Class 8 Properties of 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. Which property of rational numbers does

\frac{2}{3} + \frac{5}{7} = \frac{5}{7} + \frac{2}{3}

illustrate?

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Answer: A) Commutative property of addition

Changing the order of the two addends does not change the sum: a + b = b + a. This is the commutative property of addition.

2. Find the value of

\frac{5}{6} \times 1

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Answer: C) 0.833

Multiplying by the multiplicative identity 1 leaves the number unchanged:

\frac{5}{6} \times 1 = \frac{5}{6} = 0.8333...

3. The reciprocal of -1 is:

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Answer: A) -1

(-1) x (-1) = 1, so the reciprocal of -1 is -1.

4. A pizza is cut into equal slices. Priya colours

\frac{3}{8}

of the pizza red and

\frac{3}{8}

blue.
Using the commutative property of addition, the total coloured fraction is the same whether she adds red+blue or blue+red.
What is that total?

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Answer: A)

\frac{3}{4}

\frac{3}{8} + \frac{3}{8} = \frac{6}{8} = \frac{3}{4}

. Commutativity guarantees the order of adding the two parts does not change the sum.

5. Using properties, evaluate the expression:

(- \frac{3}{7}) \times \frac{5}{4} + (- \frac{3}{7}) \times (- \frac{9}{4}) + (- \frac{3}{7}) \times \frac{4}{4}

.
Take out the common factor and compute carefully.

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Answer: A) 0

Factor out

- \frac{3}{7}

- \frac{3}{7} \times (\frac{5}{4} - \frac{9}{4} + \frac{4}{4}) = - \frac{3}{7} \times \frac{0}{4} = - \frac{3}{7} \times 0 = 0

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