To solve the expression [tex]\(12 + (-18)\)[/tex] and show the concept of zero pairs, we can break down the problem step-by-step:
1. Start with Initial Values:
- We have [tex]\(12\)[/tex] (positive) and [tex]\(-18\)[/tex] (negative).
2. Create Zero Pairs:
- A zero pair is a pair of one positive and one negative number that sum to zero. For example, [tex]\(1\)[/tex] and [tex]\(-1\)[/tex] form a zero pair because [tex]\(1 + (-1) = 0\)[/tex].
3. Form Zero Pairs from [tex]\(12\)[/tex] and [tex]\(-18\)[/tex]:
- We can match [tex]\(12\)[/tex] positive units with [tex]\(12\)[/tex] of the [tex]\(-18\)[/tex] negative units to form zero pairs.
- [tex]\(12 + (-12) = 0\)[/tex]. This means we used up [tex]\(12\)[/tex] positive units and [tex]\(12\)[/tex] negative units out of the [tex]\(-18\)[/tex].
4. Calculate Remaining Units:
- After forming zero pairs, what is left from [tex]\(-18\)[/tex] is [tex]\(-6\)[/tex] (because [tex]\(18 - 12 = 6\)[/tex] and it remains negative since we have more negative units).
- Therefore, we are left with [tex]\(-6\)[/tex].
5. Final Answer:
- After canceling out the zero pairs, the remaining value is [tex]\(-6\)[/tex].
Thus, the result of the expression [tex]\(12 + (-18)\)[/tex] is:
[tex]\[
12 + (-18) = -6
\][/tex]
In terms of zero pairs, we canceled out all [tex]\(12\)[/tex] positive units with [tex]\(12\)[/tex] of the [tex]\(-18\)[/tex] negative units, leaving us with [tex]\(-6\)[/tex] negative units. This method shows how the positive and negative numbers interact to form zero pairs and the resulting sum.
