# Rational Numbers - Class 8 - Mathematics

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## Back Questions - Rational Numbers | NCERT | Mathematics | Class 8

Find $\frac{3}{7}+\left(\frac{-6}{11}\right)+\left(\frac{-8}{21}\right)+\left(\frac{5}{22}\right)$

The sum of the given fractions is \(-\frac{125}{462}\) or approximately \(-0.2706\).

Find \(\frac{-4}{5} \times \frac{3}{7} \times \frac{15}{16} \times\left(\frac{-14}{9}\right)\)

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Find \(\frac{2}{5} \times \frac{-3}{7}-\frac{1}{14}-\frac{3}{7} \times \frac{3}{5}\)

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Name the property under multiplication used in each of the following.

(i) \(\frac{-4}{5} \times 1=1 \times \frac{-4}{5}=-\frac{4}{5}\)

(ii) \(-\frac{13}{17} \times \frac{-2}{7}=\frac{-2}{7} \times \frac{-13}{17}\)

(iii) \(\frac{-19}{29} \times \frac{29}{-19}=1\)

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Tell what property allows you to compute \(\frac{1}{3} \times\left(6 \times \frac{4}{3}\right)\) as \(\left(\frac{1}{3} \times 6\right) \times \frac{4}{3}\).

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The product of two rational numbers is always a ________

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## Extra Questions - Rational Numbers | NCERT | Mathematics | Class 8

If $\frac{\mathrm{p}}{\mathrm{q}}$ is a rational number, then which of the following cannot be true?

A $\mathrm{p} = 0$

B $q = 0$ C) $p=q$

D $p$ and $q$ are integers.

The correct answer is **B) ( q = 0 )**.

A rational number can be defined as a number which is expressed in the form:

$$ \frac{p}{q} $$

where $p$ and $q$ are integers with the condition that $ q \neq 0 $. Hence, ( q = 0 ) violates the fundamental definition of a rational number.

The number of non-negative integers which are less than 1000 and end with only one zero is __.

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Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number: (i) $\frac{2}{5} + \frac{7}{3} + \frac{-4}{5} + \frac{-1}{3}$ (ii) $\frac{3}{7} + \frac{-4}{9} + \frac{-11}{7} + \frac{7}{9}$ (iii) $\frac{2}{5} + \frac{8}{3} + \frac{-11}{15} + \frac{4}{5} + \frac{-2}{3}$ (iv) $\frac{4}{7} + 0 + \frac{-8}{9} + \frac{-13}{7} + \frac{17}{21}$

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Prove that $\frac{1}{\sqrt{3}}$ is irrational.