### Theory:

Adding $$0$$ (zero) and multiplying $$1$$ (one) to any whole number will not change the result (or) the sum. This is called the identity property of whole numbers.
Identity property of $$0$$ (zero):
Identity property of $$0$$ (zero) states that any number added or subtracted with $$0$$ (zero) remains the same.
Consider $$a$$ is a whole number then:
• $$a + 0 = a$$
• $$a - 0 = a$$
Example:
i) $$10 + 0 = 10$$

ii) $$8 - 0 = 8$$
Identity property of $$1$$ (one):
Identity property of $$1$$ states that any number multiplied or divided by $$1$$ remains the same.
Consider $$a$$ is a whole number then:

$\begin{array}{l}\left(\phantom{\rule{0.147em}{0ex}}a×1\phantom{\rule{0.147em}{0ex}}\right)\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}a\\ \\ \left(\phantom{\rule{0.147em}{0ex}}a÷1\phantom{\rule{0.147em}{0ex}}\right)\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}a\end{array}$
Example:
i) $$10 × 1 = 10$$

ii) $$10 ÷ 1 = 10$$
Remember that $$0$$ (zero) is called an additive identity, and $$1$$ (one) is called as a multiplicative identity.