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Closure Property of Rational Numbers Video Lecture | Mathematics (Maths) Class 8

FAQs on Closure Property of Rational Numbers Video Lecture - Mathematics (Maths) Class 8

1. What is the closure property of rational numbers?

Ans. The closure property of rational numbers states that if we perform any operation (addition, subtraction, multiplication, or division) on two rational numbers, the result will also be a rational number.

2. Can you provide an example to illustrate the closure property of rational numbers?

Ans. Sure! Let's consider the rational numbers 2/3 and 5/6. If we add these two numbers, we get (2/3) + (5/6) = (4/6) + (5/6) = 9/6, which is a rational number. This example demonstrates that the sum of two rational numbers is also a rational number, proving the closure property.

3. Does the closure property hold for subtraction of rational numbers as well?

Ans. Yes, the closure property holds for subtraction of rational numbers too. Let's take an example. If we subtract the rational number 2/3 from 5/6, we get (5/6) - (2/3) = (5/6) - (4/6) = 1/6, which is a rational number. Thus, the closure property holds for subtraction as well.

4. Is the closure property applicable to multiplication of rational numbers?

Ans. Yes, the closure property is applicable to multiplication of rational numbers. For instance, if we multiply the rational numbers 3/4 and 2/5, we get (3/4) * (2/5) = 6/20, which can be simplified to 3/10. This result is a rational number, confirming the closure property for multiplication.

5. Does the closure property hold for division of rational numbers too?

Ans. No, the closure property does not hold for division of rational numbers. There may be cases where dividing two rational numbers results in an irrational number. For example, if we divide 3/4 by 2/5, we get (3/4) ÷ (2/5) = (3/4) * (5/2) = 15/8, which is not a rational number. Therefore, the closure property does not apply to division of rational numbers.

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