Rationals between two rationals — Class 8 CBSE Mathematics MCQs with Solutions
Free Class 8 CBSE Mathematics Rationals between two rationals 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 — Rationals between two rationals · easy · theory
How many rational numbers lie between two given rational numbers?
A. Exactly one
B. Exactly two
C. A finite number
D. Infinitely many (countless) ✓ Correct
Solution: Between any two rational numbers there are countless (infinitely many) rational numbers.
Q2 — Rationals between two rationals · easy · theory
By the mean method, a rational number that always lies between two rationals a and b is given by which expression?
A. (a + b)/2 ✓ Correct
B. a + b
C. (a - b)/2
D. (a × b)/2
Solution: The mean (a + b)/2 of two rationals always lies between them.
Q3 — Rationals between two rationals · easy · theory
Using the mean method, which rational number lies exactly between 0 and 1?
A. 1
B. 1/2 ✓ Correct
C. 1/3
D. 2
Solution: The mean is (0 + 1)/2 = 1/2, which lies between 0 and 1.
Q4 — Rationals between two rationals · easy · theory
What is the mean of -1 and 1, which lies between them?
A. 1
B. -1
C. 0 ✓ Correct
D. 2
Solution: The mean is (-1 + 1)/2 = 0/2 = 0, which lies between -1 and 1.
Q5 — Rationals between two rationals · easy · theory
Using the mean method, which rational number lies exactly between 1/4 and 3/4?
A. 1/2 ✓ Correct
B. 1
C. 1/4
D. 1/3
Solution: The mean is (1/4 + 3/4)/2 = 1/2, which lies between 1/4 and 3/4.
Q6 — Rationals between two rationals · easy · theory
Which rational number lies between 3/7 and 5/7?
A. 6/7
B. 2/7
C. 4/7 ✓ Correct
D. 1
Solution: With the same denominator 7, the numerator 4 lies between 3 and 5, so 4/7 lies between 3/7 and 5/7.
Q7 — Rationals between two rationals · easy · theory
Which rational number lies between 1/7 and 3/7?
A. 4/7
B. 2/7 ✓ Correct
C. 1/14
D. 6/7
Solution: With the same denominator 7, the numerator 2 lies between 1 and 3, so 2/7 lies between 1/7 and 3/7.
Q8 — Rationals between two rationals · easy · theory
Using the mean method, which rational number lies exactly between 1/2 and 1?
A. 1/2
B. 3/2
C. 1/4
D. 3/4 ✓ Correct
Solution: The mean is (1/2 + 1)/2 = (3/2)/2 = 3/4, which lies between 1/2 and 1.
Q9 — Rationals between two rationals · easy · theory
Which statement about rational numbers is TRUE?
A. Between any two rational numbers there are countless (infinitely many) rational numbers. ✓ Correct
B. Between any two rational numbers there is exactly one rational number.
C. There are no rational numbers between two negative rationals.
D. Only whole numbers lie between two rational numbers.
Solution: By the property of rationals, countless (infinitely many) rational numbers lie between any two rationals.
Q10 — Rationals between two rationals · easy · theory
Writing 1/3 and 2/3 with denominator 6 gives 2/6 and 4/6. Which rational number lies between them?
A. 5/6
B. 3/6 ✓ Correct
C. 1/6
D. 6/6
Solution: With denominator 6, the numerator 3 lies between 2 and 4, so 3/6 lies between 1/3 and 2/3.
Q11 — Rationals between two rationals · medium · theory
The mean (a+b)/2 of the rational numbers 1/2 and 1/3 lies between them. What is this mean?
A. 5/12 ✓ Correct
B. 5/6
C. 2/5
D. 1/5
Solution: 1/2 + 1/3 = 5/6, and dividing by 2 gives (5/6) ÷ 2 = 5/12, which lies between 1/3 and 1/2.
Q12 — Rationals between two rationals · medium · theory
Using the mean method, the rational number lying midway between -3/4 and 1/4 is:
A. -1/4 ✓ Correct
B. -1/2
C. -1/8
D. 1/4
Solution: (-3/4) + (1/4) = -2/4 = -1/2, and (-1/2) ÷ 2 = -1/4, which sits between -3/4 and 1/4.
Q13 — Rationals between two rationals · medium · theory
How many rational numbers with denominator 9 lie strictly between 2/9 and 6/9?
A. 3 ✓ Correct
B. 4
C. 2
D. Infinitely many
Solution: Keeping the denominator 9, the numerators between 2 and 6 are 3, 4 and 5, giving exactly three such numbers: 3/9, 4/9 and 5/9.
Q14 — Rationals between two rationals · medium · theory
There is no rational number with denominator 5 between 1/5 and 2/5. By enlarging the denominator, which rational number lies between them?
A. 3/10 ✓ Correct
B. 3/5
C. 5/10
D. 1/10
Solution: Writing 1/5 = 2/10 and 2/5 = 4/10, the numerator 3 fits between 2 and 4, so 3/10 lies between 1/5 and 2/5.
Q15 — Rationals between two rationals · medium · theory
The mean of the rational numbers 2/3 and 3/4 is:
A. 17/24 ✓ Correct
B. 17/12
C. 5/7
D. 17/48
Solution: 2/3 + 3/4 = 8/12 + 9/12 = 17/12, and (17/12) ÷ 2 = 17/24, which lies between 2/3 and 3/4.
Q16 — Rationals between two rationals · medium · theory
A rational number lying between -1/2 and -1/3, found by taking their mean, is:
A. -5/12 ✓ Correct
B. -5/6
C. 5/12
D. -1/5
Solution: (-1/2) + (-1/3) = -5/6, and (-5/6) ÷ 2 = -5/12, which lies between -1/2 and -1/3.
