Question

Simply the expression


$\frac{1}{6} \div \frac{5}{6} \div \sqrt{4} \: - \frac{1}{9}$
​

Answer 1

$\frac{1}{6} \div \frac{5}{6} \div \sqrt{4} \: - \frac{1}{9}$

to divide by a fraction multiply by the reciprocal of that fraction

$\frac{1}{6} \times \frac{6}{5} \div \sqrt{4} \: - \frac{1}{9}$

$\frac{1}{6} \div \frac{5}{6} \div \sqrt{4} \: - \frac{1}{9}$

$\frac{1}{6} \times \frac{6}{5} \div 2 - \frac{1}{9}$

dividing is equivalent to multiplying with the reciprocal

$\frac{1}{6} \times \frac{6}{5} \times \frac{1}{2} - \frac{1}{9}$

$\cancel\frac{1} {6} \times \cancel\frac{6}{5} \div 2 - \frac{1}{9}$

reduse the numbers with greatest common factor 6

$\frac{1}{5} \times \frac{1}{2} - \frac{1}{9}$

multiply the fractions

$\frac{1}{10} - \frac{1}{9}$

subtract the fraction

$- \frac{1}{90}$

Alternate form

$- 0.01, { - 90}^{ - 1}$

Answer 2

$\huge{\mathcal{\purple{A}\green{n}\pink{s}\blue{w}\purple{E}\green{R!}}}$

$\implies \frac{1}{6} \div \frac{5}{6} \div \sqrt{4} \: - \frac{1}{9}$

to divide by a fraction multiply by the reciprocal of that fraction

$\implies\frac{1}{6} \times \frac{6}{5} \div \sqrt{4} \: - \frac{1}{9} \\\\</p><p></p><p>\implies \frac{1}{6} \div \frac{5}{6} \div \sqrt{4} \: - \frac{1}{9} \\\\</p><p></p><p> \implies \frac{1}{6} \times \frac{6}{5} \div 2 - \frac{1}{9}$

dividing is equivalent to multiplying with the reciprocal

$\implies \frac{1}{6} \times \frac{6}{5} \times \frac{1}{2} - \frac{1}{9} \\\\</p><p> \cancel\frac{1} {6} \times \cancel\frac{6}{5} \div 2 - \frac{1}{9}$

reduse the numbers with greatest common factor 6

$\frac{1}{5} \times \frac{1}{2} - \frac{1}{9}$

multiply the fractions

$\frac{1}{10} - \frac{1}{9}$

subtract the fraction

$- \frac{1}{90}$