Question

Miki is trying to help her younger brother understand why 12−(−5)
is equal to 17. She draws a number line to help. Explain how a number line could help to show that 12−(−5)
is equal to 17. (1 point)
Responses

Starting at −5
on a number line, you must move 12 units in the positive direction to get to 17.
Starting at negative 5 on a number line, you must move 12 units in the positive direction to get to 17.

Starting at 12 on the number line, you must move 17 units in the negative direction to get to −5
.
Starting at 12 on the number line, you must move 17 units in the negative direction to get to negative 5 .

Starting at 12 on the number line, you must move 5 units in the negative direction to get to 7.
Starting at 12 on the number line, you must move 5 units in the negative direction to get to 7.

Starting at −5
on the number line, you must move 17 units in the positive direction to get to 12.

Answer 1

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:

1. Start at \(-5\).
2. Since we're adding \(12\), you move 12 units to the right (in the positive direction).
3. 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 \(12 - (-5) = 17\).