Class 8 Operations on Rational 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. Add:

\frac{1}{2} + \frac{1}{3}

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Answer: A)

\frac{5}{6}

LCM of 2 and 3 is 6.

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

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

. Sum =

\frac{3}{6} + \frac{2}{6} = \frac{5}{6}

2. Compute:

- \frac{3}{5} + (- \frac{1}{5})

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Answer: A)

- \frac{4}{5}

Same denominator:

\frac{- 3 + ( - 1 )}{5} = - \frac{4}{5}

3. Simplify:

(- \frac{2}{9}) - (- \frac{5}{9}) + \frac{1}{9}

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Answer: A)

\frac{4}{9}

\frac{- 2 + 5 + 1}{9} = \frac{4}{9}

4. Three rational numbers are

\frac{1}{3}

- \frac{1}{6}

and

\frac{1}{2}

. Asha adds the first two, then adds the result to the third.
What single rational number does she finally get?

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Answer: A)

\frac{2}{3}

\frac{1}{3} + (- \frac{1}{6}) = \frac{2}{6} - \frac{1}{6} = \frac{1}{6}

. Then

\frac{1}{6} + \frac{1}{2} = \frac{1}{6} + \frac{3}{6} = \frac{4}{6} = \frac{2}{3}

5. A jar is filled with sweets. Aarav takes

\frac{1}{3}

of them, then Diya takes

\frac{1}{4}

of the remaining sweets.
If 18 sweets are now left in the jar, how many sweets were there at the start?

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Answer: A) 36

After Aarav:

\frac{2}{3}

remain. Diya takes

\frac{1}{4}

of that, leaving

\frac{3}{4}

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

of the start. So

\frac{1}{2}

of total

= 18

, giving total

= 36

sweets.

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