NCERT Exemplar Class 7 Maths Unit 8 Rational Numbers - Free Printable

Let's solve each question one by one with clear explanations.

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1. A rational number is defined as a number that can be expressed in the form $\frac{p}{q}$, where $p$ and $q$ are integers and

(a) $q = 0$
(b) $q = 1$
(c) $q \ne 1$
(d) $q \ne 0$

✔ Answer: (d) $q \ne 0$

Explanation:
For a number to be rational, it must be expressible as $\frac{p}{q}$, where $p$ and $q$ are integers and $q \ne 0$. Division by zero is undefined. So, the denominator cannot be zero.

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2. Which of the following rational numbers is positive?

(a) $\frac{-8}{7}$
(b) $\frac{19}{-13}$
(c) $\frac{-3}{-4}$
(d) $\frac{-21}{13}$

✔ Answer: (c) $\frac{-3}{-4}$

Explanation:
A rational number is positive if both numerator and denominator have the same sign.

- (a): $-8/7$ → negative
- (b): $19/-13$ → negative
- (c): $-3/-4 = 3/4$ → positive ✔
- (d): $-21/13$ → negative

So, only (c) is positive.

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3. Which of the following rational numbers is negative?

(a) $-\left(\frac{-3}{7}\right)$
(b) $\frac{-5}{-8}$
(c) $\frac{9}{8}$
(d) $\frac{3}{-7}$

✔ Answer: (d) $\frac{3}{-7}$

Explanation:
Check the sign:

- (a): $-\left(\frac{-3}{7}\right) = \frac{3}{7}$ → positive
- (b): $\frac{-5}{-8} = \frac{5}{8}$ → positive
- (c): $\frac{9}{8}$ → positive
- (d): $\frac{3}{-7} = -\frac{3}{7}$ → negative ✔

So, (d) is negative.

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4. In the standard form of a rational number, the common factor of numerator and denominator is always:

(a) 0
(b) 1
(c) –2
(d) 2

✔ Answer: (b) 1

Explanation:
In standard form, a rational number has no common factors between numerator and denominator other than 1. That means the fraction is simplified completely.

Example: $\frac{6}{8}$ simplifies to $\frac{3}{4}$, where HCF(3,4)=1.

So, the common factor is always 1.

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5. Which of the following rational numbers is equal to its reciprocal?

(a) 1
(b) 2
(c) $\frac{1}{2}$
(d) 0

✔ Answer: (a) 1

Explanation:
Reciprocal of a number $x$ is $\frac{1}{x}$.

- (a) Reciprocal of 1 is $1/1 = 1$ → equal ✔
- (b) Reciprocal of 2 is $1/2$ ≠ 2
- (c) Reciprocal of $1/2$ is 2 ≠ $1/2$
- (d) Reciprocal of 0 is undefined

Only 1 equals its reciprocal.

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6. The reciprocal of $\frac{1}{2}$ is

(a) 3
(b) 2
(c) –1
(d) 0

✔ Answer: (b) 2

Explanation:
Reciprocal of $\frac{1}{2}$ is $\frac{2}{1} = 2$

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7. The standard form of $\frac{-48}{60}$ is

(a) $\frac{48}{60}$
(b) $\frac{-60}{48}$
(c) $\frac{-4}{5}$
(d) $\frac{-4}{-5}$

✔ Answer: (c) $\frac{-4}{5}$

Explanation:
Simplify $\frac{-48}{60}$:

- HCF of 48 and 60 is 12
- $\frac{-48 ÷ 12}{60 ÷ 12} = \frac{-4}{5}$

Also, in standard form, we keep the negative sign in the numerator.

So, answer is $\boxed{\frac{-4}{5}}$

Note: (d) $\frac{-4}{-5} = \frac{4}{5}$, which is positive — not correct.

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8. Which of the following is equivalent to $\frac{4}{5}$?

(a) $\frac{5}{4}$
(b) $\frac{16}{25}$
(c) $\frac{16}{20}$
(d) $\frac{15}{25}$

✔ Answer: (c) $\frac{16}{20}$

Explanation:
We check which option reduces to $\frac{4}{5}$:

- (a) $\frac{5}{4} = 1.25$ ≠ $0.8$
- (b) $\frac{16}{25} = 0.64$ ≠ $0.8$
- (c) $\frac{16}{20} = \frac{4}{5}$ ✔ (divide numerator and denominator by 4)
- (d) $\frac{15}{25} = \frac{3}{5} = 0.6$ ≠ $0.8$

So, only (c) is equivalent.

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9. How many rational numbers are there between two rational numbers?

(a) 1
(b) 0
(c) unlimited
(d) 100

✔ Answer: (c) unlimited

Explanation:
Between any two rational numbers, there are infinitely many rational numbers. For example, between 0 and 1: $0.1, 0.2, 0.11, 0.12, ...$, and so on — infinitely many.

So, answer is unlimited.

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10. In the standard form of a rational number, the denominator is always a

(a) 0
(b) negative integer
(c) positive integer
(d) 1

✔ Answer: (c) positive integer

Explanation:
In standard form:
- The denominator is positive
- The fraction is simplified (HCF of numerator and denominator is 1)

Example: $\frac{-4}{5}$ is standard; $\frac{4}{-5}$ is not (denominator negative). We write it as $-\frac{4}{5}$.

So, denominator is always a positive integer.

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11. To reduce a rational number to its standard form, we divide its numerator and denominator by their

(a) LCM
(b) HCF
(c) product
(d) multiple

✔ Answer: (b) HCF

Explanation:
To simplify a rational number, we divide both numerator and denominator by their Highest Common Factor (HCF).

Example: $\frac{12}{18}$ → HCF(12,18)=6 → $\frac{12÷6}{18÷6} = \frac{2}{3}$

So, we use HCF.

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12. Which is greater number in the following:

(a) $-\frac{1}{2}$
(b) 0
(c) $\frac{1}{2}$
(d) $-2$

✔ Answer: (c) $\frac{1}{2}$

Explanation:
Order from smallest to largest:
- $-2 < -\frac{1}{2} < 0 < \frac{1}{2}$

So, the greatest is $\frac{1}{2}$.

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✔ Final Answers Summary:

| Question | Answer |
|--------|--------|
| 1 | (d) $q \ne 0$ |
| 2 | (c) $\frac{-3}{-4}$ |
| 3 | (d) $\frac{3}{-7}$ |
| 4 | (b) 1 |
| 5 | (a) 1 |
| 6 | (b) 2 |
| 7 | (c) $\frac{-4}{5}$ |
| 8 | (c) $\frac{16}{20}$ |
| 9 | (c) unlimited |
| 10 | (c) positive integer |
| 11 | (b) HCF |
| 12 | (c) $\frac{1}{2}$ |

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