Simplify the following:
\(\frac{96}{39} (91+26) -103\)
Simplify Mathematical Expression
This solution explains how to simplify the given arithmetic expression: $$ \frac{96}{39} (91+26) -103 $$ We will follow the order of operations (PEMDAS/BODMAS) to find the simplified value.
Simplification Steps
Parentheses Simplification
First, we evaluate the expression inside the parentheses:
$$ 91 + 26 = 117 $$Fraction Simplification
Next, we simplify the fraction $$ \frac{96}{39} $$. We look for common factors. Both 96 and 39 are divisible by 3.
- \( 96 \div 3 = 32 \)
- \( 39 \div 3 = 13 \)
The simplified fraction is $$ \frac{32}{13} $$.
Multiplication Calculation
Now, we substitute the simplified values back into the original expression:
$$ \frac{32}{13} \times 117 - 103 $$Perform the multiplication. We can check if 117 is divisible by 13:
$$ \frac{117}{13} = 9 $$Multiply this result by 32:
$$ 32 \times 9 = 288 $$Subtraction Calculation
Finally, perform the subtraction:
$$ 288 - 103 = 185 $$Final Simplified Value
The final result of simplifying the expression $$ \frac{96}{39} (91+26) -103 $$ is 185.
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:
