Question

We can say that rational numbers are closed under addition, subtraction and multiplication. Is it true or false​

Answer 1

True.

The rational numbers are "closed" under addition, subtraction, and multiplication.

Answer 2

True

The sentence is true because rational numbers show the closure property under addition, subtraction and multiplication.

Example:

Let us take two rational numbers 1/2 and 1/4 respectively.

For Addition –

$\frac{1}{2} + \frac{1}{4} = \frac{2 + 1}{4} = \frac{3}{4}$

3/4 is also a rational number. Thus proved.

For Subtraction –

$\frac{1}{2} - \frac{1}{4} = \frac{2 - 1}{4} = \frac{1}{4}$

1/4 is also a rational number. Thus proved.

For Multiplication –

$\frac{1}{2} \times \frac{1}{4} = \frac{1 \times 2}{2 \times 4} = \frac{1}{8}$

1/8 is also a rational number. Thus proved.

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