Simplify Math Expression with Fractions and Decimals
To simplify the given expression $\left( 3.6 \div \frac{3}{5} \right) + \left( \frac{7}{3} \times \frac{2.4}{1.4} \right) - \left( \frac{5}{6} + \frac{14}{12} \right)$, we will solve each part separately.
Part 1 Calculation: Division
First, convert the decimal $3.6$ to a fraction:
$3.6 = \frac{36}{10} = \frac{18}{5}$Now, perform the division:
$3.6 \div \frac{3}{5} = \frac{18}{5} \div \frac{3}{5}$To divide fractions, multiply by the reciprocal of the divisor:
$\frac{18}{5} \times \frac{5}{3} = \frac{18 \times 5}{5 \times 3} = \frac{18}{3} = 6$Part 2 Calculation: Multiplication
Convert the decimals $2.4$ and $1.4$ to fractions:
$2.4 = \frac{24}{10} = \frac{12}{5}$ $1.4 = \frac{14}{10} = \frac{7}{5}$Now, perform the multiplication:
$\frac{7}{3} \times \frac{2.4}{1.4} = \frac{7}{3} \times \frac{12/5}{7/5}$Simplify the fraction within the multiplication:
$\frac{12/5}{7/5} = \frac{12}{5} \times \frac{5}{7} = \frac{12}{7}$Continue the multiplication:
$\frac{7}{3} \times \frac{12}{7} = \frac{7 \times 12}{3 \times 7} = \frac{12}{3} = 4$Part 3 Calculation: Addition
Find a common denominator for $\frac{5}{6}$ and $\frac{14}{12}$. The least common denominator is 12.
Convert $\frac{5}{6}$ to an equivalent fraction with a denominator of 12:
$\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}$Now add the fractions:
$\frac{5}{6} + \frac{14}{12} = \frac{10}{12} + \frac{14}{12} = \frac{10 + 14}{12} = \frac{24}{12} = 2$Final Simplification
Substitute the results of each part back into the original expression:
$6 + 4 - 2$Perform the addition and subtraction from left to right:
$10 - 2 = 8$The simplified value of the expression is 8.
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?
