In this set of Math Tutorials we cover Ratio and Proportion in details with clear guides, Ratio and Proportion formulas and working examples. Each tutorial includes example questions, a revision guide and supporting Ratio and Proportion calculators
We also provide online Ratio and Proportion Calculators which allow you to calculate specific Ratio and Proportion formula in support of the tutorials or to check and verify your own calculations in support of your Ratio and Proportion homework, math coursework or to help you improve your own understanding so it is easier to teach your children Ratio and Proportion.
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This chapter focuses on four important concepts used when dealing with comparable quantities. They are ratio, rate, proportion and variation.
The first tutorial deals with the definition of ratios and how to express them. The procedure used to calculate a ratio, the method of expression both in numbers and in a number line, scaling up ratios, expressing the inverse ratio, calculating a part of a whole or a part of another part of a whole, how to find the new ratio when one or both quantities change, etc. - all these are concepts and methods explained in the first tutorial of this chapter.
The second tutorial focuses on rates and their difference to ratios. First, the concept of a unit rate, including the associated unit rates is given. Then, we provide the definition of the rate of change, as an important concept used in science, especially in Physics. Some applications of rates in practice including the "golden ratio" are also discussed. This concept is related to the Fibonacci Sequence - a special sequence of numbers that allows us to identify whole numbers used in golden ratios.
The third tutorial focuses on the concept of proportion and its difference with ratio and rate. The two types of proportion and their representation are also explained. We also detail and explain the shape of the graph of each type of proportion.
In the fourth tutorial, we will deal with some properties of proportion. In addition, we will explain the concept of geometric mean and its application in practice.
The last tutorial of this chapter focuses on variation - a concept that is very similar to proportion but which has some differences. Some examples on where to use proportion and where the variation approach is more appropriate are provided. The graph of variation is another important element discussed in this tutorial. Then, the three types of variation accompanied with a number of examples for a better understanding are introduced.
The following Math Calculators are provided in support of the Ratio and Proportion tutorials.