Rational Numbers (Complete Chapter) interactive worksheet | Live ... - Free Printable

Let's solve each problem step by step from the Class 7 Maths Worksheet on Rational Numbers.

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1. The sum of two numbers is (-4/3). If one of the numbers is -5, find the other.

Let the unknown number be $ x $.
Given:
$$
x + (-5) = -\frac{4}{3}
$$
$$
x - 5 = -\frac{4}{3}
$$
Add 5 to both sides:
$$
x = -\frac{4}{3} + 5 = -\frac{4}{3} + \frac{15}{3} = \frac{11}{3}
$$

✔ Answer: $ \boxed{\left(\frac{11}{3}\right)} $

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2. The sum of two rational numbers is –8. If one of the numbers is (-15/7), find the other.

Let the unknown number be $ x $.
$$
x + \left(-\frac{15}{7}\right) = -8
$$
$$
x = -8 + \frac{15}{7} = -\frac{56}{7} + \frac{15}{7} = -\frac{41}{7}
$$

✔ Answer: $ \boxed{\left(-\frac{41}{7}\right)} $

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3. What should be added to (-7/8) so as to get (5/9)?

Let the number to be added be $ x $.
$$
-\frac{7}{8} + x = \frac{5}{9}
$$
$$
x = \frac{5}{9} + \frac{7}{8}
$$

Find LCM of 9 and 8 → 72
$$
= \frac{5 \times 8}{72} + \frac{7 \times 9}{72} = \frac{40 + 63}{72} = \frac{103}{72}
$$

✔ Answer: $ \boxed{\left(\frac{103}{72}\right)} $

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4. What number should be added to (-5/11) so as to get (26/33)?

Let the number be $ x $.
$$
-\frac{5}{11} + x = \frac{26}{33}
$$
$$
x = \frac{26}{33} + \frac{5}{11} = \frac{26}{33} + \frac{15}{33} = \frac{41}{33}
$$

✔ Answer: $ \boxed{\left(\frac{41}{33}\right)} $

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5. What number should be added to (-5/7) to get (-2/3)?

Let the number be $ x $.
$$
-\frac{5}{7} + x = -\frac{2}{3}
$$
$$
x = -\frac{2}{3} + \frac{5}{7}
$$

LCM of 3 and 7 is 21:
$$
= -\frac{14}{21} + \frac{15}{21} = \frac{1}{21}
$$

✔ Answer: $ \boxed{\left(\frac{1}{21}\right)} $

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6. What should be subtracted from ((3/4) - (2/3)) to get (-1/6)?

First compute $ \frac{3}{4} - \frac{2}{3} $:
LCM of 4 and 3 is 12:
$$
= \frac{9}{12} - \frac{8}{12} = \frac{1}{12}
$$

Let the number to be subtracted be $ x $.
$$
\frac{1}{12} - x = -\frac{1}{6}
$$
$$
-x = -\frac{1}{6} - \frac{1}{12} = -\frac{2}{12} - \frac{1}{12} = -\frac{3}{12} = -\frac{1}{4}
$$
$$
x = \frac{1}{4}
$$

✔ Answer: $ \boxed{\left(\frac{1}{4}\right)} $

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7. Evaluate (-5 × (2/15)) - (-6 × (2/9))

First term:
$$
-5 \times \frac{2}{15} = -\frac{10}{15} = -\frac{2}{3}
$$

Second term:
$$
-6 \times \frac{2}{9} = -\frac{12}{9} = -\frac{4}{3}
$$

But it's minus this term:
$$
-\left(-\frac{4}{3}\right) = +\frac{4}{3}
$$

So total:
$$
-\frac{2}{3} + \frac{4}{3} = \frac{2}{3}
$$

✔ Answer: $ \boxed{\left(\frac{2}{3}\right)} $

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8. Evaluate ((-9/4) × (5/3)) + ((13/2) × (5/6))

First part:
$$
-\frac{9}{4} \times \frac{5}{3} = -\frac{45}{12} = -\frac{15}{4}
$$

Second part:
$$
\frac{13}{2} \times \frac{5}{6} = \frac{65}{12}
$$

Now add:
$$
-\frac{15}{4} + \frac{65}{12}
$$

Convert $ \frac{15}{4} $ to twelfths: $ \frac{45}{12} $
$$
= -\frac{45}{12} + \frac{65}{12} = \frac{20}{12} = \frac{5}{3}
$$

✔ Answer: $ \boxed{\left(\frac{5}{3}\right)} $

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9. By what rational number should we multiply (-15/56) to get (-5/7)?

Let the number be $ x $.
$$
-\frac{15}{56} \times x = -\frac{5}{7}
$$

Divide both sides by $ -\frac{15}{56} $:
$$
x = \frac{-\frac{5}{7}}{-\frac{15}{56}} = \frac{5}{7} \div \frac{15}{56} = \frac{5}{7} \times \frac{56}{15}
$$

Simplify:
$$
= \frac{5 \times 56}{7 \times 15} = \frac{280}{105}
$$

Simplify fraction: divide numerator and denominator by 35:
$$
= \frac{8}{3}
$$

✔ Answer: $ \boxed{\left(\frac{8}{3}\right)} $

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10. By what number should (-33/8) be divided to get (-11/2)?

Let the number be $ x $.
$$
\frac{-\frac{33}{8}}{x} = -\frac{11}{2}
$$

So:
$$
x = \frac{-\frac{33}{8}}{-\frac{11}{2}} = \frac{33}{8} \div \frac{11}{2} = \frac{33}{8} \times \frac{2}{11}
$$

$$
= \frac{66}{88} = \frac{3}{4}
$$

✔ Answer: $ \boxed{\left(\frac{3}{4}\right)} $

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✔ Final Answers:

| Question | Answer |
|--------|--------|
| 1 | $ \left(\frac{11}{3}\right) $ |
| 2 | $ \left(-\frac{41}{7}\right) $ |
| 3 | $ \left(\frac{103}{72}\right) $ |
| 4 | $ \left(\frac{41}{33}\right) $ |
| 5 | $ \left(\frac{1}{21}\right) $ |
| 6 | $ \left(\frac{1}{4}\right) $ |
| 7 | $ \left(\frac{2}{3}\right) $ |
| 8 | $ \left(\frac{5}{3}\right) $ |
| 9 | $ \left(\frac{8}{3}\right) $ |
| 10 | $ \left(\frac{3}{4}\right) $ |

Let me know if you'd like these explained in a simpler way or with diagrams!