For instance, when a motorist travels at a faster speed, the time taken to cover a certain distance is reduced.
done by: Qimin(14) from 2A (((:
Direct Proportion
When a quantity gets larger or smaller, we say that it changes.
Sometimes a change in one quantity causes a change, or is linked to a change, in another quantity. If these changes are related through equal factors, then the quantities are said to be in direct proportion. Or one might say that the two quantities are directly proportional.
Whenever you have a direct proportion as stated above you can change it into an equation by using a proportionality constant. Here is how the direct proportion would look as an equation: y = kx
For example, suppose that you are buying cans of soup at the store. Let us imagine that they cost 50 cents, or $0.50, each.
Case #1:If you buy 4 cans. You would pay $2.00.
Case #2:If you buy 8 cans. You would pay $4.00.
So, changing the number of cans that you buy will change the amount of money that you pay.
Notice that the number of cans changed by a factor of 2, since 4 cans multiply by 2 is 8 cans.
Also, notice that the amount of money that you must pay also changed by a factor of 2, since $2.00 multiply by 2 is $4.00.
Both the number of cans and the cost changed by the same factor, 2.
When quantities are related this way we say that they are in direct proportion. That is, when two quantities both change by the same factor, they are in direct proportion.
In the above example the number of soup cans is in direct proportion to the cost of the soup cans. The number of soup cans is directly proportional to the cost of the soup cans.
Dan Jun Yuan(35) from 2A
Inverse Proportion
Two variables are inversely proportional (or varying inversely) if one of the variables is directly proportional with the multiplicative inverse of the other, or equivalently if their product is a constant. It follows, that the variable y is inversely proportional to the variable x if there exists a non-zero constant k such that y = k/x
For example, let us say that you are driving a car and you are going to travel 60 miles. Consider this to be a constant distance throughout the following discussion.
Case #1:Suppose that you spent 1 hour driving. Your average speed would be 60 mph.
Case #2:Suppose that you spent 2 hours driving. Your average speed would be 30 mph.
So, changing the number of hours that you drive will change the average speed that you will travel.
Notice that the number of hours, the time, that is, changed by a factor of 2, since 1 hour times 2 is 2 hours.
Also, notice that the speed at which you were traveling changed by a factor of 1/2, since 60 mph times 1/2 is 30 mph.
The two quantities, time and speed, changed by inverse factors. Time changed by a factor of 2; speed changed by a factor of 1/2.
When quantities are related this way we say that they are in inverse proportion. That is, when two quantities change by inverse factors, they are inversely proportional.
In the above example the time is in inverse proportion to the average speed. One could also say that the average speed was in inverse proportion to the time.
When there are 2 quantities x and y, how do we differtianate which is direct proportion or inverse peoportion? If x and y, vary in such a way that y/x is a constant then they are in direct proportion. If x and y, vary in such a way that xy is a constant then they are in inverse proportion. One of the difference between direct proportion and inverse proportion is that in direct proportion, when x increase, y also increase while in inverse proportion, when x increase, y decrease. Another difference is that when y and x are in direct proportion, the graph of y against x is a straight line which passes through the origin. However, when x and y are inversely proportion, the graph of y against x is a curve which approaches the y-axis when x is small, and it tends to the x-axis as x increase. The curve is part of a curve, called hyperbola.
One example of inverse proportion is the situation of the amount of workers and the amount of time needed to complete a building. In this situation, the building is the constant and the number of workers and the time needed are the variables. When the number of workers increase, the time needed to complete the building decrease. When the number of workers decrease, the amount of time needed to complete the building increase. An example of direct proportion is a situation where you buy a bowl of rice. The constant is the price of the rice while the other 2 quantities is the bowl of rice you buy and the amount of money you pay. If you buy more rice, the amount of money you pay increases, however if you buy fewer bowl of rice, the amount of money you pay decrease. The price of the rice remains the same.
aduial have not include any examples for its journal while eggyork.blogspot.com did not explain further what is inverse and direct proportion.
SORRY MS CHUM. I FORGOT ALL ABOUT THIS MATHS JOURNAL.AND JUST NOW THE THING JUST ERASED MY WHOLE COMMENT!!!!ARGH!!!
DIRECT PROPORTION
x&y vary in such a way that y/x is a constant
CHARACTERISTICS
*y=kx k≠0
*graph of y=kx is part of a straight line passing through the origin
EXAMPLE
one bag cost $50
two bags cost $100
SO ON AND SO FORTH..
