Question

Simplify :
$\frac{3}{4}+\frac{2}{3}\div\frac{4}{9}\div\frac{5}{2}-\frac{1}{4}\times\frac{2}{5}$

• A. 50/40
• B. 51/40
• C. 39/40
• D. 11/10

Answer 1

Answer:

A. 50/40

To simplify the given expression, we follow the standard order of operations (BODMAS/PEMDAS): perform division and multiplication from left to right first, followed by addition and subtraction.

The expression is:

$\frac{3}{4}+\frac{2}{3}\div\frac{4}{9}\div\frac{5}{2}-\frac{1}{4}\times\frac{2}{5}$

Step-by-Step Simplification

Step 1: Evaluate the division part from left to right

$\frac{2}{3}\div\frac{4}{9}\div\frac{5}{2}$

• First, compute $\frac{2}{3} \div \frac{4}{9}$ by multiplying by the reciprocal:

  $\frac{2}{3} \times \frac{9}{4} = \frac{18}{12} = \frac{3}{2}$

• Next, divide the result by $\frac{5}{2}$:

  $\frac{3}{2} \div \frac{5}{2} = \frac{3}{2} \times \frac{2}{5} = \frac{6}{10} = \frac{3}{5}$

Step 2: Evaluate the multiplication part

$\frac{1}{4}\times\frac{2}{5} = \frac{2}{20} = \frac{1}{10}$

Step 3: Substitute the values back into the expression

Now substitute these results back into the main expression:

$\frac{3}{4} + \frac{3}{5} - \frac{1}{10}$

Step 4: Perform addition and subtraction using a common denominator

The denominators are $4, 5,$ and $10$. The Least Common Multiple (LCM) is $20$.

• Convert each fraction to have a denominator of $20$:

  
  

  • $\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$

  • $\frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20}$

  • $\frac{1}{10} = \frac{1 \times 2}{10 \times 2} = \frac{2}{20}$

• Combine them:

  
  $\frac{15}{20} + \frac{12}{20} - \frac{2}{20} = \frac{15 + 12 - 2}{20} = \frac{25}{20}$

Step 5: Simplify the final fraction

$\frac{25}{20} = \frac{50}{40} \quad \text{(or } 1.25 \text{)}$

Answer

The simplified value is $\frac{50}{40}$