$\frac{2}{3} + \frac{4}{7} = ?$

1 \frac{5}{21}

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26 \frac{1}{21}

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1 \frac{6}{21}

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\frac{2}{21}

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Solution

The correct option is A $1 \frac{5}{21}$
$\frac{2}{3}$ and $\frac{4}{7}$ are unlike fractions. To add them, we first convert them into equivalent fractions so that the denominators are the same.

i.e., $\frac{2 \times 7}{3 \times 7} = \frac{14}{21}$

$\frac{4 \times 3}{7 \times 3} = \frac{12}{21}$

Now, $\frac{2}{3} + \frac{4}{7} = \frac{14}{21} + \frac{12}{21} = \frac{26}{21} = 1 \frac{5}{21} .$

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Question 22

Which of the following is an example of distributive property of multiplication over addition for rational numbers.
(a) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = [- \frac{1}{4} \times \frac{2}{3}] + [- \frac{1}{4} \times (\frac{- 4}{7})]$
(b) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = [\frac{1}{4} \times \frac{2}{3}] - (\frac{- 4}{7})$
(c) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = \frac{2}{3} + (- \frac{1}{4}) \times \frac{- 4}{7}$
(d) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = {\frac{2}{3} + (\frac{- 4}{7})} - \frac{1}{4}$