RS Aggarwal Solutions Class 7 Chapter-4 Rational Numbers (Ex 4C) Exercise 4.3

RS Aggarwal Solutions

RS Aggarwal Solutions Class 7 Chapter-4 Rational Numbers (Ex 4C) Exercise 4.3

RS Aggarwal Solutions Class 7 Chapter-4 Rational Numbers (Ex 4C) Exercise 4.3 - Free PDF

Free PDF download of RS Aggarwal Solutions Class 7 Chapter-4 Rational Numbers (Ex 4C) Exercise 4.3 solved by Expert Mathematics Teachers on Vedantu.com. All Exercise 4.3 Questions with Solutions for Class 7 Maths RS Aggarwal are provided to help you to revise the complete Syllabus and score more marks.

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Introduction of Rational numbers

The rational numbers include all whole numbers, all fractions, and all decimals. Since decimals are not rational, the set of all rational numbers is a proper subset of the set of all real numbers. Examples: 2/7, −19/12, 0, 1, 10/10, 2.0

Every rational number can be written as a fraction with an integer numerator and another integer denominator or as a decimal that either terminates or repeats endlessly. The set of rational numbers is closed under addition, subtraction, multiplication, and division. That means that the operations of addition, subtraction, multiplication, and division can be performed on any two rational numbers and will always produce a rational number as a result. The set of rational numbers is also commutative and associative. The addition and subtraction of rational numbers work the same way as for integers. Both operations are commutative, meaning that the order of two rational numbers does not matter in an addition or subtraction problem. Rational numbers are the same as the set of all integers. Numbers in this set can result from the division of two integers. For example, 25/4 = 6 because four goes into 25 twice with a remainder of 1. The quotients are also integers between 0 and 3 inclusive according to the division rules.

Properties of rational numbers mentioned in RS Aggarwal Solutions Class 7 Chapter-4 Rational Numbers (Ex 4C) Exercise 4

The addition and subtraction of rational numbers are associative and commutative. The multiplication and division of rational numbers are associative and commutative. Finally, the set of rational numbers is closed under these operations. This means that any two rational numbers, when added, subtracted, multiplied, or divided, will yield another rational number and will not result in an irrational number. Properties of rational numbers are very handy when working with fractions. For example, if we want to simplify the fraction 4/9, we can use the properties of rational numbers to rewrite it as 2/3. And if we want to multiply two fractions together, we can use the associative and commutative properties of multiplication to do so. This will make the process of multiplying fractions much simpler.

FAQs on RS Aggarwal Solutions Class 7 Chapter-4 Rational Numbers (Ex 4C) Exercise 4.3

1. What is a rational number according to RS Aggarwal Solutions Class 7 Chapter-4 Rational Numbers (Ex 4C) Exercise 4?

A rational number is a number that can be expressed as the quotient or ratio of two integers, and that is not an irrational number. The set of all rational numbers includes the natural numbers, as well as all the real numbers that are not irrational. Every rational number can be written as a fraction with an integer numerator and another integer denominator or as a decimal that either terminates or repeats endlessly. The set of rational numbers is closed under addition, subtraction, multiplication, and division. That means that the operations of addition, subtraction, multiplication, and division can be performed on any two rational numbers and will always produce a rational number as a result. The set of rational numbers is also commutative and associative.

2. What are examples of rational numbers mentioned in RS Aggarwal Solutions Class 7 Chapter-4 Rational Numbers (Ex 4C) Exercise 4?

Every rational number can be expressed as a fraction with an integer numerator and another integer denominator or as a decimal that either terminates or repeats endlessly. Some examples include 1/2, -5/28, -528/943, and π. A rational number can also be represented in radicals form as follows: √2, √3, √5, etc., are all rational numbers. Notice that when we take the square root of a perfect square, we always get a rational number. For example, √9 = 3, because 3 squares is 9. And √25 = 5 because five squared is 25. Vedantu provides the latest RS Aggarwal Solutions to the students so that they can score good marks in their examinations.

3. Can a rational number be irrational?

No, a rational number cannot be irrational. A rational number is a number that can be expressed as the quotient or ratio of two integers, and that is not an irrational number. The set of all rational numbers includes the natural numbers, as well as all the real numbers that are not irrational. Every rational number can be expressed as a fraction with an integer numerator and another integer denominator or as a decimal that either terminates or repeats endlessly and can never be an irrational number.

4. What is a terminating decimal according to RS Aggarwal Solutions Class 7 Chapter-4 Rational Numbers (Ex 4C) Exercise 4?

A terminating decimal is a decimal that eventually reaches either 0 or 1, after which it stops having digits and will not change anymore. For example, 123/100 = 1/99 … 3; another way to write this fraction would be 0.0123, and the decimal in this fraction goes on forever but eventually reaches 0. The decimal 2/3 = 0.6666…; the decimal in this fraction goes on forever but eventually reaches 1. terminating decimals are very helpful when working with fractions because we can convert any fraction to a terminating decimal by dividing the numerator by the denominator. For example, if we want to convert the fraction 5/8 to a decimal, we would divide 5 by 8 to get 0.625.