Simplify : `(5/8+3/4) of 4/(11) divide 3/(16) -1/2 xx 3/4=?`

Options

A. `3 2/(13)`
B. `3 4/(11)`
C. `2 7/(24)`
D. 1

Answer

To simplify the expression \( \left( \frac{5}{8} + \frac{3}{4} \right) \times \frac{4}{11} \div \frac{3}{16} - \frac{1}{2} \times \frac{3}{4} \), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Calculate the sum inside the parentheses:**
\[ \frac{5}{8} + \frac{3}{4} \]
To add these fractions, we need a common denominator. The least common multiple (LCM) of 8 and 4 is 8. We can convert \( \frac{3}{4} \) to have a denominator of 8:
\[ \frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8} \]
Now we can add:
\[ \frac{5}{8} + \frac{6}{8} = \frac{11}{8} \]

**Hint:** Find a common denominator to add fractions.

2. **Substitute back into the expression:**
The expression now looks like:
\[ \left( \frac{11}{8} \right) \times \frac{4}{11} \div \frac{3}{16} - \frac{1}{2} \times \frac{3}{4} \]

3. **Calculate \( \frac{11}{8} \times \frac{4}{11} \):**
The \( 11 \) in the numerator and denominator cancels out:
\[ \frac{11 \times 4}{8 \times 11} = \frac{4}{8} = \frac{1}{2} \]

**Hint:** Cancel common factors in multiplication.

4. **Now substitute this back into the expression:**
\[ \frac{1}{2} \div \frac{3}{16} - \frac{1}{2} \times \frac{3}{4} \]

5. **Calculate \( \frac{1}{2} \div \frac{3}{16} \):**
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{1}{2} \times \frac{16}{3} = \frac{16}{6} = \frac{8}{3} \]

**Hint:** Remember that dividing by a fraction means multiplying by its reciprocal.

6. **Calculate \( \frac{1}{2} \times \frac{3}{4} \):**
\[ \frac{1 \times 3}{2 \times 4} = \frac{3}{8} \]

**Hint:** Multiply the numerators and denominators directly.

7. **Now substitute back into the expression:**
\[ \frac{8}{3} - \frac{3}{8} \]

8. **Find a common denominator to subtract:**
The LCM of 3 and 8 is 24. Convert both fractions:
\[ \frac{8}{3} = \frac{8 \times 8}{3 \times 8} = \frac{64}{24} \]
\[ \frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24} \]

9. **Now subtract:**
\[ \frac{64}{24} - \frac{9}{24} = \frac{64 - 9}{24} = \frac{55}{24} \]

**Hint:** When subtracting fractions, ensure they have the same denominator.

10. **Convert to a mixed number (if necessary):**
\[ \frac{55}{24} = 2 \frac{7}{24} \]

### Final Answer:
The simplified expression is \( 2 \frac{7}{24} \).