RD Sharma Class 11 Solutions Chapter 31 - Mathematical Reasoning (Ex 31.4) Exercise 31.4 - Free PDF

Mathematical Reasoning problems are for the practice of mental balancing, as they require not only the ability to think logically but also a knowledge of mental arithmetic. The use of a set of rules for the mental calculations of interest rates and exchange rates would result in a better understanding of mental calculations, especially when the subject is approached in the form of numerical problems. 

Mental calculations are often made in connection with the solution of problems with numbers. These problems are of various kinds and types but are more appropriately termed as numerical problems. The numerical problems can be dealt with separately.

These problems are not of much use in the classroom. The teacher may need to ask the students to solve problems with numbers on occasions but an individual basis. For this, students need to understand the mathematical concepts and rules associated with the problems.

They should also be able to solve problems without getting them from books. They should apply the rules to solve the problems before making solutions. They may have to apply the rules in the real world, while they are solving a problem. Most problems are mathematical and students may be required to deal with such problems. When students solve mathematical problems in the class, they are often required to have a clear understanding of the concept involved.

They are required to learn the concepts of such problems before solving them. The rules involved in the problems should also be understood so that they are applied correctly. For many problems, the solution may be achieved from the available books, but a student may need to understand the concept before making the solution.

The mental math and numerical problems help in improving the understanding of mathematics in general, since mental math helps in understanding the mathematical processes while solving numerical problems helps in the improvement of the mental ability. Students should attempt mental math and solve numerical problems when they have problems with numbers in daily life. It helps in the understanding of concepts related to mental arithmetic.

This will also help the students to deal with problems related to addition, subtraction, multiplication, division, etc. Students may have to solve such problems on an individual basis, while they are solving the problem. A problem of similar nature may be repeated and the solutions should be checked. These checks help in improving the mental ability of the students. While solving a problem, they should also remember the steps involved in solving it.

At times, mathematics can be used in real life. Students should be able to think of an appropriate solution when the problem involves numerical problems. They need to be familiar with the mathematics involved in the problem. They should be able to recognize the concept and rules associated with such problems. They should be able to apply the rules to solve problems while in real life. This may involve mathematical operations and mental arithmetic.

The numerical operations must be correct and the mathematics must be applied to solve the problem. Students may also need to think of several real-life situations and find the answer by considering different aspects of the problem. These aspects are very useful in the development of the mathematical thinking of the students. Teachers should help the students to develop such thinking in the classroom.

When a student needs to solve such problems, the teacher must make sure that there are several objects and numbers available, which may help the student. Sometimes, the teacher must solve a problem while students are working on it. It is necessary to teach students in the same manner as in the school environment.

Students must be asked questions while solving a problem. Each question should have a solution or each step should be explained. In this way, the problem is solved with the help of a question. Mathematics is used by teachers, students, mathematicians and businesspeople. It is also used in scientific research.

Mathematical reasoning is applied for the practical purpose of solving problems. The study of the problems should be used as an exercise to develop the power of thought as well as the ability to apply the principles of mental calculation. For this purpose, problems from simple to complex should be solved. The problem-solving practice should also be introduced in the study, as it helps in developing the student's ability to develop the power of thought and application of mathematical principles.