Q17 — Rationals between two rationals · medium · theory
Which of the following rational numbers lies between 1/4 and 1/2?
A. 3/8 ✓ Correct
B. 1/8
C. 5/8
D. 2/3
Solution: Writing 1/4 = 2/8 and 1/2 = 4/8, only 3/8 falls between 2/8 and 4/8, so 3/8 lies between 1/4 and 1/2.
Q18 — Rationals between two rationals · medium · theory
Inserting a rational number between 3/8 and 1/2 by the mean method gives:
A. 7/16 ✓ Correct
B. 7/8
C. 7/32
D. 1/4
Solution: Since 1/2 = 4/8, the sum 3/8 + 4/8 = 7/8, and (7/8) ÷ 2 = 7/16, which lies between 3/8 and 1/2.
Q19 — Rationals between two rationals · medium · theory
Which of the following rational numbers lies between 5/12 and 7/12?
A. 1/2 ✓ Correct
B. 1/3
C. 2/3
D. 3/4
Solution: With denominator 12, the number between 5/12 and 7/12 is 6/12, and 6/12 simplifies to 1/2.
Q20 — Rationals between two rationals · medium · theory
To find a rational number between 1/6 and 1/4, the denominators are made equal and then enlarged. Which number lies between them?
A. 5/24 ✓ Correct
B. 5/12
C. 1/10
D. 2/5
Solution: Writing 1/6 = 4/24 and 1/4 = 6/24, the numerator 5 lies between 4 and 6, so 5/24 lies between 1/6 and 1/4.
Q21 — Rationals between two rationals · hard · theory
Using the mean method, the rational number exactly halfway between 3/7 and 5/9 is:
A. 31/63 ✓ Correct
B. 62/63
C. 5/21
D. 31/126
Solution: 3/7 = 27/63 and 5/9 = 35/63, so their sum 62/63 divided by 2 gives the mean 31/63.
Q22 — Rationals between two rationals · hard · theory
Let m be the mean of 1/2 and 3/4. Using the mean method again, the rational number midway between 1/2 and m is:
A. 9/16 ✓ Correct
B. 5/8
C. 9/8
D. 11/16
Solution: The mean of 1/2 and 3/4 is 5/8, and the mean of 1/2 and 5/8 is (1/2 + 5/8)/2 = (9/8)/2 = 9/16.
Q23 — Rationals between two rationals · hard · theory
By the equal-denominator method, which rational number lies between -4/9 and -1/3?
A. -7/18 ✓ Correct
B. -1/2
C. -5/18
D. -7/9
Solution: Writing both with denominator 18 gives -8/18 and -6/18, so -7/18 lies between them.
Q24 — Rationals between two rationals · hard · theory
How many rational numbers lie between -3/7 and 2/7?
A. Infinitely many (countless) rational numbers ✓ Correct
B. Exactly 4 (namely -2/7, -1/7, 0, 1/7)
C. Exactly 5 rational numbers
D. Only one rational number
Solution: Between any two rational numbers there are countless (infinitely many) rationals, not just the few whose numerator is a whole number over 7.
Q25 — Rationals between two rationals · hard · theory
Using the equal-denominator method, which set of three rational numbers all lie between 1/4 and 1/2?
A. 5/16, 3/8, 7/16 ✓ Correct
B. 5/8, 6/8, 7/8
C. 9/16, 5/8, 11/16
D. 1/8, 3/16, 1/4
Solution: Writing 1/4 = 4/16 and 1/2 = 8/16, the numerators 5, 6, 7 give 5/16, 3/8, 7/16, all lying between them.
Q26 — Rationals between two rationals · hard · theory
The mean of 2/3 and 5/6, which lies between them, is:
A. 3/4 ✓ Correct
B. 9/6
C. 7/9
D. 1/2
Solution: 2/3 = 4/6, so (4/6 + 5/6)/2 = (9/6)/2 = 9/12 = 3/4.
Q27 — Rationals between two rationals · hard · theory
By the equal-denominator method (enlarging the denominator when needed), which rational number lies between -2/5 and -3/10?
A. -7/20 ✓ Correct
B. -1/2
C. -7/10
D. -1/4
Solution: Writing -2/5 = -4/10 and -3/10 shows no tenth lies between them, so enlarge to twentieths: -2/5 = -8/20 and -3/10 = -6/20, and -7/20 lies between -8/20 and -6/20.
Q28 — Rationals between two rationals · hard · theory
Which statement about the rational numbers lying between 4/9 and 5/9 is TRUE?
A. There are infinitely many rational numbers between them. ✓ Correct
B. There is no rational number between them because their numerators are consecutive.
C. There are exactly 8 rational numbers between them.
D. There is exactly one rational number between them, namely 9/18.
Solution: There are infinitely many rationals between any two distinct rationals, so consecutive numerators or a single value like 9/18 cannot be the full answer.
Q29 — Rationals between two rationals · hard · theory
How many rational numbers of the form k/18 (where k is an integer) lie strictly between 1/6 and 1/3?
A. 2 ✓ Correct
B. 3
C. Infinitely many
D. 4
Solution: 1/6 = 3/18 and 1/3 = 6/18, so only 4/18 and 5/18 have the form k/18 strictly between them - exactly 2.
Q30 — Rationals between two rationals · hard · theory
The rational number midway between -3/4 and 2/3, obtained by the mean method, is:
A. -1/24 ✓ Correct
B. -1/12
C. 1/24
D. -1/48
Solution: -3/4 = -9/12 and 2/3 = 8/12, so (-9/12 + 8/12)/2 = (-1/12)/2 = -1/24.