Higher Algebra Hall & Knight Ratio (Chapter 1) Solutions

Hall and Knight Higher Algebra Solutions for Chapter 1 ‘Ratio’ are created by Maths experts at Instasolv to guide you for JEE Maths preparations. Our solutions comprise of all the vital concepts of the chapter ‘ratio’ of Hall & Knight Algebra Book which includes commensurable quantities, incommensurable quantities, inequality ratio and fraction related problems. The solutions contain detailed theory explanations to help you develop all your basics from the chapter. You will also learn about the concepts of linear equations, eliminants and cross multiplication of ratio from these solutions.  

Chapter 1 ‘Ratio’ of Higher Algebra by Hall and Knight Book with solutions has 28 questions. Once you solve these questions you will learn to tackle problems which deal with antecedents, consequents, laws of fraction, equivalent fractions, sub duplicate ratios, triplicate ratios and fraction series. Our solutions present a very engaging approach towards the revision and practice of these concepts and will help you in preparation for tough competitive exams like JEE. 

Instasolv’s solutions for Higher Algebra By H.s. Hall and S.r. Knight Chapter 1 has been formulated to ensure that you do not have to struggle with confusions and all your queries are resolved at a single platform. Our subject experts have made sure that get a productive, engaging and stress-free learning experience. With the direction of our dedicated team and your continuous efforts, nothing can come in your way of scoring high and achieving your goal.

Important Topics for Hall and Knight Higher Algebra Solutions Chapter 1: Ratio


Ratio is a topic that you would have already tackled in your junior classes. In Hall & Knight Algebra Book Chapter 1, you will again encounter some familiar concepts and some new ones. Here, you will revise the basic definition of ratio, which is a relationship that exists between two quantities of the same kind. 

The ratio can be explained as the relation which one quantity bears to another one of the similar kind such that it expresses comparison based on multiple, fractions, parts or other. You will also get to know that ratios are abstract quantities as they are an expression of the number of times one quantity is contained in another. 

Antecedent and Consequent 

In this chapter, you will also learn about the terms antecedent and consequent. Taking an example of C : D, which is a representation of the ratio of C to D. Here we can refer to C and D as the terms of the ratio. And amongst these two terms which express a ratio, whichever terms appear first is known as an antecedent and the term which appears second is known as the consequent. The chapter has numerous examples where the use of these terms has been explained and their importance has been emphasized. You will come across many such terms in the chapter and will learn to use them while deriving your solutions. 

Commensurable Ratios and Incommensurable Ratios 

The chapter ‘ratio’ of Higher Algebra by Hall & Knight deals with the terms commensurable ratios and incommensurable ratios. Basically, in case if the given ratios belonging to any two quantities can be exactly expressed by the ratio of any two integers, those quantities are termed as commensurable. 

Any quantity which does not follow the given conditions falls in the other category of incommensurable ratios. These terms play a vital role in organizing and deriving answers to the problems discussed in the chapter. 

Rule of Cross Multiplication 

One of the key fundamentals of this chapter is the rule of cross multiplication. This rule is used in order to solve problems that have two different equations containing three variable quantities in their first degrees. The given equations are written in a fractional form and after solving them they are further arranged in a symmetrical manner. The terms of coefficients of the equations are analysed and the respective coefficients of x, y and z are written separately. 

These coefficients are then multiplied across and the final product obtained is the answer. This is a very important concept and will be utilized in numerous questions from the unsolved examples. It is also important from the perspective of competitive exams. You will get to understand this concept through the detailed examples that have been listed in the chapter. 

Exercise-wise Discussions of Higher Algebra by Hall and Knight Solutions Chapter 1: Ratio

  • Hall & Knight Algebra Mathematics book with solutions for Chapter 1 ‘Ratio’ has just one exercise with 28  unsolved example questions 
  • All these questions are diverse in nature and help you understand the new concepts of ratios. 
  • The exercise begins with a very simple question which has three parts and you are required to derive their duplicate and sun duplicate ratios by compounding them.
  • There are some problems which require you to equate the given ratios in order to find the variable which has been expressed as one of the terms from the question. 
  • There are questions which require you to simplify the terms in order to prove that the right-hand side value is equal to that given at the left-hand side. 
  • Some of the questions make use of the concept of eliminant and simplification
  • The exercise also has questions based on cross multiplications rule and coefficient analysis.

Overall the entire exercise is very engaging and covers all the topics that have been tackled in the chapter. The questions range from simple to complicated and aim at providing you with a thorough insight towards the fundamentals of ratio. 

Why Use Solutions for  Higher Algebra by Hall and Knight Solutions Chapter 1: Ratio by Instasolv?

  • Our team of subject specialists has ensured that all the solutions for Elementary Algebra and Higher Algebra by Hall & Knight book are framed to address the questions with a detailed and student-friendly approach.
  • Our solutions for Hall and Knight Higher Algebra Chapter 1 ‘Ratio’ cover all the corners and questions from the chapter.
  • Our solutions are formulated by experienced and skilled individuals, who cater to your study requirements in a reliable and helpful manner. 
  • We have ensured that all answers are provided according to the guidelines of the latest syllabus for JEE Maths.
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