Expression Simplification
To simplify the expression $5\frac{1}{6} \div 6.2 \times 0.75 \div \left(\frac{1}{5} \times 40\right)$, we follow the order of operations (PEMDAS/BODMAS).
Convert Numbers to Fractions
- Mixed number: $5\frac{1}{6} = \frac{(5 \times 6) + 1}{6} = \frac{31}{6}$
- Decimal: $6.2 = \frac{62}{10} = \frac{31}{5}$
- Decimal: $0.75 = \frac{75}{100} = \frac{3}{4}$
Simplify Parenthetical Term
- The term inside the parentheses is: $\left(\frac{1}{5} \times 40\right) = \frac{40}{5} = 8$
Rewrite Expression
Substitute the fractional values back into the original expression:
$ \frac{31}{6} \div \frac{31}{5} \times \frac{3}{4} \div 8 $Calculate Step-by-Step
Perform division and multiplication operations from left to right:
- First division: $\frac{31}{6} \div \frac{31}{5} = \frac{31}{6} \times \frac{5}{31} = \frac{5}{6}$
- The expression is now: $\frac{5}{6} \times \frac{3}{4} \div 8$
- Next, multiplication: $\frac{5}{6} \times \frac{3}{4} = \frac{15}{24} = \frac{5}{8}$
- The expression is now: $\frac{5}{8} \div 8$
- Final division: $\frac{5}{8} \div 8 = \frac{5}{8} \times \frac{1}{8} = \frac{5}{64}$
Final Simplified Value
The simplified value of the expression is $\frac{5}{64}$.
Important Questions from Simplification
Simplify the following expression.
\(\left(\frac{7}{16} \div \frac{1}{2}\:of\: \frac{1}{5}\right)\times \frac{4}{5}-\frac{1}{3}\times\frac{5}{8}\div \frac{1}{2}+\frac{3}{4}\)
The value of \(\left( {2\frac{6}{7}of4\frac{1}{5} \div \frac{2}{3}} \right) \times 5\frac{1}{9} \div \left( {\frac{3}{4} \times 2\frac{2}{3}of\frac{1}{2} \div \frac{1}{4}} \right)\) is:
The value of \(\left[ {\frac{4}{7}\rm \;of\;2\frac{4}{5} \times 1\frac{2}{3} - \left( {3\frac{1}{2} - 2\frac{1}{6}} \right)} \right] \div \left( {3\frac{1}{5} \div 4\frac{1}{2}\;\rm of\;\;5\frac{1}{3}} \right)\) is:
The value of \(\frac{{0.0203 \times 2.92}}{{0.7 \times 0.0365 \times 2.9}} \div \frac{{{{\left( {12.12} \right)}^2} - {{\left( {8.12} \right)}^2}}}{{{{\left( {0.25} \right)}^2} + \left( {0.25} \right)\left( {19.99} \right)}}\) is:
The value of 4 ÷ 12 of [3 ÷ 4 of {(4 - 2) × 6 ÷ 2}] - 2 × 6 ÷ 8 + 3 is:
