NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - Fill in the Blanks
Question 120

Question. 120

Whole numbers are closed under ____ and under ____.

Addition and multiplication

What are whole numbers?
They are the numbers \(0, 1, 2, 3, \ldots\). We write this set as \(W\).
Meaning of “closed under”
If we pick any two numbers from a set and perform an operation, the answer should stay in the same set.
Symbolically, if \(a, b \in W\), then after the operation the result is also in \(W\).
Check addition
Take any two whole numbers \(a\) and \(b\).
\(a + b\) is also a whole number.
Example: \(3 + 5 = 8\), and \(8 \in W\).
Another: \(0 + 7 = 7\), and \(7 \in W\).
So, whole numbers are closed under addition: \(a, b \in W \Rightarrow a + b \in W\).
Check multiplication
Take any two whole numbers \(a\) and \(b\).
\(a \times b\) is also a whole number.
Example: \(4 \times 6 = 24\), and \(24 \in W\).
Another: \(0 \times 9 = 0\), and \(0 \in W\).
So, whole numbers are closed under multiplication: \(a, b \in W \Rightarrow a\times b \in W\).
Helpful note (why not others?)
Subtraction can leave the set: \(5 - 7 = -2\) (not a whole number).
Division can leave the set: \(7 \div 2 = 3.5\) (not a whole number).
This is why the blanks are addition and multiplication.