Class 7 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. Express

\frac{- 15}{25}

in standard form.

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Answer: A)

\frac{- 3}{5}

Denominator already positive. GCD(15, 25) = 5.

\frac{- 15}{25}

\frac{- 3}{5}

2. Compute (

\frac{3}{4}

) − (

\frac{- 1}{4}

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Answer: A) 1

Subtracting a negative adds it:

\frac{3}{4}

\frac{1}{4}

\frac{4}{4}

= 1.

3. Which of the following correctly expresses

\frac{17}{3}

as a mixed number?

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Answer: A) 5

\frac{2}{3}

17 ÷ 3 = 5 remainder 2, so

\frac{17}{3}

= 5

\frac{2}{3}

4. Which of

\frac{5}{- 6}

and

\frac{- 2}{3}

lies CLOSER to 0 on the number line?

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Answer: A)

\frac{- 2}{3}

\frac{5}{- 6}

\frac{- 5}{6}

. Distance from 0 is the absolute value:

\frac{5}{6}

against

\frac{2}{3}

\frac{4}{6}

. Since

\frac{4}{6}

\frac{5}{6}

, the number

\frac{- 2}{3}

sits closer to 0. Careful: closer to 0 also means GREATER here, because both numbers are negative.

5. A trader's ledger records a loss of

\frac{7}{4}

thousand rupees in June and a profit of

\frac{13}{4}

thousand rupees in July. What is the net result for the two months together?

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Answer: C) A profit of

\frac{3}{2}

thousand rupees

Write the loss as a negative rational:

\frac{- 7}{4}

\frac{13}{4}

\frac{6}{4}

\frac{3}{2}

. The result is positive, so it is a PROFIT of

\frac{3}{2}

thousand rupees. Adding the two sizes as if both were gains gives

\frac{20}{4}

= 5, and copying the sign of the first month gives a "loss".

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