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
If P = 0.3 × 0.3 + 0.03 × 0.03 - 0.6 × 0.03 and Q = 0.54, then \(\rm \frac{P}{Q}\) is equal to:
The value of \(\left(\frac{1}{2}\right)^{−2} \times\left(\frac{1}{3}\right)^{−2} \times\left(\frac{1}{4}\right)^{−2} \) is
The solution of the equation \(\frac{2}{3 x-4}+\frac{2}{2 x-6}=0 \) is:
What will come in the place of question mark (?) in the given expression?
\(\sqrt{21+\sqrt{49}+\sqrt{64}} \space {\%\:of\:5000}=?\)
There are 5 tasks and 5 persons. Task-1 cannot be assigned to either person-1 or person-2. Task-2 must be assigned to either person-3 or person-4. Every person is to be assigned one task. In how many ways can the assignment be done?
