Which of the following is not true
(a) rational numbers are closed under addition
(b) rational numbers are closed under subtraction
(c) rational numbers are closed under multiplication
(d) rational numbers are closed under division

Solution:

When we add any two rational numbers, the sum is a rational number.

When we subtract any two rational numbers, the difference is a rational number.

When we multiply two rational numbers, their product is a rational number.

However, when we divide rational numbers, not always their quotient is a rational number.

Consider the rational numbers 5 and 0. When we divide 5 by 0, 5/0 doesn’t exist, as per the definition of a rational number. We cannot have the denominator 0. Thus rational numbers are not closed under division.

✦ Try This: Find A ÷ B. Given A = 17/23 + 12/13, B = 7/8 - 3/5

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 1

NCERT Exemplar Class 8 Maths Chapter 1 Problem 4

Which of the following is not true (a) rational numbers are closed under addition, (b) rational numbers are closed under subtraction, (c) rational numbers are closed under multiplication, (d) rational numbers are closed under division

Summary:

Among the statements given, the rational numbers are closed under division is not true

☛ Related Questions:

• Subtraction of rational numbers is commutative. Is the given statement true or false
• -3/4 is smaller than -2. Is the given statement true or false
• 0 is a rational number. Is the given statement true or false