F4 Mathematics Direct and Inverse Proportion

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To determine and use equations involving a constant a proportionality, for directly and inversely proportional relationships.

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In our day-to-day life, we frequently encounter situations where the variation in values of a certain quantity is influenced by the variation in values of the other quantity.

​Introduction

​The definition of direct proportion states that "When the relationship between two quantities is such that if we increase one, the other will also increase, and if we decrease one the other quantity will also decrease, then the two quantities are said to be in a direct proportion".

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​Can you think of any real life examples?

​"Two quantities are in direct proportion if they both increase/decrease at the same rate. When one quantity is zero, so is the other."

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​If two quantities, y and x, are in direct proportion to each other, we write:

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​This can also be read as 'y varies directly as x'

​Remember, to ALWAYS write the equation linking the two variables FIRST.

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• ​Substitute the given values to find the constant.

• ​Write the linking equation.

​Once you know the value of the constant, i.e. k, AND you have written your equation linking the variables, you will be able to find unknown variables.

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​Let's look at a video. Just follow first and you will be given time to write after.

Volume 1

Page 319

Ex. 7k

Questions 1, 6, 8, 4(a)

aka Inverse Variation​

When the value of one quantity increases with respect to decrease in other or vice-versa, then they are said to be inversely proportional. 

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It means that the two quantities behave opposite in nature. For example, speed and time are in inverse proportion with each other. As you increase the speed, the time is reduced.

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The other terms used here for this type of proportion are inverse proportion or varying inversely or inverse variation or reciprocal proportion.

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​Can you think of any other examples?

Volume 1

Page 319

Ex. 7k

Questions 2, 3b, 7