Representation on the number line — Class 8 CBSE Mathematics MCQs with Solutions
Free Class 8 CBSE Mathematics Representation on the number line MCQs with step-by-step solutions (30 questions). Part of Rational Numbers. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Representation on the number line · easy · theory
On the number line, positive rational numbers are shown to the ___ of 0.
A. left
B. right ✓ Correct
C. exactly on 0
D. they cannot be shown on a number line
Solution: Positive rational numbers always lie to the right of 0 on the number line.
Q2 — Representation on the number line · easy · theory
On the number line, negative rational numbers lie to the ___ of 0.
A. right
B. left ✓ Correct
C. on 0 itself
D. above 0
Solution: Negative rational numbers always lie to the left of 0 on the number line.
Q3 — Representation on the number line · easy · theory
Between which two integers does -3/4 lie on the number line?
A. between 0 and 1
B. between -1 and 0 ✓ Correct
C. between -2 and -1
D. exactly at 0
Solution: -3/4 = -0.75 is negative and smaller than 1 in size, so it lies between -1 and 0.
Q4 — Representation on the number line · easy · theory
The number 7/4 lies between which two integers on the number line?
A. 0 and 1
B. 1 and 2 ✓ Correct
C. 2 and 3
D. 7 and 4
Solution: 7/4 = 1 3/4 = 1.75, which lies between 1 and 2.
Q5 — Representation on the number line · easy · theory
To represent a rational number p/q on the number line, the segment between two whole numbers is divided into how many equal parts?
A. p parts
B. q parts ✓ Correct
C. p + q parts
D. p × q parts
Solution: The denominator q tells us how many equal parts to divide the unit segment into.
Q6 — Representation on the number line · easy · theory
Where is the number 1/2 located on the number line?
A. at the point 1
B. halfway between 0 and 1 ✓ Correct
C. halfway between 1 and 2
D. to the left of 0
Solution: 1/2 divides the segment from 0 to 1 into two equal parts, so it lies exactly halfway between 0 and 1.
Q7 — Representation on the number line · easy · theory
Which of the following rational numbers lies to the left of 0 on the number line?
A. 2/7
B. -2/7 ✓ Correct
C. 4/9
D. 1/3
Solution: Only -2/7 is negative, so it is the one that lies to the left of 0.
Q8 — Representation on the number line · easy · theory
Between which two integers does -5/2 lie on the number line?
A. -2 and -1
B. -3 and -2 ✓ Correct
C. 2 and 3
D. -1 and 0
Solution: -5/2 = -2.5, which lies between -3 and -2.
Q9 — Representation on the number line · easy · theory
To mark 3/5 on the number line, the segment between 0 and 1 is divided into how many equal parts?
A. 3
B. 5 ✓ Correct
C. 8
D. 15
Solution: The denominator 5 means the unit segment is divided into 5 equal parts, and 3/5 is the third mark from 0.
Q10 — Representation on the number line · easy · theory
On the number line, which of these two numbers lies farther to the right: 1/2 or -1/2?
A. -1/2
B. 1/2 ✓ Correct
C. both lie at the same point
D. neither can be placed on a number line
Solution: 1/2 is positive (right of 0) while -1/2 is negative (left of 0), so 1/2 lies farther to the right.
Q11 — Representation on the number line · medium · theory
The segment from 0 to 2 on the number line is divided into 8 equal parts. Which rational number is located at the 5th mark from 0?
A. 5/4 ✓ Correct
B. 5/8
C. 5/2
D. 2/5
Solution: The whole length 2 split into 8 equal parts makes each part 2/8 = 1/4, so the 5th mark from 0 is 5 × 1/4 = 5/4.
Q12 — Representation on the number line · medium · theory
On the number line, the rational number -5/3 is located between which two integers?
A. -2 and -1 ✓ Correct
B. -1 and 0
C. -3 and -2
D. 1 and 2
Solution: -5/3 = -1 2/3 ≈ -1.67, which is a negative number between -2 and -1.
Q13 — Representation on the number line · medium · theory
To represent 5/7 on the number line, how should you divide the segment between 0 and 1?
A. Into 7 equal parts and take the 5th point from 0 ✓ Correct
B. Into 5 equal parts and take the 7th point from 0
C. Into 7 equal parts and take the 7th point from 0
D. Into 12 equal parts and take the 5th point from 0
Solution: For p/q, divide the unit segment into q = 7 equal parts and count p = 5 parts from 0.
Q14 — Representation on the number line · medium · theory
A point P lies to the left of 0, three of four equal parts of the way from 0 toward -1. Which rational number does P represent?
A. -3/4 ✓ Correct
B. 3/4
C. -1/4
D. -4/3
Solution: Three of four parts toward -1 (left of 0) marks -3/4.
Q15 — Representation on the number line · medium · theory
Which of the following rational numbers lies between -1 and 0 on the number line?
A. -3/5 ✓ Correct
B. -7/5
C. 3/5
D. -5/3
Solution: -3/5 = -0.6 is negative and greater than -1, so it lies between -1 and 0.
Q16 — Representation on the number line · medium · theory
When 11/4 is marked on the number line, where does it lie?
A. Between 2 and 3, three of four quarter-parts past 2 ✓ Correct
B. Between 1 and 2, three quarter-parts past 1
C. Between 2 and 3, one quarter-part past 2
D. Between 3 and 4, three quarter-parts past 3
Solution: 11/4 = 2 3/4, so it lies between 2 and 3, three of the four quarter-parts past 2.
