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Direct And Inverse Proportion Gcse Pdf Free [BETTER]


The direct proportion formula says if the quantity y is in direct proportion to quantity x, then we can say y = kx, for a constant k. y = kx is also the general form of the direct proportion equation.




Direct And Inverse Proportion Gcse Pdf Free



The graph of direct proportion is a straight line with an upward slope. Look at the image given below. There are two points marked on the x-axis and two on the y-axis, where (x)1


There are two types of proportionality that can be established based on the relation between the two given quantities. Those are direct proportion and inverse proportional. Two quantities are directly proportional to each other when an increase or decrease in one leads to an increase or decrease in the other. While on the other hand, two quantities are said to be in inverse proportion if an increase in one quantity leads to a decrease in the other, and vice-versa. The graph of direct proportion is a straight line while the inverse proportion graph is a curve. Look at the image given below to understand the difference between direct proportion and inverse proportion.


Using the direct proportion formula,y = kxSubstitute the given x and y values, and solve for k.36 = k 6k = 36/6 = 6The direct proportion equation is: y = 6xNow, substitute x = 80 and find y.y = 6 80 = 480


It is given that,Weight of apples = 8 lbCost of 8 lb apples = $10Let us consider the weight by x parameter and cost by y parameter.To find the cost of 32 lb apples, we will use the direct proportion formula.y=kx10 = k 8 (on substituting the values)k = 5/4Now putting the value of k = 5/4 when x = 32 we have,The cost of 32 lb apples = 5/4 32y =58y = 40


Solution: Let the amount received by Henry be treated as y and the number of hours he worked as x. Substitute the given x and y values in the direct proportion formula, we get,300 = k 50


Direct proportion, as the name suggests, indicates that an increase in one quantity will also increase the value of the other quantity and a decrease in one quantity will also decrease the value of the other quantity. While inverse proportion shows an inverse relationship between the two given quantities. It means an increase in one will decrease the value of the other quantity and vice-versa.


The number of people performing a particular task is inversely proportional to the time taken for completion. Let us say that 2 people take 6 days to paint the fence of a garden, then according to the inverse proportion, a team of 3 people would complete the same task in 4 days and a team of 4 people would need only 3 days for completion. Here, the product of the two variables, i.e., the number of people and number of days is equal to 12 and remains constant throughout the variation.


The number of vehicles present on a road is typically inversely proportional to the empty space on a road. This is because more number of vehicles would cover more area of the road, thereby leaving less empty space and fewer number of vehicles would need comparatively less area of the road, thereby providing more empty or free space.


Suppose you have 12 marbles that you wish to arrange in form of rows and columns. There are a number of ways to arrange them in this particular manner. An arrangement that consists of two columns would have six rows. Now, if you increase the number of columns to three, the number of rows reduces to four. Similarly, the same twelve marbles can be organised in a format that consists of four columns and three rows, and so on. In this case, you can easily observe that the product of the number of rows and columns is equal to 12 and remains constant. This means that the number of rows varies in inverse proportion to the number of columns.


When you pluck a fruit from a tree and store it in a basket, it begins to lose its freshness as time passes by. As time increases, the freshness of the fruit begins to decrease. This means that time and freshness of a flower are inversely proportional to each other. An increase in the value of one quantity tends to induce a proportionate decrease in the number of other entities.


Let us say that a person is able to completely fill a swimming pool with water in 4 hours by connecting two water pipes to it. Now, if the number of pipes connected to the swimming pool is increased to 4, then the time required to fill the pool gets reduced to 2 hours, provided the flow rate of the fluid through all pipes remain constant. This means that the two variables, i.e., the number of pipes and the time taken are inversely proportional to each other.


The number of students residing in a particular hostel is inversely proportional to the time taken to consume a particular amount of food available in the hostel mess. For instance, 100 students consume 50 kg of flour in a week. Now, if the number of students increases to 200, then the same amount of floor gets consumed in 3.5 days. Here, one can easily observe that when you double the number of students, then the time taken to consume a particular amount of food reduces to half.


The blade of a knife is tapered and is constructed in a wedge shape. Here, the surface area of the blade is inversely proportional to the sharpness of the knife or the pressure exerted by the knife. The more is the surface area of the edge of the knife blade, the less will be its sharpness. Similarly, the lesser is the surface area, the more will is the sharpness.


One of the best examples to demonstrate inverse proportionality is the relationship between volume and pressure. Let a container has multiple holes drilled along its length. When water or any other liquid is poured into the container, it begins to flow out through these holes. Water escaping through the hole that is located closest to the base experiences the maximum pressure, while water escaping through the hole present near the top or near the opening of the container would encounter minimum pressure. This means that pressure increases with a decrease in volume and pressure decrease with an increase in volume because the volume and pressure quantities are inversely related to each other.


The cost of an item is usually inversely proportional to its demand in the market. When the cost of an item reduces, more people opt to buy it, thereby increasing its demand in the market. Similarly, when the cost goes high, most people prefer not to buy the item; therefore, the demand drops low.


A see-saw is a long narrow iron or wooden beam fixed on a pivot in the middle. The seats present on the edges of the board display the inverse proportionality in real life in the easiest possible manner. When one end of the see-saw goes higher, then the other end drops down. The relationship between the altitude of both the edges is inversely proportional in nature. As the height of one edge of the board begins to increase, the altitude of the other end of the board tends to reduce proportionally and vice versa.


There exists an inverse relationship between the magnitude of force applied to squeeze a toothpaste tube and the amount of paste contained by it. If you squeeze a toothpaste tube with force, then the amount of paste left inside the tube begins to reduce. An increase in the magnitude of force applied to the tube causes a proportional decrease in the amount of the contents of the tube.


The battery power of a gadget is inversely related to the time for which it is used. Suppose a gadget is charged to 98% before use. Let us say, after using it for one hour the battery drops down to 88%, after two hours the battery percentage is equal to 78%, the charging contained by the gadget after three hours is equal to 68%, and so on. In this case, with an increase in the value of the time for which the gadget is being used, a significant and proportional decrease in the battery percentage can be observed easily.


Let us take the example of a spinning top. When the pointed end of the spinning top is placed on the ground and the rope wrapped around the top is pulled quickly with force, the top begins to spin. It must be observed that the acceleration with which the to spins is maximum in the beginning and begins to drop gradually as time passes by. This means that with an increase in the value of time, the magnitude of acceleration decreases proportionally, thereby demonstrating an inverse relationship between the magnitude of the acceleration of an object and the time.


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