Olivia has recently learned about the properties of integers. She believed that 0 is the identity element for the subtraction of integers as well as we can subtract 0 from any integer to get the same integer as the answer. Is she right? State the reason.
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Answer:
The given expression is (-20 × 15) + (-20 × 18). It can be solved by using the distributive property of integers, which states (a × b) + (a × c) = a × (b + c). So, here we can take (-20) as common out of both the terms. We get -20 × (15 + 18).
⇒ - 20 × 33
= - 660
Therefore, (-20 × 15) + (-20 × 18) = -660.
Answer:
0 is not the identity element for Subtraction.
So, Olivia is not right. Let us look at the reason. It is true that if we subtract O from any integer, we get the same integer as the answer. But to make it an identity element, its reverse should also be true. If we subtract any number from 0, we get its additive inverse. This implies, if 'a' is any integer, then a - 0 = a, but 0 - a = -a. Therefore, O is not the identity element for subtraction.
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