Fill in the blank- -13 - - -43 - 37 - - - -13 - - - - 37

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) $- \frac{1}{4} \times {\frac{2}{3} + (\frac{- 4}{7})} = {\frac{2}{3} + (\frac{- 4}{7})} - \frac{1}{4}$

Q. Simplify :

\frac{2 \frac{3}{4}}{1 \frac{5}{6}} \div \frac{7}{8} \times (\frac{1}{3} + \frac{1}{4}) + \frac{5}{7} \div \frac{3}{4}

\frac{3}{7}

-1/2+ [(-4/3)+3/7] and [(-1/2)+3/7]+(-4/3)

are there same

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Fill in the blank: (−13)+[(−43)+37]=[(−13)+.....]+37

The correct option is D −43Addition is associative for rational numbersi.e. a+(b+c)=(a+b)+c∴(−13)+[(−43)+37]=[(−13)+(−43)]+37

Fill in the blank: $(- \frac{1}{3}) + [(\frac{- 4}{3}) + \frac{3}{7}] = [(\frac{- 1}{3}) + . . . . .] + \frac{3}{7}$

The correct option is D $\frac{- 4}{3}$
Addition is associative for rational numbers
i.e. $a + (b + c) = (a + b) + c$
$∴ (- \frac{1}{3}) + [(\frac{- 4}{3}) + \frac{3}{7}] = [(\frac{- 1}{3}) + (\frac{- 4}{3})] + \frac{3}{7}$