Question

test review packet: integers, rational numbers, and the coordinate plane
part 1: number lines, integers, and rational numbers
a. plotting on a number line
plot each number on the number line provided.

1. -4, 2, 0, 3
2. -1.5, 0, 2.5, -3
3. \\(\frac{1}{2}\\), -2, \\(-\frac{3}{4}\\), 1

Explanation:

1. Plotting -4, 2, 0, 3

Step1: Draw a number line

Draw a horizontal line with a zero in the middle. Mark negative numbers to the left of zero and positive numbers to the right.

Step2: Locate -4

Find the position 4 units to the left of 0 and mark -4.

Step3: Locate 2

Find the position 2 units to the right of 0 and mark 2.

Step4: Locate 0

Mark the point at the center of the number line as 0.

Step5: Locate 3

Find the position 3 units to the right of 0 and mark 3.

2. Plotting -1.5, 0, 2.5, -3

Step1: Draw a number line

Draw a horizontal line with 0 in the middle. Mark negative numbers left, positive right.

Step2: Locate -1.5

Find the position halfway between -1 and -2 (since -1.5 is 1.5 units left of 0) and mark -1.5.

Step3: Locate 0

Mark the center as 0.

Step4: Locate 2.5

Find the position halfway between 2 and 3 (2.5 units right of 0) and mark 2.5.

Step5: Locate -3

Find the position 3 units left of 0 and mark -3.

3. Plotting $\frac{1}{2}$, -2, $-\frac{3}{4}$, 1

Step1: Draw a number line

Draw a horizontal line with 0 in the middle. Mark negative numbers left, positive right.

Step2: Locate $\frac{1}{2}$

$\frac{1}{2} = 0.5$, so find the position halfway between 0 and 1 (0.5 units right of 0) and mark $\frac{1}{2}$.

Step3: Locate -2

Find the position 2 units left of 0 and mark -2.

Step4: Locate $-\frac{3}{4}$

$-\frac{3}{4} = -0.75$, so find the position three - fourths of the way from 0 to -1 (0.75 units left of 0) and mark $-\frac{3}{4}$.

Step5: Locate 1

Find the position 1 unit right of 0 and mark 1.

Answer:

For each set of numbers, they are plotted on the number line as described in the respective steps. (Note: Since this is a plotting task, the final answer is the visual representation on the number line as per the steps above. If a written description of the positions is needed:

1. -4 (left of 0), 2 (right of 0), 0 (center), 3 (right of 0)
2. -1.5 (left of 0, between -1 and -2), 0 (center), 2.5 (right of 0, between 2 and 3), -3 (left of 0)
3. $\frac{1}{2}$ (right of 0, between 0 and 1), -2 (left of 0), $-\frac{3}{4}$ (left of 0, between 0 and -1), 1 (right of 0))