Fractions are everywhere.
They are so common that we even invented three other ways to represent fractions in everyday life. We have decimals, percentages, and ratios – all of which represent the process of dividing integers by other integers in different ways. And all of these show up on standardized tests, and the mastery of all of them is required to ace the quant section.
This book is dedicated to ratios. We encounter ratios in many common everyday scenarios:
1. Recipes: The relative proportions of ingredients in cooking recipes are often denoted through ratios rather than through fractions, decimals, or percentages. This convention makes it very necessary to master the ratio concept as early as possible, because most of us are likely to look up a recipe at some point, and making an error could render our precious meals inedible.
2. In mixtures in general: Whether we need to mix paints and water, or different chemicals in a school chemistry experiment, the relative proportions of the elements of a mixture are usually expressed in the form of ratios. This is another reason to get the fundamentals right.
This book is divided into three major sections. In the first section, I give the reader a thorough grounding in the notation of the ratio, and how to quickly convert among ratios, fractions, decimals, and percentages.
In the second section, I introduce a few solved examples in each of the main types of ratio problems that are encountered in standardized tests and in daily life, to ease the reader into the problem solving tools needed for this important concept.
Finally, I conclude with a series of carefully chosen exercise drills, to cement the skills learnt. If you go through even 30% of the practice problems in this book, you will find that calculating the required quantities whenever you are given a ratio becomes second nature, and that you are easily able to do these arithmetic computations both quickly and accurately.
Therefore, this can be used as both a book of concepts and exercises, and as a mental mathematics book; there is something for every reader who wants to master basic mathematical concepts. I wish you the best!
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