Using the appropriate properties of operations of rational numbers, evaluate the following:
$\frac{3}{13} \times \frac{4}{5} \times \frac{7}{5} \times \frac{4}{13} \times \frac{5}{13}$

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Solution

We have,

$\frac{3}{13} \times \frac{4}{5} \times \frac{7}{5} \times \frac{4}{13} \times \frac{5}{13}$

$= \frac{336}{10985}$

Hence, this is the answer.

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Similar questions

Q. Using the appropriate properties of operations of rational numbers, evaluate the following:

\frac{5}{7} \times \frac{2}{11} \times \frac{- 8}{7} \times \frac{6}{11}

Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

(i) $\frac{2}{5} + \frac{7}{3} + \frac{- 4}{5} + \frac{- 1}{3}$

(ii) $\frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9}$

(iii) $\frac{2}{5} + \frac{8}{3} + \frac{- 11}{15} + \frac{4}{5} + \frac{- 2}{3}$

(iv) $\frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{21}$

Evaluate each of the following: $(i) \frac{2}{3} - \frac{3}{5} (i i) \frac{- 4}{7} - \frac{2}{- 3} (i i i) \frac{4}{7} - \frac{- 5}{- 7} (i v) - 2 - \frac{5}{9} (v) \frac{- 3}{- 8} - \frac{- 2}{7} (v i) \frac{- 4}{13} - \frac{- 5}{26} (v i i) \frac{- 5}{14} - \frac{- 2}{7} (v i i i) \frac{13}{15} - \frac{12}{25} (i x) \frac{- 6}{13} - \frac{- 7}{13} (x) \frac{7}{24} - \frac{19}{36} (x i) \frac{5}{63} - \frac{- 8}{21}$

Q. Name the property of rational numbers illustrated by the given statement.

\frac{7}{4} \times (\frac{- 8}{3} + \frac{- 13}{12}) = \frac{7}{4} \times \frac{- 8}{3} + \frac{7}{4} \times \frac{- 13}{12}

Q. Out of the rational numbers

\frac{7}{- 13}, \frac{- 5}{13}, \frac{- 11}{13}

which is smaller ?

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Using the appropriate properties of operations of rational numbers, evaluate the following:313×45×75×413×513

We have, 313×45×75×413×513 =33610985 Hence, this is the answer.

Using the appropriate properties of operations of rational numbers, evaluate the following:
$\frac{3}{13} \times \frac{4}{5} \times \frac{7}{5} \times \frac{4}{13} \times \frac{5}{13}$

We have,

$\frac{3}{13} \times \frac{4}{5} \times \frac{7}{5} \times \frac{4}{13} \times \frac{5}{13}$

$= \frac{336}{10985}$

Hence, this is the answer.