What is the value of `80-:40-10-5xx4` of `((1)/(3)-:(10)/(3))?`

Options

A. `-12`
B. `(40)/(3)`
C. `(22)/(5)`
D. `-10`

Answer

To solve the expression \( 80 \div 40 - 10 - 5 \times \left( \frac{1}{3} \div \frac{10}{3} \right) \), we will follow the order of operations (BODMAS/BIDMAS rules).

### Step-by-Step Solution:

1. **Evaluate the Division in the Bracket**:
\[ \frac{1}{3} \div \frac{10}{3} = \frac{1}{3} \times \frac{3}{10} = \frac{1 \times 3}{3 \times 10} = \frac{3}{30} = \frac{1}{10} \]
**Hint**: To divide fractions, multiply by the reciprocal of the divisor.

2. **Substitute Back into the Expression**:
Now, substitute \(\frac{1}{10}\) back into the expression:
\[ 80 \div 40 - 10 - 5 \times \frac{1}{10} \]

3. **Evaluate the Division**:
\[ 80 \div 40 = 2 \]
**Hint**: Division is the same as multiplying by the reciprocal.

4. **Substitute the Result**:
Now the expression becomes:
\[ 2 - 10 - 5 \times \frac{1}{10} \]

5. **Evaluate the Multiplication**:
\[ 5 \times \frac{1}{10} = \frac{5}{10} = \frac{1}{2} \]
**Hint**: Multiplication of a whole number by a fraction can be simplified by multiplying the numerator.

6. **Substitute the Result**:
Now the expression is:
\[ 2 - 10 - \frac{1}{2} \]

7. **Combine the Terms**:
First, combine \(2 - 10\):
\[ 2 - 10 = -8 \]
Now, we have:
\[ -8 - \frac{1}{2} \]

8. **Convert to a Common Denominator**:
To subtract \(-8\) and \(-\frac{1}{2}\), convert \(-8\) to a fraction:
\[ -8 = -\frac{16}{2} \]
Now the expression is:
\[ -\frac{16}{2} - \frac{1}{2} = -\frac{16 + 1}{2} = -\frac{17}{2} \]

9. **Final Result**:
The final answer is:
\[ -\frac{17}{2} \]

### Conclusion:
The value of the expression \( 80 \div 40 - 10 - 5 \times \left( \frac{1}{3} \div \frac{10}{3} \right) \) is \( -\frac{17}{2} \).