Direct proportion
Direct proportion occurs when one quantity increases in the same proportion as another quantity. For example, A is directly proportional to B. An example of direct proportion is when B = 4 and A = 0.8. What is A when B is 3? A and B are directly proportional.
K is the constant in direct proportion. Direct proportion with squares and roots can be seen in the example where w is directly proportional to r3. For instance, if w = 43.2g and v = 3mm, we can use the equation w = Kv3 to solve for K and then find the direct proportion relationship as w = 1.6v³.
Another example of direct proportion with squares and roots is when p is directly proportional to the square root of m. For instance, when m = 36, and p = 18, we can solve for K and find the relation as p = 3√m.
Inverse proportion
Inverse proportion occurs when one quantity increases, and the other decreases in the same proportion. For example, y is inversely proportional to x. So, if x = 6 and y = 8, we need to find y when x = 9 using the formula y = k/x. In this case, we find that y = 5.33 to 3sf.
Another example of inverse proportion is when the square of a is inversely proportional to the square of b. For instance, if a = 12 and b = 2, the relation can be expressed as a = k/b².
Written proportion questions such as man hours
For example, if 3 mechanics can service a car in 40 mins, how long would it take 5 mechanics? When solving this type of problem, it's necessary to assume that people work at the same rate for the same job, and that more people means a shorter time due to inverse proportion.
Graph to show proportions
Graphs can be used to depict proportions. In a direct proportion, the graph forms a line that passes through the origin. For example, y is directly proportional to the square root of x can be depicted as y = k√x. Similarly, in an inverse proportion, the graph is a curve. An example of this is y = k/x².
