Class 8 Rational Numbers Between Two Numbers — practice questions with answers

Rational Numbers · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Which rational number lies exactly between

\frac{1}{2}

and 1 (i.e. their average)?

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Answer: A)

\frac{3}{4}

Average =

\frac{1/2 + 1}{2} = \frac{3/2}{2} = \frac{3}{4}

2. Which rational number lies between

\frac{5}{7}

and

\frac{6}{7}

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Answer: A)

\frac{11}{14}

\frac{5}{7} = \frac{10}{14}

and

\frac{6}{7} = \frac{12}{14}

, so

\frac{11}{14}

lies between them.

3. To find a rational number between

\frac{1}{2}

and

\frac{1}{2} + \frac{1}{100}

, the average is:

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Answer: A)

\frac{101}{200}

\frac{1}{2} + \frac{1}{100} = \frac{51}{100}

. Mean =

\frac{1/2 + 51/100}{2} = \frac{50/100 + 51/100}{2} = \frac{101/100}{2} = \frac{101}{200}

4. A recipe uses between

\frac{2}{3}

cup and

\frac{3}{4}

cup of sugar.
Neha wants to use a quantity exactly midway in this range.
How many cups of sugar should she use?

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Answer: A)

\frac{17}{24}

\frac{2}{3} = \frac{16}{24}

\frac{3}{4} = \frac{18}{24}

. Mean =

\frac{16/24 + 18/24}{2} = \frac{34}{48} = \frac{17}{24}

cup.

5. Kavya must list as many rational numbers as she can strictly between

\frac{1}{3}

and

\frac{2}{3}

, but only with denominator 9.
How many such numbers

\frac{k}{9}

are there, and which is the largest of them?

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Answer: A) 2 numbers; largest is

\frac{5}{9}

\frac{1}{3} = \frac{3}{9}

and

\frac{2}{3} = \frac{6}{9}

. Strictly between:

\frac{4}{9}

and

\frac{5}{9}

, i.e. 2 numbers, the largest being

\frac{5}{9}

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