Find the sum: (i) (ii) (iii)

(i) Given, L.C.M. of 5 and 10 = 10. Hence, . (ii) Given, L.C.M. of 12 and 8 = 24. Hence, . (iii) Given, L.C.M. of 7 and 14 = 14. Hence, .

Mathematics

Find the sum:
(i) $\dfrac{2}{5} + \dfrac{3}{10}$
(ii) $\dfrac{7}{12} + \dfrac{5}{8}$
(iii) $-\dfrac{4}{7} + \dfrac{3}{14}$

Whole Numbers

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Answer

(i) Given, $\dfrac{2}{5} + \dfrac{3}{10}$

L.C.M. of 5 and 10 = 10.

$\Rightarrow \dfrac{2}{5} + \dfrac{3}{10} \\[1em] \Rightarrow \dfrac{2 \times 2}{5 \times 2} + \dfrac{3}{10} \\[1em] \Rightarrow \dfrac{4}{10} + \dfrac{3}{10} \\[1em] \Rightarrow \dfrac{4 + 3}{10} \\[1em] \Rightarrow \dfrac{7}{10}.$

Hence, $\dfrac{2}{5} + \dfrac{3}{10} = \dfrac{7}{10}$ .

(ii) Given, $\dfrac{7}{12} + \dfrac{5}{8}$

L.C.M. of 12 and 8 = 24.

$\Rightarrow \dfrac{7}{12} + \dfrac{5}{8} \\[1em] \Rightarrow \dfrac{7 \times 2}{12 \times 2} + \dfrac{5 \times 3}{8 \times 3} \\[1em] \Rightarrow \dfrac{14}{24} + \dfrac{15}{24} \\[1em] \Rightarrow \dfrac{14 + 15}{24} \\[1em] \Rightarrow \dfrac{29}{24}.$

Hence, $\dfrac{7}{12} + \dfrac{5}{8} = \dfrac{29}{24}$ .

(iii) Given, $-\dfrac{4}{7} + \dfrac{3}{14}$

L.C.M. of 7 and 14 = 14.

$\Rightarrow -\dfrac{4}{7} + \dfrac{3}{14} \\[1em] \Rightarrow -\dfrac{4 \times 2}{7 \times 2} + \dfrac{3}{14} \\[1em] \Rightarrow -\dfrac{8}{14} + \dfrac{3}{14} \\[1em] \Rightarrow \dfrac{-8 + 3}{14} \\[1em] \Rightarrow -\dfrac{5}{14}.$

Hence, $-\dfrac{4}{7} + \dfrac{3}{14} = -\dfrac{5}{14}$ .

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Mathematics

Find the sum:
(i) $\dfrac{2}{5} + \dfrac{3}{10}$
(ii) $\dfrac{7}{12} + \dfrac{5}{8}$
(iii) $-\dfrac{4}{7} + \dfrac{3}{14}$

Whole Numbers

Answer

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Find the sum:
(i) $\dfrac{2}{5} + \dfrac{3}{10}$
(ii) $\dfrac{7}{12} + \dfrac{5}{8}$
(iii) $-\dfrac{4}{7} + \dfrac{3}{14}$

Prove that the following rational numbers are equal:
(i) $\dfrac{2}{3}$ and $\dfrac{4}{6}$
(ii) $\dfrac{5}{4}$ and $\dfrac{10}{8}$
(iii) $-\dfrac{3}{5}$ and $-\dfrac{6}{10}$
(iv) $\dfrac{9}{3}$ and $3$

Find the difference:
(i) $\dfrac{5}{6} - \dfrac{1}{4}$
(ii) $\dfrac{11}{8} - \dfrac{3}{4}$
(iii) $-\dfrac{7}{9} - \left(-\dfrac{2}{3}\right)$

Find the product:
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(ii) $\dfrac{7}{11} \times \dfrac{5}{8}$
(iii) $-\dfrac{4}{7} \times \dfrac{5}{14}$