INVERSE PROPORTION
x&y vary in such a way that xy is a constant
CHARACTERISTICS
*xy=k k≠0
*graph of y against x is part of a curve called a hyperbola
*graph of y against 1/x
is part of a straight line that passes through the origin
EXAMPLE
t&N=k k is a constant
N=9, t=20:
20x9=180
k=180
tN=180
N=6,
tx6=180
t=180/6
=30
YEAHHHHHHH~~~~~~
DONE!!
Jennay, I have no idea who you are. Aduial, if you are reading this, please tell me who you are too!
Fot the rest of you, if your comment has not appeared, it means that I have not received it. It also means you have not successfully sent it. So please send it again, or else I won't be able to give you a grade
Chapter 1 is about proportion.First,we learn about scales.we also learn how to convert distance from a map to an actual distance.For example if the scale of the map is 1:30000,then things which are 1 cm long on the map will be 30000cm long on actual distance.If we are looking ar area,we would have to square both 1 and 30000.
next we learn about inverse and direct proportion.In direct proportion,we will take the formula ky=x.For example if a television set cost $1000(y),3 sets will cost $3000(x).which is 3 times more(k).For inverse proportion,the formula is xy=k,that is for example it will take 15days(x) for 20 men(y) to constuct a buliding.It will also take 30 days (x) for 10 men 9y) to construct a buliding.k is a constant,which in this case 300.^^
`Angela phua (19)
Direct proportion
When two quantities are in proportion , a change in one quantity corresponds to a change in the other . A proportion is an equation showing two ratios are equivalent .
In Direct Proportion , when one quantity increases , the other quantity will also increase . When one quantity decreases , the other quantity also decreases . Here , the two quantities are always in the same ratio .
If y is directly proport ional to x , then
a) y= kx or y/x=k where k is a constant and k =/= 0 .
b) The graph of y=kx is a straight line which passes through the origin .
c) y1/y2=x1/x2 or y1/x1=y2/x2 where (x1,y1 ) and (x2,y2) are any two pairs of values of x and y
Inverse Proportion
In Inverse Proportion , when one quantity increases , the other quantity decreases . When one quantity decreases , the other quantity increases . However , the product of the two quantities is a constant .
If y is inversely proportional to x . then
a) a) xy =k or y= k/x where k is a constant and k =/= 0
b) the graph of y against x is part of a curve called hyperbola . ( the curve tends to the y-axis when x is small and it tends to the x-axis when x increases .)
c) c) the graph of y against 1/x is a straight line passing through the origin ( since 1/x is never zero , the point (0,0) is not on the graph . We draw a small circle at the origin to indicate this .
d) d) x1,y1=x2,y2 where (x1,y1 ) and (x2,y2) are any two pairs of values of x and y .
Direct Proportion
When two quantities are in direct proportion, a change in one quantity corresponds to a change in the other. A proportion is an equation showing two are equivalent. In direct proportion, when one quantity increases, the other quantity also increases.
Example
A mechanic is paid at hourly rate. He is paid a certain amount after working for a few hours. If he works for a longer time, he will be able to earn more money. That's because his pay varies directly as the number of hours worked. As his hours increase, so does the amount of his paycheck.
Inverse proportion
When one quantity increases, the other decreases. When one quantity decreases, the other quantity increases. However, the product of the two quantities is a constant.
Example
A caterer who takes a watermelon to a picnic knows that each person will receive more watermelon if there are fewer attendees, but each person will receive less watermelon if there are more attendees. That's because the amount of watermelon for each person varies inversely as the number of attendees. The more people, the less each person gets.
If I divide the values in the columns of a table and keep getting the same number, there is a direct proportion. If I multiply the values in the columns of a table and keep getting the same number, there is an inverse proportion.
One example of direct proportion would be time traveled (constant speed) and distance traveled. As y=kx, speed would be k, and by dividing distance(y) by time(x), I can get the speed(y=kx is also equals to y/x=k). They increase or decrease at the same rate.
One example of inverse proportion would be speed of a car and time spent traveling. As xy=k, by multiplying speed(x) and time(y), I will also be able to get distance.(k) However when one quantity increases, the other decreases.
Wanying(11)
When two quantities x and y are in direct proportion,both x and y increase or decrese in the same rate.
When two quantities x and y are in inverse proportion,when x increase ,y will decrease and vice versa.
When x and y are in direct proportion,y=kx,where k is a constant.
Whereas, when x and y are in inverse proportion,xy=k,where k is a constant and k is not equal to 0.
The cost of riding a car is (directly proportional) to the number of days the car is being rented for.
The speed of a bullet fired is (inversely proportional) to the square root of its mass.
This is straight forward.
