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
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:
