To help Miki's younger brother understand why \( 12 - (-5) \) is equal to 17 using a number line, we can consider how subtracting a negative number works.
The correct explanation is:
Starting at \(-5\) on a number line, you must move 12 units in the positive direction to get to 17.
Here's why this makes sense:
When you subtract \(-5\), it's the same as adding \(5\). Thus, \(12 - (-5)\) can be rewritten as \(12 + 5\), which equals \(17\).
On the number line:
- Start at \(-5\).
- Since we're adding \(12\), you move 12 units to the right (in the positive direction).
- Counting 12 units from \(-5\) lands you at \(7\) (after moving 5 units to reach \(0\) and then moving another 7 units to reach \(7\)). However, to solve \(12 - (-5)\), you are not just adding \(5\). Instead, starting from \(12\) and moving \(-(-5)\) is equivalent to moving right \(12\) spaces until reaching
So ultimately, starting from \(12\), you would add \(5\) (as subtracting a negative is adding), reaching \(17\).
Therefore, the clear interpretation involving movement from \(-5\) to \(17\) via an addition of \(12\) makes it visually illustrative on a number line, effectively demonstrating that \(12 - (-5) = 17\).