Ncert solutions

Ncert solutions

Grade 8

Rational Numbers | Exercise 1.1

Question 1

Q1) Using appropriate properties find.

(i) -\frac{2}{3}\ \times\ \frac{3}{5}\ +\ \frac{5}{2}-\frac{3}{5}\times\frac{1}{6}

(ii) \frac{2}{5}\times\left(-\frac{3}{7}\right)-\frac{1}{6}\times\frac{3}{2}+\frac{1}{14}\times\frac{2}{5}

Solution 1:

(i):

\left(\frac{-2}{3}\times\frac{3}{5}\right)+\frac{5}{2}-\left(\frac{3}{5}\times\frac{1}{6}\right)\

=\frac{-2}{5}+\frac{5}{2}-\frac{3}{30}

=\frac{-2}{5}+\frac{5}{2}-\frac{1}{10}

\frac{-4+25-1}{10} Taking LCM of 5, 2 and 10

=\frac{25-5}{10}

=\frac{20}{10}=2

(ii):

\frac{2}{\frac{5}{ }}\times\left[-\frac{3}{7}\right]-\frac{1}{6}\times\frac{3}{2}+\frac{1}{14}\times\frac{2}{5}=\frac{2}{5}\times\left[-\frac{3}{7}\right]+\frac{1}{14}\times\frac{2}{5}-\frac{1}{6}\times\frac{3}{2}

(By commutativity)

=\frac{2}{5}\times\left[-\frac{3}{7}+\frac{1}{14}\right]-\frac{1}{4}

(By distributivity)

=\frac{2}{5}\times\left[-\frac{3\times2+1}{14}\right]-\frac{1}{4}

=\frac{2}{5}\times\left[-\frac{5}{14}\right]-\frac{1}{4}

=-\frac{1}{7}-\frac{1}{4}

\frac{-4-7}{28}=\frac{-11}{28}

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Question 1

Q1) Using appropriate properties find.

(i) -\frac{2}{3}\ \times\ \frac{3}{5}\ +\ \frac{5}{2}-\frac{3}{5}\times\frac{1}{6}

(ii) \frac{2}{5}\times\left(-\frac{3}{7}\right)-\frac{1}{6}\times\frac{3}{2}+\frac{1}{14}\times\frac{2}{5}

Solution 1:

(i):

\left(\frac{-2}{3}\times\frac{3}{5}\right)+\frac{5}{2}-\left(\frac{3}{5}\times\frac{1}{6}\right)\

=\frac{-2}{5}+\frac{5}{2}-\frac{3}{30}

=\frac{-2}{5}+\frac{5}{2}-\frac{1}{10}

\frac{-4+25-1}{10} Taking LCM of 5, 2 and 10

=\frac{25-5}{10}

=\frac{20}{10}=2

(ii):

\frac{2}{\frac{5}{ }}\times\left[-\frac{3}{7}\right]-\frac{1}{6}\times\frac{3}{2}+\frac{1}{14}\times\frac{2}{5}=\frac{2}{5}\times\left[-\frac{3}{7}\right]+\frac{1}{14}\times\frac{2}{5}-\frac{1}{6}\times\frac{3}{2}

(By commutativity)

=\frac{2}{5}\times\left[-\frac{3}{7}+\frac{1}{14}\right]-\frac{1}{4}

(By distributivity)

=\frac{2}{5}\times\left[-\frac{3\times2+1}{14}\right]-\frac{1}{4}

=\frac{2}{5}\times\left[-\frac{5}{14}\right]-\frac{1}{4}

=-\frac{1}{7}-\frac{1}{4}

\frac{-4-7}{28}=\frac{-11}{28}

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