Use unmarked number lines to evaluate these expressions:

Question

Homi · Accepted Answer

Understand the Question

Rules for moving on a number line:
- Adding a negative number or subtracting a positive number means moving to the left.
- Subtracting a negative number is equivalent to adding a positive number, meaning we move to the right ( $a - (-b) = a + b$ ).

(a) Evaluate $-125 + (-30)$

Step 1 · Evaluate on Number Line

Start at $-125$ . Adding $-30$ means moving $30$ units to the left. Diagram 1

\begin{aligned} -125 + (-30) &= -125 - 30 \\ &= -155 \end{aligned}

Answer

(a) $-155$

(b) Evaluate $+105 - (-55)$

Step 1 · Evaluate on Number Line

Start at $+105$ . Subtracting $-55$ is equivalent to adding $55$ , so move $55$ units to the right. Diagram 2

\begin{aligned} +105 - (-55) &= +105 + 55 \\ &= +160 \end{aligned}

Answer

(b) $+160$

(c) Evaluate $+80 - (-150)$

Step 1 · Evaluate on Number Line

Start at $+80$ . Subtracting $-150$ is equivalent to adding $150$ , so move $150$ units to the right. Diagram 3

\begin{aligned} +80 - (-150) &= +80 + 150 \\ &= +230 \end{aligned}

Answer

(c) $+230$

(d) Evaluate $-99 - (-200)$

Step 1 · Evaluate on Number Line

Start at $-99$ . Subtracting $-200$ is equivalent to adding $200$ , so move $200$ units to the right:

\begin{aligned} -99 - (-200) &= -99 + 200 \\ &= +101 \end{aligned}

Answer

(d) $+101$

Common Mistakes

Double Negative Sign Error: Forgetting that subtracting a negative number turns into addition: $-(-b) = +b$ .
Wrong Direction on Number Line: Moving left instead of right when subtracting a negative integer.

Question 14