Let's break down the expression [tex]\( 7+(-11)+4 \)[/tex] step-by-step and place dots on the number line to represent the resulting sums as we add from left to right.
1. Starting Point:
- Begin by placing a dot on the number line at 7. This represents the first number in the expression.
[tex]\[
\text{Number Line: } \dots \cdots \cdots \mathbf{7} \cdots \cdots \cdots \dots
\][/tex]
2. First Addition:
- Add the second number, [tex]\(-11\)[/tex], to the first number, 7.
- Calculate [tex]\(7 + (-11)\)[/tex]:
- Moving 11 units to the left from 7 gives us:
- [tex]\(7 - 11 = -4\)[/tex]
- Place a dot on the number line at [tex]\(-4\)[/tex].
[tex]\[
\text{Number Line: } \dots \cdots -4 \cdots \cdots \mathbf{7} \cdots \cdots \cdots \dots
\][/tex]
3. Second Addition:
- Add the third number, 4, to the result from the first addition, [tex]\(-4\)[/tex].
- Calculate [tex]\(-4 + 4\)[/tex]:
- Moving 4 units to the right from [tex]\(-4\)[/tex] gives us:
- [tex]\(-4 + 4 = 0\)[/tex]
- Place a dot on the number line at 0.
[tex]\[
\text{Number Line: } \dots \cdots \cdots -4 \cdots \cdots \mathbf{0} \cdots \cdots \mathbf{7} \cdots \cdots \cdots \dots
\][/tex]
Therefore, the intermediate results as we add each number in the given sequence are 7, [tex]\(-4\)[/tex], and 0. The dots placed on the number line at these positions represent the sums [tex]\(7\)[/tex], [tex]\(7 + (-11) = -4\)[/tex], and [tex]\((-4) + 4 = 0\)[/tex].
