Simplify : `(9)/(13)div(18)/(26)div(90)/(52)`

A. `45//26`

B. `13//45`

C. `26//45`

D. `45//13`

Options

A. B
B. A
C. D
D. C

Answer

To simplify the expression \((9/13) \div (18/26) \div (90/52)\), we can follow these steps:

### Step 1: Rewrite the Division as Multiplication
We know that dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the expression:

\[ (9/13) \div (18/26) \div (90/52) = (9/13) \times (26/18) \times (52/90) \]

### Step 2: Simplify Each Fraction
Now, we can simplify each of the fractions:

1. \( \frac{26}{18} \) can be simplified:
- Both 26 and 18 can be divided by 2:
\[ \frac{26 \div 2}{18 \div 2} = \frac{13}{9} \]

2. \( \frac{52}{90} \) can be simplified:
- Both 52 and 90 can be divided by 2:
\[ \frac{52 \div 2}{90 \div 2} = \frac{26}{45} \]

### Step 3: Substitute Back into the Expression
Now substituting back into the expression, we have:

\[ (9/13) \times (13/9) \times (26/45) \]

### Step 4: Cancel Out Common Terms
Notice that \(9\) in the numerator and denominator cancels out, as well as \(13\):

\[ = 1 \times 1 \times \frac{26}{45} = \frac{26}{45} \]

### Final Answer
Thus, the simplified expression is:

\[ \frac{26}{45} \]

### Conclusion
The correct option is **C. \(26/45\)**.