Envision Math 2.0: Grade 8, Volume 1
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Exercise 3 Page 5

Consider each part of the defined term one at a time.

integer

Practice makes perfect

We want to complete the following sentence.

A(n) is either a counting number, the opposite of a counting number, or zero.

We are asked to complete it with one of the terms from the given box.

To find which of these is a term defined by the sentence, let's consider each part of the definition one at a time. We are told that it can be a counting number. When we count something, we start from 1, then we say 2, then 3, and so on. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... We are also told that it can be the opposite of a counting number. An opposite number is found by changing the sign of a number. Let's change the signs of the counting numbers that we listed so that we can see more numbers that fit the given definition. -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, ... Finally, we know that this term can also be 0. We can see, that the term describes all negative numbers, all positive numbers, and zero. It does not include numbers with non-zero decimals. We call a number that is either a counting number, the opposite of a counting number, or zero an integer. Now, we can complete the given sentence.

An integer is either a counting number, the opposite of a counting number, or zero.