Class 7 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 between 0 and 1?

A $\frac{5}{4}$
B $\frac{3}{2}$
C $- \frac{1}{2}$
D $\frac{1}{2}$

Show answer

Answer: D)

\frac{1}{2}

\frac{1}{2}

= 0.5 is more than 0 and less than 1.

\frac{3}{2}

and

\frac{5}{4}

are more than 1, and

- \frac{1}{2}

is less than 0.

2. Riya says there is no rational number between

\frac{5}{7}

and

\frac{6}{7}

because 5 and 6 are next to each other. Is she right?

ANo, $\frac{5}{14}$ lies between
BNo, $\frac{6}{14}$ lies between
CYes, she is right
DNo, $\frac{11}{14}$ lies between

Show answer

Answer: D) No,

\frac{11}{14}

lies between

Write both with denominator 14:

\frac{10}{14}

and

\frac{12}{14}

. Now

\frac{11}{14}

lies between.

\frac{6}{14}

is only

\frac{3}{7}

3. How many fractions with denominator 10 lie strictly between

\frac{1}{5}

and

\frac{4}{5}

Show answer

Answer: D) 5

\frac{1}{5} = \frac{2}{10}

and

\frac{4}{5} = \frac{8}{10}

. Numerators 3, 4, 5, 6, 7 lie strictly between: 5 fractions. (7 wrongly includes the ends.)

4. Find a rational number between

\frac{1}{7}

and

\frac{1}{6}

A $\frac{1}{13}$
B $\frac{3}{13}$
C $\frac{13}{84}$
D $\frac{1}{8}$

Show answer

Answer: C)

\frac{13}{84}

With denominator 84:

\frac{1}{7} = \frac{12}{84}

\frac{1}{6} = \frac{14}{84}

, so

\frac{13}{84}

lies between.

\frac{1}{8}

and

\frac{1}{13}

are smaller than

\frac{1}{7}

;

\frac{3}{13}

is too big.

5. For positive fractions with

\frac{a}{b} < \frac{c}{d}

, which number always lies between them?

A $\frac{a + c}{b + d}$
B $\frac{a + c}{b \times d}$
C $\frac{a \times c}{b \times d}$
D $\frac{b + d}{a + c}$

Show answer

Answer: A)

\frac{a + c}{b + d}

Adding tops and adding bottoms (the mediant) always gives a number in between, e.g.

\frac{1}{3}, \frac{2}{5}, \frac{1}{2}

. The product

\frac{a c}{b d}

can be smaller than both (

\frac{1}{3} \times \frac{1}{2} = \frac{1}{6}

Practise all 50 questions free →

10 free questions a day without an account — unlimited with a free account.