Question

solve. 2 jessie uses the number line below to help write $-2 + (-4)$ as a subtraction problem. a. what is wrong with jessie’s number line? number line with ticks at -6, -4, -2, 0, 2, 4, 6, 8, 10; a dot near -2 and a downward arrow b. write the subtraction problem and the answer.

Explanation:

Part a: What's wrong with Jessie's number line?

Step1: Analyze the operation

The operation is \(-2 + (-4)\), which is adding a negative number. When adding a negative number, we move left on the number line (since negative numbers represent moving in the negative direction).

Step2: Check the direction

Jessie's arrow is pointing down (or right? Wait, the number line has positive to the right, negative to the left. Wait, the number line has marks at -6, -4, -2, 0, 2, 4, 6, 8, 10. The starting point is at -2? Wait, no, the dot is at -2? Wait, the arrow is pointing down (but on a number line, direction should be left/right). Wait, actually, for \(-2 + (-4)\), we start at -2 and move 4 units to the left (because we're adding -4, which is equivalent to subtracting 4). But Jessie's arrow is pointing in the positive direction (right) or maybe the direction is wrong. Wait, the number line: starting at -2, adding -4 should move left (towards more negative numbers), but the arrow is pointing towards positive numbers (since the arrow is going from -2 towards 2, 4, etc.). So the direction of the arrow is incorrect. When adding a negative number, we should move left (decreasing the value), but the arrow is moving right (increasing), which is wrong.

Step1: Convert addition to subtraction

Using the rule \(a + (-b)=a - b\), for \(-2 + (-4)\), we have \(a = -2\) and \(b = 4\), so it becomes \(-2 - 4\).

Step2: Calculate the result

To calculate \(-2 - 4\), we can think of it as starting at \(-2\) and moving 4 units to the left (since subtracting 4 means moving in the negative direction). \(-2 - 4=-6\).

Answer:

For the operation \(-2 + (-4)\), we start at \(-2\) and add \(-4\) (which means moving 4 units in the negative direction, i.e., to the left on the number line). Jessie’s arrow is pointing in the positive (right) direction, which is incorrect. She should move left from \(-2\) (towards \(-6\)) instead of right.

Part b: Write the subtraction problem and the answer

First, recall that adding a negative is equivalent to subtracting the positive: \(a + (-b)=a - b\). So \(-2 + (-4)\) can be written as a subtraction problem: \(-2 - 4\).