Galaxy Coaching Classes: worksheet class 8 ch-1 rational numbers - Free Printable

Let's solve each question one by one from the given worksheet on Rational Numbers for Class 8.

---

(1) Which of the following pairs are not additive inverses of each other?

Additive inverse means: $ a + (-a) = 0 $. So, two numbers are additive inverses if their sum is zero.

- (a) $ \frac{11}{15}, -\frac{11}{15} $ → Sum = 0 → Additive inverses
- (b) $ \frac{-17}{21}, \frac{17}{21} $ → Sum = 0 → Additive inverses
- (c) $ \frac{8}{-9}, \frac{8}{9} $ → $ \frac{8}{-9} = -\frac{8}{9} $, so $ -\frac{8}{9} + \frac{8}{9} = 0 $ → Additive inverses
- (d) $ \frac{-25}{-52}, \frac{25}{52} $ → $ \frac{-25}{-52} = \frac{25}{52} $, so both are same → Sum = $ \frac{25}{52} + \frac{25}{52} = \frac{50}{52} \neq 0 $

So, (d) is not a pair of additive inverses.

✔ Answer: (d)

---

(2) Which among the following pairs are reciprocals?

Reciprocal means: $ a \times b = 1 $

- (a) $ \frac{12}{17}, \frac{-11}{-12} = \frac{11}{12} $ → $ \frac{12}{17} \times \frac{11}{12} = \frac{11}{17} \ne 1 $
- (b) $ \frac{-13}{27}, \frac{27}{-13} = -\frac{27}{13} $ → $ \frac{-13}{27} \times \left(-\frac{27}{13}\right) = 1 $ ✔
- (c) $ \frac{8}{-9}, \frac{8}{9} $ → $ \frac{8}{-9} \times \frac{8}{9} = -\frac{64}{81} \ne 1 $
- (d) $ \frac{-25}{-52}, \frac{25}{52} $ → Both equal to $ \frac{25}{52} $ → Product = $ \left(\frac{25}{52}\right)^2 \ne 1 $

Only (b) gives product 1.

✔ Answer: (b)

---

(3) The multiplicative inverse of $ \frac{-3}{5} \times \frac{8}{11} $ is

First compute the product:

$$
\frac{-3}{5} \times \frac{8}{11} = \frac{-24}{55}
$$

Multiplicative inverse = reciprocal of $ \frac{-24}{55} = \frac{-55}{24} $

✔ Answer: (c) $ \frac{-55}{24} $

---

(4) The standard form of which of the following rational numbers is correct?

Standard form means simplified fraction with no common factors and positive denominator.

- (a) $ \frac{-8}{36} = \frac{-2}{9} $, but it says $ \frac{-4}{9} $ → ✘ Incorrect
- (b) $ \frac{-63}{-210} = \frac{63}{210} = \frac{3}{10} $ → But written as $ \frac{3}{-10} = -\frac{3}{10} $ → ✘ Sign wrong
- (c) $ \frac{165}{-275} = -\frac{165}{275} = -\frac{3}{5} $ → Given as $ \frac{-3}{5} $ → ✔ Correct
- (d) $ \frac{108}{-96} \times \frac{-8}{9} $ — This is an expression, not a single number. Not a valid comparison.

So only (c) is correctly simplified.

✔ Answer: (c)

---

(5) If the denominator of $ \frac{-16}{18} $ is 162, then its numerator is equal to

We are scaling $ \frac{-16}{18} $ so that denominator becomes 162.

Find scale factor:
$ \frac{162}{18} = 9 $

Multiply numerator: $ -16 \times 9 = -144 $

So new fraction: $ \frac{-144}{162} $

✔ Answer: (d) -144

---

(6) If the numerator of $ \frac{25}{35} $ is 65, then its denominator is equal to

Simplify $ \frac{25}{35} = \frac{5}{7} $

Now we want a fraction equivalent to $ \frac{5}{7} $ with numerator 65.

So:
$ \frac{5}{7} = \frac{65}{x} $

Cross-multiply:
$ 5x = 65 \times 7 = 455 $
$ x = 91 $

✔ Answer: (c) 91

---

(7) A rational number can be expressed as a terminating decimal if its denominator has factors

A rational number has a terminating decimal if, when simplified, the denominator has only prime factors of 2 and/or 5.

So, denominator must have factors of 2 or 5 only.

✔ Answer: (d) 2 or 5

---

(8) The product of $ \frac{-2}{5} $ and $ \frac{-4}{5} $ is

$$
\frac{-2}{5} \times \frac{-4}{5} = \frac{8}{25}
$$

✔ Answer: (c) $ \frac{8}{25} $

---

(9) The sum of $ \frac{-4}{5} $ and $ \frac{14}{5} $ is equal to

$$
\frac{-4 + 14}{5} = \frac{10}{5} = 2
$$

✔ Answer: (b) 2

---

(10) The number of rational numbers between -1 and +1 is

Between any two real numbers, there are infinitely many rational numbers.

So even between -1 and 1, there are infinite rational numbers.

✔ Answer: (b) Infinite

---

(11) The multiplicative inverse of $ \frac{0}{1} $ is

$ \frac{0}{1} = 0 $

Multiplicative inverse of 0 is undefined, because $ \frac{1}{0} $ is undefined.

✔ Answer: (a) Undefined

---

(12) Value of $ \left| \frac{1}{5} - \frac{2}{7} \right| $ is

First find difference:

LCM of 5 and 7 is 35

$$
\frac{1}{5} = \frac{7}{35},\quad \frac{2}{7} = \frac{10}{35}
$$

$$
\frac{7}{35} - \frac{10}{35} = \frac{-3}{35}
$$

Absolute value: $ \left| \frac{-3}{35} \right| = \frac{3}{35} $

But none of the options show $ \frac{3}{35} $. Wait — let's check the image again.

Wait — no options listed for Q12 in your image. Probably missing.

But based on calculation:
✔ Answer should be $ \frac{3}{35} $

But since options aren't visible, maybe they're implied?

Possibly typo or missing in image.

But assuming standard format, answer is $ \boxed{\frac{3}{35}} $

---

✔ Final Answers Summary:

| Q | Answer |
|---|--------|
| 1 | (d) |
| 2 | (b) |
| 3 | (c) |
| 4 | (c) |
| 5 | (d) |
| 6 | (c) |
| 7 | (d) |
| 8 | (c) |
| 9 | (b) |
|10 | (b) |
|11 | (a) |
|12 | $ \frac{3}{35} $ (but no options shown) |

---

Let me know if you'd like explanations in Hindi or need this formatted for printing!