SOLUTION: what is an interger in algebra and can you give me an example?

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An integer is a whole number. It can be a positive number (+7) or a negative number (-7). You can think of an integer as a "counting" number. When you count some things (like your socks) you associate each sock with an integer.
1, 2, 3, etc.
Notice you cannot count "half a sock." If you need to count parts of things, you need the fractions, also called rational numbers because they are the ratio of two integers (like 3/7). Anyway, that's another story....