What should be placed in the empty space '?' so that the sum of fractions on each side of the triangle is same?

\frac{7}{15}

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\frac{9}{15}

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\frac{6}{15}

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\frac{8}{15}

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Solution

The correct option is B $\frac{8}{15}$
We have, $\frac{2}{15}$ + $\frac{4}{15}$ + $\frac{5}{15}$ = $\frac{11}{15}$ ,
$\frac{1}{15}$ + $\frac{5}{15}$ + $\frac{5}{15}$ = $\frac{11}{15}$
And $\frac{1}{15}$ + ? + $\frac{2}{15}$ = $\frac{11}{15}$ or, $\frac{1}{15}$ + $\frac{8}{15}$ + $\frac{2}{15}$ = $\frac{11}{15}$
$∴$ ? = $\frac{8}{15}$

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Name the property of multiplication illustrated by each of the following statements :

(i) $\frac{- 15}{8} \times \frac{- 12}{7} = \frac{- 12}{7} \times \frac{- 15}{8}$

(ii) $(\frac{- 2}{3} \times \frac{7}{9}) \times \frac{- 9}{5} = \frac{- 2}{3} \times (\frac{7}{9} \times \frac{- 9}{5})$

(iii) $\frac{- 3}{4} \times (\frac{- 3}{4} \times \frac{- 5}{6}) + (\frac{- 3}{4} \times \frac{7}{8})$

(iv) $\frac{- 16}{9} \times 1 = 1 \times \frac{- 16}{9} = \frac{- 16}{9}$

(v) $\frac{- 11}{15} \times \frac{15}{- 11} = \frac{15}{- 11} \times \frac{- 11}{15} = 1$

(vi) $\frac{- 7}{5} \times 0 = 0$

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