CBSE Class 8 Mathematics Rational Numbers Worksheet Set B - Free Printable

Let's solve each question from the worksheet step by step and explain the reasoning behind each solution.

---

1. The sum of a rational number and its additive inverse is equal to ________

Answer: 0

Explanation:
The additive inverse of a number $ a $ is $ -a $. So, $ a + (-a) = 0 $.
This is true for any rational number.

---

2. Write the multiplicative inverse of $ \left( -\frac{2}{3} \times \frac{3}{10} \right) $

Step 1: Multiply the two fractions:

$$
-\frac{2}{3} \times \frac{3}{10} = -\frac{6}{30} = -\frac{1}{5}
$$

Step 2: Multiplicative inverse of $ -\frac{1}{5} $ is $ -5 $

Answer: $ -5 $

---

3. Check whether $ 2\frac{1}{4} $ is the multiplicative inverse of 2.2

Step 1: Convert $ 2\frac{1}{4} $ to improper fraction:

$$
2\frac{1}{4} = \frac{9}{4}
$$

Step 2: Convert 2.2 to fraction:

$$
2.2 = \frac{22}{10} = \frac{11}{5}
$$

Step 3: Check if their product is 1:

$$
\frac{9}{4} \times \frac{11}{5} = \frac{99}{20} \neq 1
$$

So, no, it is not the multiplicative inverse.

Answer: No

---

4. Find the product of $ \frac{13}{15} $ and the additive inverse of $ -\frac{5}{26} $

Step 1: Additive inverse of $ -\frac{5}{26} $ is $ \frac{5}{26} $

Step 2: Multiply:

$$
\frac{13}{15} \times \frac{5}{26} = \frac{65}{390} = \frac{1}{6}
$$

(Simplify: divide numerator and denominator by 65)

Answer: $ \frac{1}{6} $

---

5. Show $ \left( \frac{2}{5} - \frac{4}{15} \right) $ on the number line

Step 1: Simplify the expression:

$$
\frac{2}{5} - \frac{4}{15} = \frac{6}{15} - \frac{4}{15} = \frac{2}{15}
$$

Step 2: On the number line:
- Mark 0.
- Divide the segment between 0 and 1 into 15 equal parts.
- Locate $ \frac{2}{15} $, which is 2 parts from 0.

Answer: $ \frac{2}{15} $, shown on number line as a point $ \frac{2}{15} $ units to the right of 0.

---

6. Write the additive inverse of $ \frac{7}{8} + \frac{4}{3} - \frac{3}{2} + \frac{1}{2} $

Step 1: First compute the expression:

Convert all to common denominator (LCM of 8,3,2 is 24):

$$
\frac{7}{8} = \frac{21}{24},\quad \frac{4}{3} = \frac{32}{24},\quad \frac{3}{2} = \frac{36}{24},\quad \frac{1}{2} = \frac{12}{24}
$$

Now compute:

$$
\frac{21}{24} + \frac{32}{24} - \frac{36}{24} + \frac{12}{24} = \frac{(21+32-36+12)}{24} = \frac{29}{24}
$$

Step 2: Additive inverse of $ \frac{29}{24} $ is $ -\frac{29}{24} $

Answer: $ -\frac{29}{24} $

---

7. Write four rational numbers between $ -\frac{2}{3} $ and $ \frac{2}{3} $

We can pick numbers like:

- $ -\frac{1}{2} $
- $ -\frac{1}{3} $
- $ 0 $
- $ \frac{1}{3} $

These are all between $ -\frac{2}{3} $ and $ \frac{2}{3} $

Answer: $ -\frac{1}{2}, -\frac{1}{3}, 0, \frac{1}{3} $ (any four such numbers)

---

8. Divide the sum of $ 7\frac{2}{3} $ and $ 2\frac{1}{2} $ by their difference

Step 1: Convert mixed numbers:

$ 7\frac{2}{3} = \frac{23}{3} $, $ 2\frac{1}{2} = \frac{5}{2} $

Sum:

$$
\frac{23}{3} + \frac{5}{2} = \frac{46 + 15}{6} = \frac{61}{6}
$$

Difference:

$$
\frac{23}{3} - \frac{5}{2} = \frac{46 - 15}{6} = \frac{31}{6}
$$

Divide sum by difference:

$$
\frac{61}{6} \div \frac{31}{6} = \frac{61}{6} \times \frac{6}{31} = \frac{61}{31}
$$

Answer: $ \frac{61}{31} $

---

9. By what number should $ -5\frac{1}{2} $ be divided to get $ \frac{11}{2} $?

Let the unknown number be $ x $

$$
\frac{-5\frac{1}{2}}{x} = \frac{11}{2}
$$

Convert $ -5\frac{1}{2} = -\frac{11}{2} $

So:

$$
\frac{-\frac{11}{2}}{x} = \frac{11}{2} \Rightarrow -\frac{11}{2x} = \frac{11}{2}
$$

Multiply both sides by $ 2x $:

$$
-11 = 11x \Rightarrow x = -1
$$

Answer: $ -1 $

---

10. What should be subtracted from $ \frac{3}{12} $ to get $ -\frac{10}{3} $?

Let $ x $ be the number to subtract:

$$
\frac{3}{12} - x = -\frac{10}{3}
$$

Simplify $ \frac{3}{12} = \frac{1}{4} $

$$
\frac{1}{4} - x = -\frac{10}{3}
\Rightarrow -x = -\frac{10}{3} - \frac{1}{4} = -\left( \frac{40 + 3}{12} \right) = -\frac{43}{12}
$$