Q17 — Representation on the number line · medium · theory
The segment between 0 and 1 is divided into 8 equal parts. Which mark from 0 represents 3/4?
A. The 6th mark ✓ Correct
B. The 3rd mark
C. The 4th mark
D. The 8th mark
Solution: 3/4 = 6/8, so it falls on the 6th of the eight equal parts from 0.
Q18 — Representation on the number line · medium · theory
Which of the following rational numbers is closest to 0 on the number line?
A. 1/6 ✓ Correct
B. -1/4
C. 2/5
D. -1/2
Solution: Distances from 0 are 1/6 ≈ 0.17, 1/4 = 0.25, 2/5 = 0.4, 1/2 = 0.5, so 1/6 is nearest to 0.
Q19 — Representation on the number line · medium · theory
Which of the following rational numbers lies to the right of 1 on the number line?
A. 9/8 ✓ Correct
B. 7/8
C. 5/8
D. -9/8
Solution: 9/8 = 1 1/8 = 1.125, which is greater than 1, so it lies to the right of 1.
Q20 — Representation on the number line · medium · theory
A point on the number line lies exactly halfway between -2 and -3. Which rational number does it represent?
A. -5/2 ✓ Correct
B. 5/2
C. -3/2
D. -2/5
Solution: The midpoint of -2 and -3 is (-2 + -3)/2 = -5/2 = -2.5.
Q21 — Representation on the number line · hard · theory
The segment between -2 and -1 on a number line is divided into 5 equal parts. Starting at -2 and moving toward -1, which rational number is located at the 3rd mark?
A. -7/5 ✓ Correct
B. -13/5
C. -8/5
D. -3/5
Solution: Each part is 1/5, so the 3rd mark is -2 + 3/5 = -10/5 + 3/5 = -7/5.
Q22 — Representation on the number line · hard · theory
On a number line, between which two integers does -23/6 lie, and if that unit segment is divided into 6 equal parts, at which mark (counting from the left integer) does it fall?
A. Between -4 and -3, at the 1st mark from -4 ✓ Correct
B. Between -3 and -2, at the 1st mark from -3
C. Between -4 and -3, at the 5th mark from -4
D. Between -4 and -3, at the 4th mark from -4
Solution: Since -23/6 = -24/6 + 1/6, it lies just 1/6 to the right of -4, i.e. between -4 and -3 at the 1st of the six marks.
Q23 — Representation on the number line · hard · theory
Point A represents -5/3 and point B represents 4/3 on a number line. Which rational number does the midpoint of segment AB represent?
A. -1/6 ✓ Correct
B. -1/3
C. 3/2
D. 1/6
Solution: The midpoint is the mean: (-5/3 + 4/3)/2 = (-1/3)/2 = -1/6.
Q24 — Representation on the number line · hard · theory
A student wants to mark BOTH 5/8 and 3/4 exactly on division marks of the segment from 0 to 1. What is the least number of equal parts the segment must be divided into?
A. 8 ✓ Correct
B. 32
C. 12
D. 4
Solution: Writing 3/4 as 6/8, both are eighths, so 8 equal parts (the LCM of 8 and 4) suffice and it is the least.
Q25 — Representation on the number line · hard · theory
Which rational number lies exactly halfway between -5/6 and -1/6 on the number line?
A. -1/2 ✓ Correct
B. -1
C. -2/3
D. -1/3
Solution: The halfway point is the mean: (-5/6 + (-1/6))/2 = (-6/6)/2 = -1/2.
Q26 — Representation on the number line · hard · theory
The segment from 0 to 1 is divided into 7 equal parts, giving marks at 1/7, 2/7, ..., 6/7. Which of these marks is closest to 2/3?
A. 5/7 ✓ Correct
B. 4/7
C. 3/7
D. 6/7
Solution: Writing both with denominator 21: 2/3 = 14/21 and 5/7 = 15/21, which differs from 2/3 by only 1/21, while 4/7 = 12/21 differs by 2/21. So 5/7 is closest to 2/3.
Q27 — Representation on the number line · hard · theory
On a number line marked in steps of 1/12, how many equal parts of length 1/12 lie between the points -1/4 and 5/6?
A. 13 ✓ Correct
B. 7
C. 12
D. 26
Solution: The distance is 5/6 - (-1/4) = 10/12 + 3/12 = 13/12, which is 13 parts of length 1/12.
Q28 — Representation on the number line · hard · theory
A number line has equally spaced marks 3/10 apart, starting from 0. Which rational number is represented by the 7th mark to the LEFT of 0?
A. -21/10 ✓ Correct
B. 21/10
C. -7/10
D. -10/21
Solution: Moving to the left makes the value negative and multiplies the spacing by 7: 7 × (-3/10) = -21/10.
Q29 — Representation on the number line · hard · theory
The segment from 2/5 to 4/5 on the number line is divided into 3 equal parts. Which rational number is located at the first division mark, counting from 2/5?
A. 8/15 ✓ Correct
B. 2/3
C. 3/5
D. 2/15
Solution: The segment length is 4/5 - 2/5 = 2/5, so each of the 3 parts is 2/15. The first mark is 2/5 + 2/15 = 6/15 + 2/15 = 8/15.
Q30 — Representation on the number line · hard · theory
On a number line, M is the midpoint between 1/2 and 5/6, and N is the midpoint between M and 5/6. Which rational number does N represent?
A. 3/4 ✓ Correct
B. 2/3
C. 5/6
D. 7/12
Solution: M = (1/2 + 5/6)/2 = 2/3, then N = (2/3 + 5/6)/2 = (9/6)/2 = 3/4.