The simplified value of `(4)/(15)"of" (5)/(8) xx 6 + 15 - 10` is

Options

A. 6
B. 3
C. 5
D. 4

Answer

To simplify the expression \(\frac{4}{15} \text{ of } \frac{5}{8} \times 6 + 15 - 10\), we will follow the order of operations, often remembered by the acronym BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Identify the "of" operation**:
The term "of" in mathematics typically indicates multiplication. Therefore, we rewrite the expression:
\[ \frac{4}{15} \times \frac{5}{8} \times 6 + 15 - 10 \]

2. **Calculate \(\frac{4}{15} \times \frac{5}{8}\)**:
To multiply the fractions, multiply the numerators and the denominators:
\[ \frac{4 \times 5}{15 \times 8} = \frac{20}{120} \]
Now, simplify \(\frac{20}{120}\):
\[ \frac{20 \div 20}{120 \div 20} = \frac{1}{6} \]

3. **Substitute back into the expression**:
Now, replace \(\frac{4}{15} \times \frac{5}{8}\) with \(\frac{1}{6}\):
\[ \frac{1}{6} \times 6 + 15 - 10 \]

4. **Calculate \(\frac{1}{6} \times 6\)**:
This simplifies to:
\[ 1 \]

5. **Now substitute back into the expression**:
The expression now reads:
\[ 1 + 15 - 10 \]

6. **Perform the addition and subtraction**:
First, add:
\[ 1 + 15 = 16 \]
Then subtract:
\[ 16 - 10 = 6 \]

### Final Answer:
The simplified value of the expression is \(6\).