So $ x = \frac{43}{12} $

Answer: $ \frac{43}{12} $

---

11. Simplify: $ -\frac{6}{7} - \frac{3}{14} - \frac{24}{14} $

Note: $ -\frac{3}{14} - \frac{24}{14} = -\frac{27}{14} $

Now:

$$
-\frac{6}{7} - \frac{27}{14} = -\frac{12}{14} - \frac{27}{14} = -\frac{39}{14}
$$

Answer: $ -\frac{39}{14} $

---

12. Simplify by using suitable property:

#### i) $ \frac{3}{4} \times \left( \frac{8}{5} - \frac{16}{15} \right) $

First simplify inside:

$$
\frac{8}{5} - \frac{16}{15} = \frac{24 - 16}{15} = \frac{8}{15}
$$

Now multiply:

$$
\frac{3}{4} \times \frac{8}{15} = \frac{24}{60} = \frac{2}{5}
$$

Answer: $ \frac{2}{5} $

---

#### ii) $ \left( -\frac{5}{6} \times \frac{4}{15} \right) \times \frac{3}{10} \times -\frac{5}{9} $

Use associative property.

First compute:

$$
-\frac{5}{6} \times \frac{4}{15} = -\frac{20}{90} = -\frac{2}{9}
$$

Then:

$$
-\frac{2}{9} \times \frac{3}{10} = -\frac{6}{90} = -\frac{1}{15}
$$

Then:

$$
-\frac{1}{15} \times -\frac{5}{9} = \frac{5}{135} = \frac{1}{27}
$$

Answer: $ \frac{1}{27} $

---

#### iii) $ \frac{3}{2} + \frac{5}{4} - \frac{3}{2} \times \frac{3}{4} \times 7 $

Follow order of operations (BODMAS): multiplication first.

Compute $ \frac{3}{2} \times \frac{3}{4} = \frac{9}{8} $, then $ \frac{9}{8} \times 7 = \frac{63}{8} $

Now:

$$
\frac{3}{2} + \frac{5}{4} - \frac{63}{8}
$$

Convert to eighths:

$$
\frac{12}{8} + \frac{10}{8} - \frac{63}{8} = \frac{22 - 63}{8} = -\frac{41}{8}
$$

Answer: $ -\frac{41}{8} $

---

#### iv) $ \frac{5}{7} \times \frac{3}{14} + \frac{3}{7} \times \frac{3}{5} $

No common factor; just compute:

$$
\frac{5}{7} \times \frac{3}{14} = \frac{15}{98}
$$

$$
\frac{3}{7} \times \frac{3}{5} = \frac{9}{35}
$$

Now add:

LCM of 98 and 35 is 490

$$
\frac{15}{98} = \frac{75}{490},\quad \frac{9}{35} = \frac{126}{490}
\Rightarrow \frac{75 + 126}{490} = \frac{201}{490}
$$

Answer: $ \frac{201}{490} $

---

13. The sum of two rational numbers is -3. If one of them is $ -\frac{4}{3} $, find the other number.

Let the other number be $ x $

$$
-\frac{4}{3} + x = -3 \Rightarrow x = -3 + \frac{4}{3} = -\frac{9}{3} + \frac{4}{3} = -\frac{5}{3}
$$

Answer: $ -\frac{5}{3} $

---

14. The product of two rational numbers is $ -\frac{28}{27} $. If one of them is $ -\frac{4}{9} $, find the other number.

Let the other number be $ x $

$$
-\frac{4}{9} \times x = -\frac{28}{27}
\Rightarrow x = \frac{-\frac{28}{27}}{-\frac{4}{9}} = \frac{28}{27} \times \frac{9}{4} = \frac{252}{108} = \frac{7}{3}
$$

(Simplify: divide numerator and denominator by 36 → $ \frac{7}{3} $)

Answer: $ \frac{7}{3} $

---

15. Find the area of a square park with each side $ 5\frac{1}{2} $ m

Side = $ 5\frac{1}{2} = \frac{11}{2} $ m

Area of square = $ \text{side}^2 = \left( \frac{11}{2} \right)^2 = \frac{121}{4} = 30.25 $ m²

Answer: $ \frac{121}{4} $ m² or $ 30.25 $ m²

---

✔ Final Answers Summary:

| Q.No | Answer |
|------|--------|
| 1 | 0 |
| 2 | -5 |
| 3 | No |
| 4 | $ \frac{1}{6} $ |
| 5 | $ \frac{2}{15} $ (on number line) |
| 6 | $ -\frac{29}{24} $ |
| 7 | $ -\frac{1}{2}, -\frac{1}{3}, 0, \frac{1}{3} $ (example) |
| 8 | $ \frac{61}{31} $ |
| 9 | -1 |
| 10 | $ \frac{43}{12} $ |
| 11 | $ -\frac{39}{14} $ |
| 12i | $ \frac{2}{5} $ |
| 12ii | $ \frac{1}{27} $ |
| 12iii| $ -\frac{41}{8} $ |
| 12iv | $ \frac{201}{490} $ |
| 13 | $ -\frac{5}{3} $ |
| 14 | $ \frac{7}{3} $ |
| 15 | $ \frac{121}{4} $ m² or 30.25 m² |

Let me know if you'd like a PDF version or diagrams (e.g., number line).