Question

the number line shows two unknown numbers, u and v. is u + v positive or negative? positive negative submit

Explanation:

Step1: Analyze positions of u and v

From the number line, \( u \) is between \( 1 \) and \( v \), and \( v \) is to the right of \( u \) (since the arrow is down, but number line direction: positive is up? Wait, no, standard number line: 0 is middle, 1 is to the right of 0 (up in the image? Wait, the number line has 0 at the top - like, 0 is above 1? Wait, no, the labels: 0 is a tick, then 1 is a tick below 0? Wait, the green dot is \( u \) at some point between 0 and 1? Wait, no, the vertical number line? Wait, the image shows a vertical number line: 0 is at the top, 1 is below 0, \( u \) is a green dot below 1, \( v \) is a blue dot below \( u \). Wait, no, vertical number line: upward is positive? Wait, no, standard number line is horizontal, but here it's vertical. So 0 is at the top, 1 is below 0 (so 1 is positive? Wait, no, 0 is the origin. So if 1 is below 0, that would mean 1 is negative? Wait, no, maybe the number line is drawn vertically with upward as positive. So 0 is the middle, upward is positive, downward is negative. Wait, the labels: 0 is a tick, then 1 is a tick below 0? That can't be. Wait, maybe the number line is horizontal but rotated? No, the text says "the number line shows two unknown numbers, u and v". Let's re - interpret: the number line is vertical, with 0 at the top, 1 at some point below 0, u is a green dot between 0 and 1 (wait, no, the green dot is labeled u, and blue dot is v below u. Wait, maybe the number line is vertical, upward is positive. So 0 is at the top, 1 is below 0 (so 1 is positive? No, 1 should be positive, so upward is positive, 0 is the origin, 1 is above 0? Wait, the image is a bit confusing. Wait, the key is: u and v are both below 0? No, wait, the green dot (u) is between 0 and 1? Wait, no, the labels: 0 is a tick, then 1 is a tick, then u is a green dot, then v is a blue dot. Wait, maybe it's a horizontal number line with 0 on the left, 1 on the right, but the image is rotated. Wait, no, the text: "the number line shows two unknown numbers, u and v". Let's assume it's a horizontal number line (rotated 90 degrees). So 0 is at the left, 1 is to the right of 0 (positive direction). Then u is a green dot to the right of 1? No, the green dot is labeled u, blue dot v to the right of u? Wait, no, the image shows 0 at the top, 1 below 0, u below 1, v below u. So vertical number line: upward is positive. So 0 is the origin, upward is positive, downward is negative. So 1 is below 0 (so 1 is negative? That can't be. Wait, maybe the number line is drawn with 0 in the middle, upward is positive, so 0 is the top, 1 is above 0? No, the labels: 0 is a tick, 1 is a tick below 0. So maybe the number line is reversed: downward is positive. So 0 is at the top, 1 is below 0 (so 1 is positive), u is below 1 (more positive), v is below u (most positive)? No, that doesn't make sense. Wait, maybe the problem is that u and v are both negative? Wait, no, let's think about the sum. If u and v are both negative (since they are below 0), then their sum is negative. Wait, but maybe u is positive and v is negative? Wait, no, the green dot (u) is between 0 and 1 (if 1 is positive), and v is below u (so v is more negative). Wait, no, the key is: on a number line, if u and v are both negative (below 0), then \( u + v \) is negative. Wait, but maybe the number line is such that u is positive (between 0 and 1) and v is negative (below 0)? No, the positions: u is a green dot, v is a blue dot below u. So if the number line is vertical with upward as positive, 0 is at the top, u is below 0 (so u is negative), v is below u (more negative). Then \( u + v \): two negative numbers added together, the sum is negative.

Step2: Determine the sign of \( u + v \)

If both u and v are negative (since they are below 0 on the number line, assuming downward is negative), then the sum of two negative numbers is negative. For example, if \( u=-1 \) and \( v = - 2 \), then \( u + v=-3\) (negative). If \( u=-0.5 \) and \( v=-1 \), then \( u + v=-1.5\) (negative). So regardless of the exact values (as long as both are negative), their sum is negative.

Answer:

negative