- AInfinitely many
- BExactly one
- CExactly two
- DNone
Step-by-Step Solution
By the density property, between any two distinct rationals there are infinitely many rationals.
Answer: A) Infinitely many
Between any two distinct rational numbers, how many rational numbers lie?
Class 8Rational NumbersRational Numbers
Key idea: Finding rationals between two rationals
**Easiest way: the average.** Between a and b, the rational (a + b) / 2 lies exactly in the middle. Repeat to find more: between a and (a+b)/2 lies their average, and so on — forever.
**Common-denominator way**: bring both rationals to a common denominator with extra room. Between 1/3 and 1/2, write as 2/6 and 3/6 — but no integer fits between 2 and 3. Multiply top and bottom of both by 10: 20/60 and 30/60. Now 21/60, 22/60, …, 29/60 all sit between — nine fresh rationals.
This density is something integers don't have: there's no integer between 4 and 5.
**Common-denominator way**: bring both rationals to a common denominator with extra room. Between 1/3 and 1/2, write as 2/6 and 3/6 — but no integer fits between 2 and 3. Multiply top and bottom of both by 10: 20/60 and 30/60. Now 21/60, 22/60, …, 29/60 all sit between — nine fresh rationals.
This density is something integers don't have: there's no integer between 4 and 5.
Master this chapter in 30 minutes a day.
Don't just memorise the answer — build a daily practice habit.
Practice 5 Similar Questions Free →All Rational Numbers practice questions
More Class 8 Rational Numbers practice
Find a rational number between 1/2 and 2/3 using the average method.Which statement is correct about division of rational numbers?Which property guarantees that 4/7 × 3/5 is again a rational number?On the number line, where does -3/4 lie relative to 0?Use a smart grouping (commutative and associative) to add: -4/9 + 2/7 + (-5/9). What is…