However some questionsrequires some thinking to decide if it requires inverse or direct proportion.
Example(direct proportion)
68 workers took 3oh to make 500 slippers.How long would it take for the same group of workers to produce 900 slippers?
(Inverse Proportion)
Mrs Tan takes 1/2 an hour to drive from school to library at 60km/h.How long would it take for her if she drives at 90km/h?
Vampire: sori ms chum, i was nt able to do this earlier as my com is spoiled..so sori=)
Direct proportion is when x and y increase or decrease in the same rate.
Eg. if two bags of chocolates cost $4 than four bags of chocolates wil cost $8.
Inverse proportion is xy=k which means that when one side increase the other decrease.
Eg. if 80 men take ten days to build a tower, 20 men take forty days to build a tower.
draken, you have explain throughly and used the term hyperbola. Like what kai bin said, Aduial you didnt give out some examples to let others get a better understanding of direct proportion and indirect proportion. Eggyork.blogspot.com didnt further explain about the examples given.
Ask to define these two si peh chim sia, i now chiong lorhs.
Direct proportion :)
When two quantities,x and y,vary in such a way that y/x is a constant, they are said to be in direct proportion, or y is said to be directly proportional to x.
When two quantities, x and y, are in direct proportion,
y = kx, where k is a constant and k is not = to 0,
the graph of y = kx is a straight line passing through the origin.
Indirect proportion :)
When two quantities, x and y, vary in such a way that xy is a constant, they are said to be in inverse proportion, or y is said to be inversely proportional to x.
When two quantities, x and y, are in inversely proportion,
xy = k, where k is a constant anf k is not equal to 0.
the graph of y against x is part of a curve called the hyperbola.
the graph of y against 1/x is part of a straight line which passes through the origin.
DIRECT PROPORTION
Direct proportion involves situations where two values vary, but the ratio between the values stays the same.
~~If an object travels at a constant speed, then the distance traveled is proportional to the time spent traveling, with the speed being the constant of proportionality.
Eg.(Formula) y=xk(constant)
When y=20=distance travelled,
x=10=time taken, k=constant speed
y=kx
20=k(10)
k=2
40=2x
x=20
Therefore, we can see thatwhen the distance travelled is x2, the time taken will also x2.
INVERSE PROPORTION
Two variables are inversely proportional (or varying inversely) if one of the variables is directly proportional with the multiplicative inverse of the other, or equivalently if their product is a constant.
~~If a car needs to travel a k(a constant)distance, then the speed is inversely proportional to the time spent travelling, with the distance being constant.
Eg. (Formula) y=k/x
When y=40=speed,
x=20=time taken,
k=constant distance
y=k/x
40=k/(20)
k=800
80=800/x
x=10
Therefore, we can see that when the speed is x2, the time taken is /2.
Sorry, Ms Chum. I posted 3 times on Saturday but it is not shown here. So, i try it today and it works. (:
Direct Proportion
Direct proportion involves situations where two values vary, but the ratio between the values stays the same. When two quantities are related to each other, their changes may follow a certain pattern.
When two quantities,x and y, vary in such a way that y/x is a constant, they are said to be in direct proportion, or y is said to be directly proportional to x. Both x and y increase and decrease at the same rate. Also, we see that the points, x and y, lie on a straight line passing through the origin.
Summary
When two quantities, x and y, are in direct proportion:
- y=kx,where k is a constant and not 0
- the graph of y=kx is a straight line passing through the origin.
For example:
1. If a pen cost $1.50 at the book shop, you will have to pay $3 for two pens and $4.50 for three pen and so on. So, the ratio will be 3:2. Thus the amount you pay is related to the number of pens
bought.
2. If a car travel 60km/h, it will travel 120km in 2 hours and 180km in 3 hours and so on. Thus, in direct proportion, a quantity increasing will lead to a corresponding increase of the other related
quantity.
Inverse Proportion
When an increase in one quantity results in a corresponding decrease in another related quantity or vice versa, it is called inverse proportion. For instance, when a motorist travels at a faster speed, the time taken to cover a certain distance is reduced.
When two quantities, x and y, vary in such a way that xy is a constant, they are said to be in inverse proportion, or y is said to be inversely proportional to x. When x and y are plotted on the graph, the graph of y against x is a curve which approaches the y-axis when x is small and it tends to the x-axis as x increase. The curve is part of a curve, called hyperbola. However, the graph of y against 1/x is part of a straight line which passes through the origin. Since 1/x is never zero, the origin is not on the graph.
