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Give properties of addition and subtraction for whole numbers.
Properties of addition for whole numbers:
i. Closure property for addition: When we add two whole numbers we get a whole number.
For example, $2+3=5$. Here, 2, 3 and 5 are all whole numbers.
ii. Commutative property for addition: We can add whole numbers in any order.
For example, $2+3=3+2=5$
iii. Associative property for addition: When we add two or more whole numbers grouped in any order we get the same result.
For example, $(2+3 )+5 = 2+(3+5)=10$
iv. Identity property for addition: When you add a zero to any whole number we get the same number.
For example, $2+0=2+0=2$
Properties of Subtraction:
i. If a and b are two whole numbers such that $a > b$ or $a = b$, then $a – b$ is a whole number. If $a < b$, then subtraction $a – b$ is not possible in whole numbers.
ii. The subtraction of whole numbers is not commutative, that is, if a and b are two whole numbers, then in general $a – b$ is not equal to $(b – a)$.
iii. If a is any whole number other than zero, then $a – 0 = a$ but $0 – a$ is not equal to a.
iv. The subtraction of whole numbers is not associative. That is, if a, b, c are three whole numbers, then in general $a – (b – c)$ is not equal to $(a – b) – c$.
v. If a, b and c are whole numbers such that $a – b = c$, then $b + c = a$.
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