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
The value of {5 - 5 ÷ (10 - 12) × 8 + 9} × 3 + 5 + 5 × 5 ÷ 5 of 5 is:
What should come in place of the question mark (?) in the following question?
[((16 ÷ 4) × 4) ÷ 4] = ?
Simplify the following expression.
\(\frac{{6\frac{1}{2} + 2\frac{5}{7} \times \frac{{14}}{{19}} - \frac{1}{2} \div 2\ of\frac{1}{4}}}{{11 \times 12 \div 12 + 12}}\)
The value of \(\left( {\frac{7}{5} \div \frac{7}{{10}}of\frac{3}{4}} \right) \div \frac{4}{9} + \left( {\frac{7}{{16}} \div 10\frac{1}{2} \times 7\frac{1}{5}} \right) \times \frac{5}{{12}} \) is:
The value of \(\left( {{1 \over 2}} \right)\) [{–2(12 + 2)}10] is:
