Proportion Scales and Maps Direct Proportion Inverse Proportion The scale of a map is defined as the ratio of a distance on the map to the corresponding distance on the ground. The scale of a map is expressed using a line, with separations marked by smaller intersecting lines, similar to a ruler. One side of the scale represents the distance on the map, while the other side represents the true distances of the objects in real life. Representative Fraction (RF)is usually written as a fraction and indicates the relationship of distance measured on a map and the corresponding distance on the ground. The practical uses of a map scale is to measure the distance between one point and another on a map. We can use a map scale. For example, the scale of a map is 1:500. So, if the actual distance given is 4500m, the distance between the two points would be 4500/500 = 9cm. Given the distance between two points on the map, how do you calculate the actual distance between them? Can you give examples?

We can use a map scale. For example, the scale of a map is 1:500. Thus, if the distance measured on the map by your ruler is 5cm, the actual distance would be 5 x 500 = 2500m. What is the relationship between the ratio of areas and the scale of a map?

In order to get the ratio of areas, you would need to square the numbers of the scale of the map respectively. For example, the scale of the map is 1:100. In order to get the ratio of the areas, you could simply square the number 1 and 100 respectively in the scale of the map. Thus, the ratio of areas would be 1:10000. How do you calculate the area of a region from the scale of map?

Using the formula just now, you can square the numbers of the scale of the map, for e.g. the scale of map is 1:10, thus, the ratios of area would be 1:100. Then, you can use the area of the land on the map

and multiply by 100, which gives you the actual area of the region. Sometimes a change in one quantity causes a change/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.

If an increase in one quantity causes an increase in the other quantity. Or a decrease in one quantity causes decrease in other quantity, then we say that they are related directly (They are are said to be in direct proportion.) Suppose the price of one piece of soap is $2.

If a person wants to buy a dozen pieces of soap, then he has to pay $24. If he wants to buy two dozen pieces of soap, he has to pay $48 dollars and so on.

During a test, the more questions I had gotten correct, the more marks I get. If a bowl of noodles cost $1 at the school canteen, you will need to pay $2 for 2 bowls of noodles and $3 for 3 bowls of noodles and so on. Thus, the amount you pay is related to the number of bowls of noodles ordered.

So in this case, the bowl of noodles is directly proportional to the amount of money needed to pay for the bowl of noodles. How to apply direct proportion to solve problems Inverse proportion: An increase in one quantity results in a corresponding decrease in another related quantity or vice-versa. Differences between direct and inverse proportion...

When two quantities x and y are in direct proportion, their change may follow a certain pattern such that both x and y increase (or decrease) at the same rate. However, when two quantities are in inverse proportion, an increase or decrease in x results in an increase or decrease in y respectively. Examples of inverse proportion

When a motorist travels at a faster speed, the time taken to cover a certain distance is reduced.

As the amount of money we spent increases, the amount of money we had left decreases.

As the prices of the air tickets increases, the number of people going overseas decreases. How do you know if two quantities are in inverse proportion?

When two quantities, x and y, are in inverse proportion,

xy=k, where k is a constant and k 0, the graph of a inverse proportion would not be a linear line, but of a curved line, called hyperbola.

Another example would be, if xy=k, y=k(1/x). The graph of y against 1/x is part of a straight line passing through the origin, as x1y1=x2y2, where(x1, y1) and (x2, y2) are any two pairs of values of x and y.

X and Y will be in inverse proportion if XY=k, where k is a constant and k 0.

Since xy=k, where k is a constant and k 0 and when one quantity (X) increases, the other related quantity (Y) will decrease, and we can determine that these two quantities are in inverse proportion. 1 x 120 = 120 2x 60 = 120 3 x 40 = 120 4 x 30 = 120 5 x 24 = 120 6 x 20 = 120 How to apply the properties of inverse proportion to solve problems

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