#### Solved Examples and Worksheet for Locating Integers on a Number Line

Q1Which of the number lines represents the integers - 3, 3 and - 2? A. Figure 1
B. Figure 2
C. Figure 3
D. None of the above

Step: 1
-3 is a negative number; plot 3 units to the left of zero.
Step: 2
-2 is also a negative number; plot 2 units to the left of zero.
Step: 3
3 is a positive number; plot 3 units to the right of zero. Step: 4
Figure 1 is the correct choice.
Correct Answer is :   Figure 1
Q2Which figure represents the sum of - 6 and 5 and the opposite of their sum, on a number line? A. Figure 1
B. Figure 2
C. Both figure 1 and figure 2
D. None of the above

Step: 1
To add two numbers having opposites, first subtract the smaller number from the larger number and then put the sign of the larger number to the result.
Step: 2
So, to add - 6 and 5, first subtract 5 from 6.
6 - 5 = 1

Step: 3
The number - 6 has a negative sign. So, put the '-' sign to the result, 1.
So, - 6 + 5 = - 1

Step: 4
- 1 is a negative number, which is 1 unit to the left of 0. So, its opposite is 1, which is 1 unit to the right of 0.
[Positive numbers will be to the right and negative numbers will be to the left of 0 on the number line.] Step: 5
So, Figure 1 is the correct representation of the sum of - 6 and 5 and the opposite of their sum on the number line.
Correct Answer is :   Figure 1
Q3Which figure represents the difference of 6 and 4 and the opposite of their difference, on a number line? A. Figure 1
B. Figure 2
C. Both A and B
D. None of the above

Step: 1
6 - 4
[Original expression.]
Step: 2
= 2
[Subtract.]
Step: 3
The opposite of 2 is -2.
[Represent both 2 and -2 on the number line.] Step: 4
So, figure-1 is the correct representation of the difference of 6 and 4 and the opposite of the difference.
Correct Answer is :   Figure 1
Q4Which figure represents the sum of -3 and - 2 and the opposite of their sum, on a number line? A. Figure 1
B. Figure 2
C. Both A and B
D. None of the above

Step: 1
-3 + (-2)
[Original expression.]
Step: 2
= - 3 - 2
[To add -2, subtract its opposite, 2.]
Step: 3
= -5
[Simplify.]
Step: 4
-5 will be 5 units to the left of 0 and its opposite is +5 which is 5 units to the right of 0 on the number line.
Step: 5
So, Figure 1 represents the sum of -3 and -2 and the opposite of their sum.
Correct Answer is :   Figure 1
Q5Which of the number lines represents the number 3 and its opposite correctly? A. Figure 1
B. Figure 2
C. both Figure 1 and Figure 2
D. none of these

Step: 1
Numbers that are at the same distance from zero on a number line but in opposite directions are called opposites.
Step: 2
The numbers 3 and -3 both are 3 units far from zero. Step: 3
So, -3 and 3 are opposites, which are represented on the number line in Figure 2.
Correct Answer is :   Figure 2
Q6Which is the correct representation of the opposite of the opposite of -6 on a number line? A. Figure 1
B. Figure 2
C. both Figure 1 and Figure 2
D. none of these

Step: 1
Numbers that are at the same distance from zero on a number line but in opposite directions are called opposites.
Step: 2
Opposite of the opposite of -6.
[Given statement.]
Step: 3
Opposite of -6 is 6 and the opposite of 6 is -6.
Step: 4
Represent opposite of the opposite of -6 i.e -6 on the number line as shown below. Correct Answer is :   Figure 1
Q7Which number is 7 spaces to the left of 4 on the number line? A. - 2
B. - 4
C. - 3
D. 3

Step: 1
The number that is 7 spaces to the left of 4 on the number line is - 3 as shown below. Correct Answer is :   - 3
Q8Which number is 5 spaces to the left of 3 on the number line? A. - 2
B. 6
C. - 4
D. - 3

Step: 1
The number that is 5 spaces to the left of 3 on the number line is - 2. Correct Answer is :   - 2
Q9Which number is 3 spaces to the left of 0 on the number line? A. - 3
B. - 1
C. 3
D. - 2

Step: 1
The number that is 3 spaces to the left of 0 on the number line is -3 as shown below. Correct Answer is :   - 3
Q10Which number is 3 spaces to the right of - 4 on the number line? A. - 1
B. 0
C. - 2
D. 1

Step: 1
The number that is 3 spaces to the right of - 4 on the number line is - 1. Correct Answer is :   - 1
Q11Identify the opposite of 8 and represent it on a number line. A. + 8, Figure 3
B. - 8, Figure 1
C. ± 8, Figure 2
D. none of these

Step: 1
Opposite of 8 is - 8.
[To write the opposite, change the sign of the number.]
Step: 2
As - 8 is negative number, it will be 8 units to the left of 0 on the number line.
[Negative numbers will be to the left of 0 and positive numbers will be to the right of 0 on the number line.]
Step: 3
So, - 8 is represented on the number line as shown below. Correct Answer is :   - 8, Figure 1
Q12Which integer does P represent on the number line? A. - 22
B. - 12
C. - 15
D. - 32

Step: 1
Every interval represents 11 units.
[The numbers to the left of zero are negative integers.] Step: 2
Therefore, the point P represents - 22 on the number line.
Correct Answer is :   - 22
Q13Which number line has an arrow indicating the location of - 2 ? A. Number line 4
B. Number line 2
C. Number line 1
D. Number line 3

Step: 1
The number - 2 is located 2 units to the left of zero.
Step: 2
Move 2 units to the left of zero to indicate - 2 by an arrow as shown in Number line 3.
Step: 3
Number line 3 is the number line that has an arrow indicating the location of - 2.
Correct Answer is :   Number line 3
Q14Which of these numbers does the point O represent on the number line ? A. - 5
B. - 6
C. - 4
D. - 3

Step: 1
On the number line, the point O is located 3 units to the left of - 2.
Step: 2
- 2 - 3 = - 5
[As the point is located to the left of - 2, subtract 3 from - 2.]
Step: 3
The point O represents the number - 5 on the number line.
Correct Answer is :   - 5
Q15Which of these numbers does the point B represent on the number line ? A. - 5
B. - 4
C. - 3
D. - 6

Step: 1
On the number line, the point B is located 4 units to the left of - 2.
Step: 2
- 2 - 4 = - 6
[As the point is located to the left of - 2, subtract 4 from - 2.]
Step: 3
The point B represents the number - 6 on the number line.
Correct Answer is :   - 6