Question

plot a point at $-2\frac{1}{4}$ on the number line.

Explanation:

Step1: Understand the number

First, convert the mixed number \(-2\frac{1}{4}\) to an improper fraction or decimal. \(-2\frac{1}{4}=-\frac{9}{4}=-2.25\).

Step2: Analyze the number line

The number line has a mark at \(-3\), and the next marks are evenly spaced. The distance between \(-3\) and the next mark (let's say \(-2\)) is 1 unit. So each small interval between the ticks should represent \(\frac{1}{4}\) of a unit? Wait, no, let's see the spacing. From \(-3\) to the next tick (let's assume the ticks are at integers first, but wait, the number line has ticks at -3, then the next ones. Wait, actually, the number line shown has ticks at -3, then the next tick would be -2, but between -3 and -2, we can divide into 4 parts? Wait, no, \(-2\frac{1}{4}\) is between \(-2\) and \(-3\)? Wait, no: \(-2\frac{1}{4}\) is equal to \(-2 - \frac{1}{4}\), so it's between \(-3\) and \(-2\)? Wait, no: \(-3 < -2\frac{1}{4} < -2\). So between \(-3\) and \(-2\), the distance is 1 unit. To plot \(-2\frac{1}{4}\), we need to find the position 1/4 of the way from \(-3\) to \(-2\)? Wait, no: from \(-3\) to \(-2\) is 1 unit. \(-2\frac{1}{4}\) is \(\frac{1}{4}\) unit away from \(-2\) towards \(-3\), or \(\frac{3}{4}\) unit away from \(-3\) towards \(-2\). Wait, let's calculate the position. The value \(-2\frac{1}{4}\) is equal to \(-2 - \frac{1}{4}\), so starting from \(-2\), moving left (towards negative) by \(\frac{1}{4}\) unit. But on the number line, the first tick after \(-3\) (to the right) is at \(-3 + 1 = -2\)? Wait, no, maybe the ticks are at -3, then the next tick is at -3 + 1 = -2? Wait, no, the number line has ticks at -3, then the next ones. Wait, the number line shown has a tick at -3, then four more ticks (since there are five intervals from -3 to the last tick). Wait, the number line has ticks at -3, then the next tick (first to the right of -3) is at \(-3 + \frac{1}{4}\times1\)? No, maybe the spacing between the ticks is 1 unit, but we need to find where \(-2\frac{1}{4}\) is. Wait, \(-2\frac{1}{4}\) is \(-2.25\). So between \(-3\) and \(-2\), the distance is 1 unit. So to find the position: from \(-3\), moving towards \(-2\) (to the right) by \(|-2\frac{1}{4} - (-3)| = |\frac{3}{4}| = \frac{3}{4}\) unit? Wait, no: \(-2\frac{1}{4} - (-3) = -2.25 + 3 = 0.75 = \frac{3}{4}\). So from \(-3\), move \(\frac{3}{4}\) unit to the right? Wait, no, the number line's direction: the arrow is to the left, but the numbers increase to the right. So from \(-3\) (leftmost tick shown), moving right (towards positive) by \(\frac{3}{4}\) unit? Wait, no, let's think again. The value \(-2\frac{1}{4}\) is greater than \(-3\) (since \(-2\frac{1}{4} = -2.25\) and \(-3 = -3.0\), so \(-2.25 > -3.0\)), so it's to the right of \(-3\). The distance between \(-3\) and \(-2\) is 1 unit. So we can divide the interval between \(-3\) and \(-2\) into 4 equal parts (since we have a fraction with denominator 4). Each part is \(\frac{1}{4}\) unit. So starting at \(-3\), moving right: first part: \(-3 + \frac{1}{4} = -2\frac{3}{4}\), second part: \(-3 + \frac{2}{4} = -2\frac{2}{4} = -2\frac{1}{2}\), third part: \(-3 + \frac{3}{4} = -2\frac{1}{4}\), fourth part: \(-3 + 1 = -2\). Ah, there we go. So the third tick (after -3) is at \(-2\frac{1}{4}\). Wait, the number line has ticks at -3, then the next tick (first to the right) is at \(-3 + \frac{1}{4}\)? No, wait, the number line as drawn has a tick at -3, then the next ticks are at equal intervals. Let's count the intervals: from -3 to the next tick (let's say the first tick to the right of -3) is one interval, then the next, etc. So to plot \(-2\frac{1}{4}\), we need to find the position 3/4 of the way from -3 to -2? Wait, no, as we calculated, \(-2\frac{1}{4}\) is 3/4 of a unit to the right of -3 (since -3 + 3/4 = -2.25 = -2\frac{1}{4}). So on the number line, the tick at -3, then the next tick (first to the right) is at -3 + 1/4? No, that can't be. Wait, maybe the number line has ticks at integers: -3, -2, -1, 0, etc. But \(-2\frac{1}{4}\) is between -3 and -2. So between -3 and -2, we divide the segment into 4 equal parts. So each part is 1/4. So the first part (closest to -3) is -3 + 1/4 = -2.75 (-2 3/4), the second is -2.5 (-2 2/4), the third is -2.25 (-2 1/4), and the fourth is -2.0. So the third tick to the right of -3 is at -2 1/4. So we need to drag the blue dot (the point) to that position.

Step3: Plot the point

So on the number line, starting at -3, move 3 intervals (each of 1/4 unit) to the right. So the position is the third tick to the right of -3.

Answer:

The point should be plotted at the third tick mark to the right of \(-3\) on the number line, which corresponds to \(-2\frac{1}{4}\). (Visually, on the given number line, the ticks are at -3, then the next ones: the first tick right of -3 is -3 + 1/4 = -2.75, second is -2.5, third is -2.25 (which is \(-2\frac{1}{4}\)), so place the point there.)