Summary
When two quantities, x and y are in inverse proportion:
- xy=k, where k is a constant and not 0
- the graph of y against x is part of a curve called the hyperbola
- the graph against 1/x is part of a straight line which passes through the origin
For example:
1. If a car travel 60km/h, it will take 3 hours to reach its destination. However, if it traval 90km/h, it will take 2 hours to reach its destination.
2. If 6 workers are needed to paint a wall in two days, 3 workers can paint a wall in 4 days.
Proportion is mainly about direct and inverse proportion. In direct proportion, the graph is a hyperbola in which the straight line passes through the origin. The formula is x=ky, in which y will increase correspondingly with x. An example would be, a meal cost $3(y), 5sets of meals(k) will cost 5 times more, making a total of $15(x).
Inverse proportion is different to direct proportion. The graph of inverse proportion is in a decreasing manner. Therefore, we can get a formula which is k=xy. An example is it takes 500 workers(x) 3years(y) to build a stadium. However it will take 300 workers(x) 5years(y) to construct a similar stadium. Both inverse and direct proportion plays a part in our lifes, therefore we should understand it thoroughly, so that we will be able to use it in the future!
Adelyn Sim Qian Yun(1)
DIRECT PROPORTION
When two quantities are related to each other, their changes may follow a certain pattern. For instance, if a bowl of noodles costs $1 at your school canteen, you will have to pay $2 for two bowls of noodles and $3 for three bowls of noodles and so on. Thus the amount you pay is related to the number of bowls of noodles ordered. When two quantities, x and y, vary in such a way that y/x is a constant, they are said to be in direct proportion, or y is said to be directly proportional to x.
When two quantities, x and y, are in direct proportion,
� y = kx, where k is a constant and k is not equal to 0,
� the graph of y = kx is a straight line passing through the origin.
When two quantities, x and y, are in direct proportion ( i.e. y = kx, where k is a constant and k is not equal to 0 ), we have x1/x2 = y1/y2, where ( x1,y1 ) and ( x2, y2 ) are ant two pairs of values of x and y, x2 is not equal to 0 and y2 is not equal to 0.
For example:
It is given that w is directly proportional to t. When t = 4, w = 20. Find�
(a) the value of w when t = 6
(b) the value of t when w = 45
Answer:
(a) w = kt
20 = k ( 4 )
k = 20/4
k = 5
w = 5t
when t = 6
w = 5 x 6
w = 30
(b) w = 5t
when w = 45
45 = 5t
t = 45/5
t = 9
Eugenia Teh Shu Wen (4)
2A
INVERSE PROPORTION
When there is an increase in one quantity results in a corresponding decrease in another related quantity or vice-versa. When two quantities, x and y, vary in such a way that xy is a constant, they are said to be in inverse proportion, or y is said to be inversely proportional to x.
When two quantities, x and y, are in inverse proportion:
• xy = k, where k is a constant and k is not equal to 0
• the graph of y against x is part of a curve called a hyperbola
• the graph of y against 1/x is part of a straight line which passes through the origin
When two quantities, x and y, are in inverse proportion ( i.e. xy = k, where k is a constant and k is not equal to 0 ), we have x1y1 = x2y2, where ( x1, y1 ) and ( x2, y2 ) are any two pairs of values of x and y.
For example:
Determine whether x and y are in inverse proportion in each of the following tables.
(a)
x 1 2 3 4
y 12 10 8 6
1 x 12 = 12
2 x 10 = 20
3 x 8 = 24
4 x 6 = 24
Answer: x and y are not in inverse proportion.
(b)
x 2 4 6 8
y 12 6 4 3
2 x 12 = 24
4 x 6 = 24
6 x 4 = 24
8 x 3 =24
Answer: x and y are in inverse proportion.
Eugenia Teh Shu Wen (4)
2A
Direct Proportion
When two quantities are related to each other, their change may follow a certain pattern.
Eg. If a plate of chicken rice cost $1 at our school canteen, we will have to pay $2 for two plates of chicken rice and $3 for three plates of chicken rice and so on and so forth. Thus the amount we pay is related to the number of plates of chicken rice ordered.
Eg. If we drive a car, the longer the distance we drive, the more patrol the car needs! Thus the distance we drive in our car is related to the amount of patrol used to finish the distance.
Formula: y=kx
Inverse proportion
When an increase in one quantity will results in a corresponding decrease in another related quantity or vice-versa.
Eg. When a motorists travels at a faster speed, the time taken to cover a certain distance is reduced.
Eg. If 1 painter use 1 month to paint a house, 30 painters will take 1 day to paint the house!!
Formula: K=xy
Thus We can use what we learnt in chapter 1 in many real life scenarios!
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