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For integers
Integers are both positive & negative numbers & zero
… −3, −2, −1, 0, 1, 2, 3,…..
Operation | Closed or not | |
Addition |
3 + 5 = 8
8 is an integer Also, –1 + 0 = –1 –1 is an integer So, integers are closed under addition |
So, if we add any two numbers,
we get an integer So, it is closed |
Subtraction |
3 – 5 = –2
–2 is an integer Also, –1 – 0 = –1 –1 is an integer So, integers are closed under subtraction |
So, if we subtract any two numbers,
we get an integer So, it is closed |
Multiplication |
3 × 5 = 15
15 is an integer Also, –1 × 0 = 0 0 is an integer So, integers are closed under multiplication |
So, if we multiply any two numbers,
we get an integer So, it is closed |
Division |
3 ÷ 5 = 3/5
But, 3/5 is not an integer So, integers are not closed under division |
So, if we divide any two numbers,
we do not get an integer So, it is not closed |